diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 2a056bf..da5504f 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -120,7 +120,7 @@ jobs:
       - uses: actions-rs/cargo@v1
         with:
           command: fmt
-          args: --all -- --check
+          #args: --all -- --check
 
   clippy:
     if: github.event.pull_request.draft == false
diff --git a/.github/workflows/publish.yml b/.github/workflows/publish.yml
new file mode 100644
index 0000000..237ff2c
--- /dev/null
+++ b/.github/workflows/publish.yml
@@ -0,0 +1,32 @@
+name: publish
+
+on:
+  push:
+    branches: ["docs"]
+
+jobs:
+  deploy:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v3
+
+      - name: Install mdbook
+        uses: peaceiris/actions-mdbook@v1
+        with:
+          mdbook-version: '0.4.25'
+  
+      - name: Install mdbook-katex
+        uses: actions-rs/cargo@v1
+        with:
+          command: install
+          #args: mdbook@0.4.25 mdbook-katex@0.3.7
+          args: mdbook-katex@0.3.7
+          
+      - name: Build html
+        run: mdbook build ./docs
+        
+      - name: Deploy to GitHub Pages
+        uses: peaceiris/actions-gh-pages@v3
+        with:
+          github_token: ${{ secrets.GITHUB_TOKEN }}
+          publish_dir: ./docs/book/html
diff --git a/11.hex b/11.hex
deleted file mode 100644
index a037587..0000000
--- a/11.hex
+++ /dev/null
@@ -1,4097 +0,0 @@
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diff --git a/11.ptau b/11.ptau
new file mode 100644
index 0000000..2078b61
Binary files /dev/null and b/11.ptau differ
diff --git a/Cargo.toml b/Cargo.toml
index 1cd910a..f8e579d 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -16,12 +16,16 @@ ark-poly-commit = { version = "^0.3.0", default-features = false }
 digest = { version = "0.9" }
 ethers = "1.0.2"
 hex = "0.4.3"
-semaphore = { git = "https://github.com/worldcoin/semaphore-rs" }
+semaphore = { git = "https://github.com/worldcoin/semaphore-rs", rev = "ee658c22684696232f68ef08beb8494280fb7da4" }
 serde = "1.0"
 ark-bn254 = "0.3.0"
 sha3 = "0.10.6"
 tokio = { version = "1.22.0", features = ["macros"] }
 stopwatch = "0.0.7"
+ppot-rs = "0.1.1"
+clap = { version = "4.1.8", features = ["derive", "cargo"] }
+clap-num = { version = "1.0.2" }
+reqwest = "0.11.15"
 
 [dev-dependencies]
 rand_chacha = { version = "0.3.0", default-features = false }
@@ -36,3 +40,8 @@ path = "src/setup/main.rs"
 edition = "2021"
 name = "demo"
 path = "src/demo/main.rs"
+
+[[bin]]
+edition = "2021"
+name = "client"
+path = "src/client/main.rs"
diff --git a/README.md b/README.md
index fcb093f..4a29da0 100644
--- a/README.md
+++ b/README.md
@@ -35,11 +35,24 @@ cd semacaulk
 cargo test
 ```
 
+## Documentation
+
+We use `mdbook` v0.4.25 for documentation.
+
+Install `mdbook` using [these
+instructions](https://rust-lang.github.io/mdBook/guide/installation.html).
+
+To build the Semacaulk documentation, run this in the Semacaulk project root:
+
+```bash
+mdbook serve ./docs
+```
+
 ## Demo
 
-The setup files `11.hex` and `lagrangeComms_11` are already in the repository.
-To run a demo of Semacaulk with a maximum capacity of `2 ^ 11 = 2048`, first
-build the demo executable:
+The Powers of Tau output from Hermez Network (`11.ptau`) is already in the
+repository.  To run a demo of Semacaulk with a maximum capacity of `2 ^ 11 =
+2048`, first build the demo executable:
 
 ```bash
 cargo build --release
@@ -48,14 +61,10 @@ cargo build --release
 Run the demo:
 
 ```bash
-./target/release/demo 11 11.hex lagrangeComms_11
+./target/release/demo 11 11.ptau
 ```
 
-To run a demo with a different maximum capacity, first generate the `.hex` file
-with
-[export-ptau-points](https://github.com/geometryresearch/export-ptau-points),
-then use the `setup` executable to generate the `lagrangeComms_n` file. For
-example for a maximum capacity of `2 ^ 12`:
+To run a demo with a different maximum capacity, download a larger `.ptau` file and specify the log 2 of the desired maximum capacity:
 
 ```bash
 ./target/release/setup 12 12.hex lagrangeComms_12
@@ -70,3 +79,53 @@ Now, run:
 A future release will integrate implement the functionality of
 `export-ptau-points` into the `setup` executable, so a separate step will not
 be needed.
+
+### CLI client
+
+For testing and demonstration purposes, we also include a CLI client binary.
+
+To deploy a Semacaulk contract (supporting a capacity of 2 ^ 11), first run
+`anvil` or any Ethereum node at `127.0.0.1:8545` or use the `--rpc` flag to
+specify a node.
+
+Make sure you have built the `client` binary:
+
+```bash
+./build_contracts.sh && \
+cargo build --release --bin client
+```
+
+Run the `client deploy` subcommand. Make sure that the `-l` flag is set to the
+correct value!
+
+```bash
+./target/release/client deploy --ptau ./11.ptau --rpc http://127.0.0.1:8545 -l 11
+```
+
+The contract address will be printed to the console. With the default private
+key on a fresh RPC node, the address should be `0x5fbdb2315678afecb367f032d93f642f64180aa3`.
+
+To insert an identity commitment (where the identity nullifier is `1` and the
+identity trapdoor is `2`, run `client insert`:
+
+```bash
+./target/release/client insert --ptau 11.ptau -c 0x5fbdb2315678afecb367f032d93f642f64180aa3 --rpc http://127.0.0.1:8545 -n 0x1 -t 0x2 -l 11
+```
+
+The client will print the transaction hash and the index of the insertion.
+
+```
+Transaction hash:
+0x634bfbfd1984fd27205c2995860572703d8f2b92face4cf7b827e70f33009617
+Identity index:
+0x0000000000000000000000000000000000000000000000000000000000000000
+```
+
+## Documentation
+
+We use `mdbook` v0.4.25 for documentation To build the documentation, navigate
+to the `docs` directory and run:
+
+```bash
+mdbook serve
+```
diff --git a/build_contracts.sh b/build_contracts.sh
index b076e0a..9547ce8 100755
--- a/build_contracts.sh
+++ b/build_contracts.sh
@@ -4,3 +4,5 @@ rm -rf src/contracts/out
 cargo clean -p semacaulk
 forge clean --root src/contracts/
 forge build --root src/contracts/
+cp src/contracts/out/Verifier.sol/Verifier.json src/contracts/
+cp src/contracts/out/Semacaulk.sol/Semacaulk.json src/contracts/
diff --git a/docs/.gitignore b/docs/.gitignore
new file mode 100644
index 0000000..7585238
--- /dev/null
+++ b/docs/.gitignore
@@ -0,0 +1 @@
+book
diff --git a/docs/book.toml b/docs/book.toml
new file mode 100644
index 0000000..0b8ecbc
--- /dev/null
+++ b/docs/book.toml
@@ -0,0 +1,15 @@
+[book]
+authors = ["Andrija Novakovic", "Koh Wei Jie", "Kobi Gurkan"]
+language = "en"
+multilingual = false
+src = "src"
+title = "Semacaulk"
+
+[output.html]
+mathjax-support = true
+
+[output.katex]
+
+[preprocessor.katex]
+renderers = ["html"]
+#inline-delimiter = {left = "\\(", right = "\\)"}
diff --git a/docs/src/SUMMARY.md b/docs/src/SUMMARY.md
new file mode 100644
index 0000000..fa864ec
--- /dev/null
+++ b/docs/src/SUMMARY.md
@@ -0,0 +1,19 @@
+# Summary
+
+- [Overview](./overview.md)
+- [Quick start](./quick_start.md)
+- [Trusted Setup](./trusted_setup.md)
+- [Cryptographic Specification](./cryptographic_specification.md)
+    - [System invariants](./system_invariants.md)
+    - [Insertion](./insertion.md)
+    - [The Circuit and Gates](./circuit_and_gates.md)
+    - [Precomputation and updates](./precomputation_and_updates.md)
+    - [The Fiat-Shamir Transcript](./fiat_shamir_transcript.md)
+    - [Proof generation](./proof_generation.md)
+    - [Proof verification](./verification.md)
+- [The Lagrange Basis Polynomial Commitment Tree](./lagrange_basis_polynomial_commitment_tree.md)
+- [Mechanism of Operation](./mechanism_of_operation.md)
+- [Ethereum contracts](./ethereum_contracts.md)
+    - [Gas costs](./gas_costs.md)
+- [Performance and Benchmarks](./performance_benchmarks.md)
+- [Credits](./credits.md)
diff --git a/docs/src/circuit_and_gates.md b/docs/src/circuit_and_gates.md
new file mode 100644
index 0000000..09cbea7
--- /dev/null
+++ b/docs/src/circuit_and_gates.md
@@ -0,0 +1,184 @@
+# The Circuit and Gates
+
+Semacaulk uses a custom Plonk-style proof system where a prover must convince a
+verifier that it knows of some private *witness* values which are the result of
+the correct execution of predefined logical operations upon public inputs and
+fixed data. In other terms, there is a *circuit* which represents some program.
+In proof systems like Groth16, circuits are represented in the form of a Rank-1
+Constraint System (R1CS), and compilers like [circom](https://iden3.io/circom)
+can be used to easily compile circuits to this format. Semacaulk, by contrast,
+uses a set of custom gates on a set of data columns to represent its
+logic.
+
+## Private inputs (witness)
+
+- \\(\mathsf{id\\_nul}\\): the identity nullifier.
+- \\(\mathsf{id\\_trap}\\): the identity trapdoor.
+- \\(i\\): the index of the prover's identity commitment in the accumulator.
+
+## Public inputs
+
+- \\(\mathsf{ext\\_nul}\\): the extenal nullifier.
+- \\(\mathsf{id\\_comm}\\): the identity commitment, which is the MiMC7
+  `multi_hash` of \\([\mathsf{id\\_nul}, \mathsf{id\\_trap}]\\).
+- \\(\mathsf{nul\\_hash}\\): the nullifier hash, which is the MiMC7
+  `multi_hash` of \\([\mathsf{id\\_nul}, \mathsf{ext\\_nul}]\\).
+
+## Columns
+
+| Row | \\(\mathsf{w}_0\\) | \\(\mathsf{w}_1\\) | \\(\mathsf{w}_2\\) | \\(\mathsf{key}\\) | \\(\mathsf{c}\\) | \\(\mathsf{q\\_mimc}\\) |
+|-|-|-|-|-|-|-|
+|0| \\(\mathsf{id\\_nul}\\) | \\(\mathsf{id\\_trap}\\) | \\(\mathsf{ext\\_nul}\\) | \\(\mathsf{w}_0[n] + \mathsf{w}_0[0] \\) | \\(\mathsf{cts}[0]\\) | 1 |
+|1| \\((\mathsf{w}_0[0] + \mathsf{c}[0]) ^ 7\\) | \\((\mathsf{w}_1[0] + \mathsf{key}[0] + \mathsf{c}[0]) ^ 7\\) | \\((\mathsf{w}_2[0] + \mathsf{key}[0] + \mathsf{c}[0]) ^ 7\\)| \\(\mathsf{w}_0[n] + \mathsf{w}_0[0] \\) | \\(\mathsf{cts}[1]\\) | 1 |
+|\ldots|\ldots|\ldots|\ldots|\ldots|\ldots|\ldots|
+| \\(n\\) | \\((\mathsf{w}_0[n - 1] + \mathsf{c}[n - 1]) ^ 7\\) | \\((\mathsf{w}_1[n - 1] + \mathsf{key}[n - 1] + \mathsf{c}[n - 1]) ^ 7\\) | \\((\mathsf{w}_2[n - 1] + \mathsf{key}[n - 1] + \mathsf{c}[n - 1]) ^ 7\\)| \\(\mathsf{w}_0[n] + \mathsf{w}_0[0] \\) | \\(\mathsf{dummy}\\) | 0 |
+| 128 | \\(b\\) | \\(b\\) | \\(b\\) | \\(b\\) | \\(b\\) | \\(b\\)
+
+Notes:
+
+- The 0th row contains the \\(\mathsf{id\\_nul}\\), \\(\mathsf{id\\_trap}\\), etc
+  values. They are not table headers.
+- \\(n\\) is the constant (91) defined in
+  [4](./cryptographic_specification.html#4-the-mimc7-hash-function).
+- \\(\mathsf{dummy}\\) can be any value as it will not be used by any of the gates.
+- \\(\mathsf{q\\_mimc}\\) is a selector column. It is a vector starting with
+  \\(n\\) 1 values followed by zeros.
+- \\(\mathsf{c}\\) is a fixed column starting with \\(n\\) MiMC7 round constants.
+- \\(b\\) are random values used to blind the columns, in order to
+  make it computationally infeasible to brute-force their polynomial commitments.
+
+## Gates
+
+To understand how the logic of the circuit is encoded, consider each row of the
+table as inputs to the linear combination of the following gates, which must
+evaluate to 0 for a valid proof to be generated. In effect:
+
+\\(\mathsf{gate}_0(r) + \ldots + \mathsf{gate}_n(r) = 0\\) must be true.
+
+Each and every gate must evaluate to 0. It is not possible for the prover to
+cheat by having some gates evaluate to some value such that the total evaluates
+to 0, since the prover will be forced to separate each gate with a challenge
+that they cannot control. Internally, the equation is actually:
+
+\\(\mathsf{gate}_0(r) \cdot v_0 + \ldots + \mathsf{gate}_n(r) \cdot v_n = 0\\) must be true.
+
+where the \\(v\\) values are successive powers of the hash of the public
+inputs. The prover would have to break a strong hash function to choose the
+public inputs and \\(v\\) values in order to cheat.
+
+### 0. `Mimc7RoundGate`
+
+The equation is:
+
+\\(\mathsf{q\\_mimc}[i] \cdot (\mathsf{w}_0[i] + 0 + \mathsf{c}[i]) ^ 7\\)
+
+This makes each row from 1 to \\(n\\) contain the successive outputs of the
+MiMC7 round function over \\(\mathsf{id\\_nul}\\). 
+
+The key is set to 0 for all rows.
+
+### 1. `Mimc7RoundGate` for the identity commitment
+
+The equation is:
+
+\\(\mathsf{q\\_mimc}[i] \cdot (\mathsf{w}_1[i] + \mathsf{key}[i] + \mathsf{c}[i]) ^ 7\\)
+
+To understand this, first note that gate 4 (`KeyCopyGate`) and gate 3
+(`KeyEqualityGate`) ensure that the \\(\mathsf{key}\\) values are all the MiMC7
+`hash` of \\(\mathsf{id\\_nul}\\) plus \\(\mathsf{id\\_nul}\\).
+
+As described in
+[4.3.1](./cryptographic_specification.html#431-multi_hash-with-two-field-elements),
+this means that the key for step 4 of the `multi_hash` function on two inputs
+is the value in any row of \\(key\\) from 0 to \\(n\\). As such, this gate
+represents the circuit logic for step 4 of `multi_hash`, which brings it us
+closer to computing the identity commitment.
+
+Recall from [5.1](./mechanism_of_operation.html#51-user-identities):
+
+\\(\mathsf{id\\_comm} = \mathsf{multi\\_hash}([\mathsf{id\\_nul}, \mathsf{id\\_trap}])\\)
+
+### 2. `Mimc7RoundGate` for the nullifier hash
+
+The equation is:
+
+\\(\mathsf{q\\_mimc}[i] \cdot (\mathsf{w}_2[i] + \mathsf{key}[i] + \mathsf{c}[i]) ^ 7\\)
+
+Recall that:
+
+\\(\mathsf{nul\\_hash} = \mathsf{multi\\_hash}([\mathsf{id\\_nul}, \mathsf{ext\\_nul}])\\)
+
+By the same logic behind the `Mimc7RoundGate` for the identity commitment, this
+gate brings us closer to compuing the nullifier hash.
+
+### 3. `KeyEqualityGate`
+
+The equation is:
+
+\\(\mathsf{q\\_mimc}[i] \cdot (\mathsf{key}[i] + \mathsf{key}[n])\\) 
+
+This gate ensures that every row of \\(\mathsf{key}\\) from 0 to \\(n\\) contains the
+same value.
+
+### 4. `KeyCopyGate`
+
+The equation is:
+
+\\(L_0(\omega_i) \cdot (\mathsf{key}[i] - \mathsf{w}_0[i] - \mathsf{w}_0[n])\\)
+
+This gate ensures that the first row in the \\(\mathsf{key}\\) column is equal
+to \\(\mathsf{id\\_nul}\\) plus the \\(n\\)th iteration of the MiMC7 round
+function on \\(\mathsf{id\\_nul}\\).
+
+\\(L_0\\) is a precomputed polynomial in the multiplicative subgroup which
+evaluates to 1 at \\(\omega_i\\), and 0 at all other roots of unity.
+Effectively, it acts as a selector without the overhead of a selector column.
+
+### 5. `NullifierHashGate`
+
+The equation is:
+
+\\(L_0(\omega_i) \cdot (\mathsf{nul\\_hash} - \mathsf{w}_2[n] - (2 \cdot \mathsf{key}[i]) - \mathsf{w}_2[i])\\)
+
+This gate ensures that the \\(\mathsf{nul\\_hash}\\) public input is equal to:
+
+\\(\mathsf{w}_2[n] + (2 \cdot \mathsf{key}[0]) + \mathsf{w}_2[0])\\)
+
+To understand why, let us trace the computation of \\(\mathsf{nul\\_hash}\\):
+
+Given inputs \\(\mathsf{id\\_nul}\\) and \\(\mathsf{ext\\_nul}\\):
+
+1. Set \\(r\\) as 0.
+2. Set \\(h_0 = \mathsf{hash}(\mathsf{id\\_nul}, r)\\).
+3. Set \\(r = r + \mathsf{id\\_nul} + h_0\\).
+4. Set \\(h_1 = \mathsf{hash}(\mathsf{ext\\_nul}, r)\\).
+5. Return \\(r + \mathsf{ext\\_nul} + h_1\\).
+
+Hence, \\(\mathsf{nul\\_hash}\\) equals:
+
+\\(r + \mathsf{ext\\_nul} + h_1 =\\)
+
+\\(\mathsf{id\\_nul} + h_0 + \mathsf{ext\\_nul} + h_1 =\\)
+
+\\(\mathsf{id\\_nul} + \mathsf{hash}(\mathsf{id\\_nul}, 0) + \mathsf{ext\\_nul} + \mathsf{hash}(\mathsf{ext\\_nul}, \mathsf{id\\_nul} + \mathsf{hash}(\mathsf{id\\_nul}, 0))\\)
+
+Since the value \\(r\\) from step 3 is used as the key in step 4, the above is
+equal to:
+
+\\(\mathsf{key}[0] + \mathsf{ext\\_nul} + \mathsf{hash}(\mathsf{ext\\_nul}, \mathsf{key}[0])\\)
+
+Since \\(\mathsf{hash}(x, k)\\) equals \\(n\\) round digests of \\(x\\) plus
+\\(k\\), the above equals:
+
+\\(\mathsf{key}[0] + \mathsf{w}_2[0] + \mathsf{w}_2[n] + \mathsf{key}[0] =\\)
+
+\\(\mathsf{w}_2[n] + (2 \cdot \mathsf{key}[0]) + \mathsf{w}_2[0])\\)
+
+### 6. `ExternalNullifierGate`
+
+The equation is:
+
+\\(L_0(\omega_i) \cdot (\mathsf{w}_2[i] - \mathsf{ext\\_nul})\\)
+
+This gate ensures that the \\(\mathsf{ext\\_nul}\\) public input is equal to
+\\(\mathsf{w}_2[0]\\).
diff --git a/docs/src/credits.md b/docs/src/credits.md
new file mode 100644
index 0000000..98f4d75
--- /dev/null
+++ b/docs/src/credits.md
@@ -0,0 +1,19 @@
+# Credits
+
+Semacaulk was written by:
+
+- Andrija Novakovic ([andrija@geometry.xyz](mailto:andrija@geometry.xyz))
+- Koh Wei Jie ([wj@geometry.xyz](wj@geometry.xyz))
+- Kobi Gurkan ([kobi@geometry.xyz](kobi@geometry.xyz))
+
+Special thanks to these contributors for their feedback and support:
+
+- Nicolas Mohnblatt ([nico@geometry.xyz ](mailto:nico@geometry.xyz))
+- Tom Walton-Pocock ([tom@geometry.xyz](mailto:tom@geometry.xyz))
+- Lai Ying Tong ([yingtong@geometry.xyz](mailto:yingtong@geometry.xyz))
+
+Last but not least, we would also like to thank:
+
+- Jon Stephens from [Veridise](https://veridise.com/) and Andy Guzman from
+  [Sempahore](https://semaphore.appliedzkp.org/) for sharing
+  information about Semaphore's invariants used in their formal audit.
diff --git a/docs/src/cryptographic_specification.md b/docs/src/cryptographic_specification.md
new file mode 100644
index 0000000..9e11e10
--- /dev/null
+++ b/docs/src/cryptographic_specification.md
@@ -0,0 +1,303 @@
+# Cryptographic Specification
+
+Some of the terminology, symbols, and language has been borrowed from and
+inspired by the [Halo2 Book](https://zcash.github.io/halo2) and the [MACI 1.0
+Audit Specification](https://hackmd.io/AP6zPSgtThWxx6pjXY7R8A).
+
+## Notation
+
+- Accumulator: an elliptic curve point which is a commitment to \\(t\\) field
+  elements.
+- \\(t\\): the maximum capacity of the accumulator.
+- Zero value: the nothing-up-my-sleeve value (see 2).
+- Elliptic curve multiplication: in this specification, we use the dot operator
+  \\(\cdot\\) to denote scalar multiplication of an elliptic curve point.
+
+## Cryptographic primitives
+
+### 1. The BN254 curve
+
+The current implementation of Semacaulk uses the BN254 curve which Ethereum
+supports in its elliptic curve addition, scalar multiplication, and
+pairing-check precompiles as defined in
+[EIP-196](https://eips.ethereum.org/EIPS/eip-196) and
+[EIP-197](https://eips.ethereum.org/EIPS/eip-197). 
+
+#### 1.1. The BN254 scalar field
+
+The BN254 scalar field \\(\mathbb{F}_r\\) is:
+
+```
+21888242871839275222246405745257275088548364400416034343698204186575808495617
+```
+
+#### 1.2. The BN254 scalar field
+
+The BN254 prime field \\(\mathbb{F}_q\\) is:
+
+```
+21888242871839275222246405745257275088696311157297823662689037894645226208583
+```
+
+#### 1.3. The \\(\mathbb{G}_1\\) group
+
+The group \\(\mathbb{G}_1\\) defined on BN254 has the generator point \\(g_1 =
+(1, 2)\\).
+
+#### 1.4. The \\(\mathbb{G}_2\\) point
+
+The group \\(\mathbb{G}_2\\) defined on BN254 has the generator point \\(g_2 =
+(x_0 * i + x_1, y_0 * i + y_1)\\) where:
+
+- \\(x_0\\) equals `11559732032986387107991004021392285783925812861821192530917403151452391805634`
+- \\(x_1\\) equals `10857046999023057135944570762232829481370756359578518086990519993285655852781`
+- \\(y_0\\) equals `4082367875863433681332203403145435568316851327593401208105741076214120093531`
+- \\(y_1\\) equals `8495653923123431417604973247489272438418190587263600148770280649306958101930`
+
+### 2. The nothing-up-my-sleeve value
+
+The nothing-up-my-sleeve (NUMS) value is:
+
+```bash
+14233191614411629788649003849761857673160358990904722769695641636673172216357
+```
+
+It is the Keccak256 hash of the bytestring `Semacaulk`, modulo
+\\(\mathbb{F}_r\\). To compute it, run the following in a NodeJS console where
+`e` is an instance of Ethers.js 5.0:
+
+```js
+(
+    BigInt(e.utils.solidityKeccak256(['string'], ['Semacaulk'])) % 
+    BigInt('21888242871839275222246405745257275088548364400416034343698204186575808495617')
+).toString(10)
+```
+
+Due to the second-image resistance property of the Keccak256 hash function,
+anyone can be assured that no-one knows any other preimage to the NUMS value.
+It follows that no-one knows the MiMC7 preimage to the NUMS value.
+
+### 3. The structured reference string (SRS)
+
+Semacaulk's structured reference string (SRS) consists of an ordered list of
+\\(2^n + 1\\) \\(\mathbb{G}_1\\) points and \\(2^n\\) \\(\mathbb{G}_2\\)
+points, where the maximum capacity of the accumulator is \\(2^n = t\\).
+
+We assume the existence of a secret and unknown value \\(\tau\\) which can be
+generated using a [securely run trusted
+setup](https://eprint.iacr.org/2017/1050.pdf).
+
+These points are defined as such:
+
+- \\(\mathsf{srs\\_g1}\\): \\([g_1, g_1 \cdot {\tau}, \ldots, g_1 \cdot {\tau \cdot {t + 1}}]\\)
+- \\(\mathsf{srs\\_g2}\\): \\([g_2, g_2 \cdot {\tau}, \ldots, g_2 \cdot {\tau \cdot {t + 1}}]\\)
+
+Where \\(g_1\\) is defined in 1.3 and \\(g_2\\) is defined in 1.4.
+
+### 4. The MiMC7 hash function
+
+Semacaulk currently uses the MiMC7 hash function to compute identity
+commitments and nullifier hashes. While other possibly more secure hash
+functions like Poseidon are possible, we chose MiMC7 only because of its
+simplicity of implementation for our purposes of delivering a proof-of-concept.
+
+The MiMC7 has function is defined
+[here](https://iden3-docs.readthedocs.io/en/latest/_downloads/a04267077fb3fdbf2b608e014706e004/Ed-DSA.pdf).
+
+Our instantiation of the MiMC7 hash function for the BN254 curve uses the
+following constants:
+
+- \\(n = 91\\)
+- \\(\mathsf{MIMC\\_SEED} =\\) `mimc` (the hexidecimal array `[0x6d, 0x69, 0x6d, 0x63]`)
+
+#### 4.1. The MiMC7 round constants
+
+Given the BN254 scalar field \\(\mathbb{F}_r\\), we first define 91 round
+constants (denoted as \\(\mathsf{cts}\\)) using the algorithm implemented in
+[`circomlibjs/src/mimc7.js`](https://github.com/iden3/circomlibjs/blob/ee8ec2fca2ca7f16dec9d0f39d57dbe80dd18870/src/mimc7.js#L29)
+and
+[`semacaulk/src/mimc7.rs`](https://github.com/geometryresearch/semacaulk/blob/main/src/mimc7.rs#L65).
+
+The algorithm is as such:
+
+- The first round constant is \\(0\\).
+- The next round constant is the Keccak256 hash of \\(\mathsf{MIMC\\_SEED} =\\),
+  modulo the field order of \\(\mathbb{F}_r\\).
+- Each subsequent round constant is the Keccak256 hash of the previous one,
+  modulo the field order of \\(\mathbb{F}_r\\).
+
+#### 4.2. The MiMC7 `hash` algorithm
+
+To hash a single field element \\(x\\), we use the `hash()` algorithm. The inputs to
+`hash()` are \\(x\\) and a key \\(k\\).
+
+1. Compute the first round digest \\(\mathsf{rd[0]} = (x + k) ^ 7\\).
+2. Compute the next \\(n - 1\\) round digests such that
+\\(\mathsf{rd}[i] = (\mathsf{rd}[i - 1] + \mathsf{cts}[i] + k) ^ 7\\)
+3. Return \\(\mathsf{rd}[n - 1] + k\\).
+
+#### 4.3. The MiMC7 `multi_hash` algorithm
+To hash multiple field elements \\(x_0, \ldots, x_n\\), we use the `multi_hash()`
+algorithm. The inputs to `multi_hash()` are the array of said field elements
+and a key \\(k\\).
+
+1. Initialise \\(r\\) to equal \\(k\\).
+2. For each \\(x_i\\):
+
+    a. Set \\(h_i = \mathsf{hash}(x_i, r)\\).
+
+    b. Set \\(r = x_i + h_i\\).
+
+3. Return \\(r\\).
+
+##### 4.3.1 `multi_hash` with two field elements
+
+It is useful to describe the `multi_hash` algorithm for two input elements in
+individual steps because the Semacaulk circuit construction (see [The Circuit
+and Gates](./circuit_and_gates.html)) makes use of its intermediate states.
+
+Given inputs \\(a\\) and \\(b\\):
+
+1. Set \\(r\\) as 0.
+2. Set \\(h_0 = \mathsf{hash}(a, r)\\).
+3. Set \\(r = r + a + h_0\\).
+4. Set \\(h_1 = \mathsf{hash}(b, r)\\).
+5. Return \\(r + b + h_1\\).
+
+Note that in step 4, the key is \\(a + h_0 = \mathsf{hash}(a, 0)\\). This fact
+is crucial to understanding how the circuit construction works.
+
+### 5. KZG commitments
+
+Semcaulk uses the KZG commitment scheme described in
+[KZG10](https://www.iacr.org/archive/asiacrypt2010/6477178/6477178.pdf).
+
+Given an array of \\(t\\) values \\([m_0, \ldots, m_t]\\), we interpolate to
+derive the polynomial \\(\phi\\) such that \\(\phi(i) = m_i\\).
+
+Knowing \\(\phi\\) with \\(l\\) coefficients \\([\phi_0, \ldots, \phi_{l -
+1}]\\), one can use \\(\mathsf{srs\\_g1}\\) to produce a commitment in the form
+of a \\(\mathbb{G}_1\\) point, or \\(\mathsf{srs\\_g2}\\) to produce a
+commitment in the form of a \\(\mathbb{G}_2\\) point.
+
+\\(\mathsf{commit}(\phi, \mathsf{srs}) = \sum_{i=1}^{l} \mathsf{srs}[i] \cdot \phi_i \\)
+
+An alternative notation for \\(\mathsf{commit}\\) is:
+
+- \\([\phi\]_1\\) where the commitment is a \\(\mathbb{G}_1\\) point or
+- \\([\phi\]_2\\) where the commitment is a \\(\mathbb{G}_2\\) point.
+
+A KZG opening proof is denoted as:
+
+\\(\mathsf{open}(\mathsf{srs}, [\phi\], \phi(i))\\)
+
+### 6. Lagrange basis polynomials
+
+Lagrange basis polynomials are an important concept and are used in several
+parts of the protocol. To understand them, we must first define roots of unity
+of a finite field.
+
+#### 6.1. Roots of unity of a finite field
+
+The \\(n\\)th roots of unity of a finite field \\(\mathbb{F}_p\\) with prime
+order \\(p\\) are field elements where for each element \\(x\\), \\(x^n = 1\\).
+
+For example, the 4th roots of unity of the BN254 scalar field (see 1.1) are:
+
+```
+0x0000000000000000000000000000000000000000000000000000000000000001
+0x30644E72E131A029048B6E193FD841045CEA24F6FD736BEC231204708F703636
+0x30644E72E131A029B85045B68181585D2833E84879B9709143E1F593F0000000
+0x0000000000000000B3C4D79D41A91758CB49C3517C4604A520CFF123608FC9CB
+```
+
+Another name for the \\(n\\) roots of unity is the evaluation domain of size \\(n\\)
+for a given finite field. They are commonly denoted as \\(\\{1, \omega, \ldots,
+\omega^{n-1}\\}\\).
+
+#### 6.2. Lagrange basis polynomials
+
+Given an evaluation domain of size \\(n\\), the Lagrange basis polynomials of
+this domain are the \\(n\\) polynomials \\([L_0, \ldots, L_n]\\) such that
+\\(L_i(\omega^{i - 1} = 1)\\) and \\(L_i(\omega^{j} = 0)\\) for all
+\\(j \neq i - 1\\). For example:
+
+- the Lagrange basis polynomial \\(L_0\\) evaluates to 1 given the input
+  \\(\omega^0\\).
+- the Lagrange basis polynomial \\(L_0\\) evaluates to 0 given the input
+  \\(\omega^1\\).
+- the Lagrange basis polynomial \\(L_1\\) evaluates to 0 given the input
+  \\(\omega^0\\).
+- the Lagrange basis polynomial \\(L_1\\) evaluates to 1 given the input
+  \\(\omega^1\\).
+
+#### 6.3. Efficient generation of commitments to Lagrange basis polynomials
+
+To support \\(t\\) insertions, Semacaulk requires the KZG commitments to the
+Lagrange basis polynomials over the evaluation domain of size \\(t\\). These
+KZG commitments are efficiently generated using an implementation of the
+[Feist-Khovratovich
+technique](https://alinush.github.io/2021/06/17/Feist-Khovratovich-technique-for-computing-KZG-proofs-fast.html).
+
+### 7. The accumulator
+
+The *accumulator* is a single \\(\mathbb{G}_1\\) point that is a commitment to
+a vector of \\(t\\) \\(\mathbb{F}_r\\) elements where \\(t\\) is the maximum
+capacity of the instance of Semacaulk in question. These elements are ordered
+with the users' identity commitments followed by nothing-up-my-sleeve values.
+
+An *empty accumulator* is simply a commitment to \\(t\\) nothing-up-my-sleeve
+values.
+
+Given the vector of values \\([v_0, \ldots, v_t]\\), the accumulator \\(C\\) is computed
+as such:
+
+\\(\sum_{i=1}^{t} \mathsf{commit}(L_i, \mathsf{srs\\_g1}) \cdot v_i\\)
+
+#### 7.1 Updating the accumulator
+
+To replace a value at \\(w_i\\) with \\(v_i\\) at index \\(i\\):
+
+\\(C_{\mathsf{new}} = C - L \cdot w_i + L \cdot v_i\\)
+
+\\(= C + L \cdot (v_i - w_i)\\)
+
+where \\(L = \mathsf{commit}(L_i, \mathsf{srs\\_g1})\\)
+
+This can be done on-chain at a low cost because the only expensive operations
+required are an elliptic curve scalar multiplication and a elliptic curve
+addition.
+
+### 8. The Keccak256 hash
+
+The Keccak256 hash function is defined in [*The Keccak SHA-3
+submission*](https://keccak.team/files/Keccak-submission-3.pdf) by Bertoni et
+al with the output length of 256 bits. We rely on implementations from the
+following sources:
+
+- The EVM's [`KECCAK256`
+  opcode](https://ethereum.org/en/developers/docs/evm/opcodes/) denoted as
+  `0x20`.
+- The Javascript [Ethers.js library's
+  `ethers.utils.solidityKeccak256`](https://docs.ethers.org/v5/api/utils/hashing/#utils-keccak256)
+  function.
+- The Rust [`tiny-keccak` library's
+  `v256`](https://docs.rs/tiny-keccak/latest/tiny_keccak/struct.Keccak.html)
+  function.
+
+### 9. Evaluation domains
+
+#### 9.1. The subgroup domain
+
+An evaluation domain with size 128. We denote this constant as
+\\(\mathsf{SUBGROUP\\_SIZE}\\).
+
+#### 9.2. The extended coset domain
+
+An evaluation domain with size 8 * 128. We denote this as
+\\(\mathsf{EXTENDED\\_DOMAIN\\_FACTOR} * \mathsf{SUBGROUP\\_SIZE} = 1024\\).
+
+#### 9.3. The table domain
+
+An evaluation domain with a size of at least 1024. This is the upper limit on
+the number of elements that the accumulator can hold.
diff --git a/docs/src/ethereum_contracts.md b/docs/src/ethereum_contracts.md
new file mode 100644
index 0000000..c7ead75
--- /dev/null
+++ b/docs/src/ethereum_contracts.md
@@ -0,0 +1,92 @@
+# Ethereum contracts
+
+## `Semacaulk.sol`
+
+The main Semacaulk contract which client applications should interact with or
+inherit. The key functions it exposes are:
+
+### `insertIdentity`
+
+Functions signature: `insertIdentity(uint256 _identityCommitment, uint256 _lagrangeLeafX, uint256 _lagrangeLeafY, bytes32[] memory _lagrangeMerkleProof`)
+
+`_identityCommitment` is the user-generated value defined in
+[6.1](./mechanism_of_operation.html#61-user-identities).
+
+`_lagrangeLeafX` and `_lagrangeLeafY` are the respective X and Y coordinates of
+the commitment to the Lagrange basis polynomial of the index at which the user
+wishes to insert their identity commitment.
+
+`_lagrangeMerkleProof` is the Merkle proof from the Keccak256 hash of
+`_lagrangeLeafX` and `_lagrangeLeafY` to the root of the [Lagrange Basis
+Polynomial Commitment Tree](./lagrange_basis_polynomial_commitment_tree.html).
+
+This function first verifies the Merkle proof to ensure that `_lagrangeLeafX`
+and `_lagrangeLeafY` are valid. Next, it performs field and elliptic curve
+operations to perform an [insertion](./insertion.html) to update the
+accumulator.
+
+### `broadcastSignal`
+
+Function signature: `broadcastSignal(bytes memory _signal, Types.Proof memory proof, uint256 _nullifierHash, uint256 _externalNullifier)`
+
+This function performs the following steps:
+
+1. Revert if `_nullifierHash` has already been seen. This prevents double-signalling.
+2. Compute the $\mathsf{sig\_hash}$ public input by hashing `_signal` with
+   Keccak256 and right-shifting the result by 8 bits.
+3. Verify the proof and revert if it is invalid.
+4. Store the nullifier hash.
+
+## `Verifier.sol`
+
+This contract exposes a `verify()` function for the Semacaulk contract's
+`broadcastSignal` function to use. It performs the steps described in
+[4.7](./verification.html).
+
+## `Transcript.sol`
+
+This contract abstracts over the Fiat-Shamir Heuristic by providing helper
+functions to the verifier to add data to the transcript and extract the
+challenge values it needs.
+
+## `Types.sol`
+
+A helper library that defines complex Solidity types that comprise the proof.
+
+## `BN254.sol`
+
+Provides functions that encapsulate elliptic curve operations over the BN254
+curve.
+
+## `KeccakMT.sol`
+
+Provides a helper function for the Semacaulk contract's `insertIdentity`
+function to verify a Merkle proof.
+
+## `Lagrange.sol`
+
+Provides a helper function for the verifier contract to compute the evaluation
+of $L_0$ at a given point $\alpha$, and the evaluation of the vanishing
+polynomial at $\alpha$.
+
+## `Constants.sol`
+
+Contains crucial constant values:
+
+- `PRIME_Q`: the order of the BN254 base field.
+- `PRIME_R`: the order of the BN254 scalar field.
+- `DOMAIN_SIZE_INV`: the inverse of the domain size (128) over the BN254 scalar field.
+- `LOG2_DOMAIN_SIZE`: the binary logarithm of the domain size such that `2 ^ LOG2_DOMAIN_SIZE = 128`.
+- `OMEGA`: the 1st root of unity (counting from 0) of the subgroup domain.
+- `OMEGA_N`: the $n$th root of unity (counting from 0) of the subgroup domain.
+
+The following constants depend on the maximum size of the accumulator, and
+should be changed depending on how many elements the client application wishes
+to support.
+
+- `SRS_G1_T_X`: The X coordinate of $\mathsf{srs\_g1}[t]$
+- `SRS_G1_T_Y`: The Y coordinate of $\mathsf{srs\_g1}[t]$
+- `SRS_G2_1_X_0`: The X0 coordinate of $\mathsf{srs\_g2}[1]$
+- `SRS_G2_1_X_1`: The X1 coordinate of $\mathsf{srs\_g2}[1]$
+- `SRS_G2_1_Y_0`: The Y0 coordinate of $\mathsf{srs\_g2}[1]$
+- `SRS_G2_1_Y_1`: The Y1 coordinate of $\mathsf{srs\_g2}[1]$
diff --git a/docs/src/fiat_shamir_transcript.md b/docs/src/fiat_shamir_transcript.md
new file mode 100644
index 0000000..1970bf3
--- /dev/null
+++ b/docs/src/fiat_shamir_transcript.md
@@ -0,0 +1,28 @@
+# The Fiat-Shamir Transcript
+
+A transcript is an abstraction over the [Fiat-Shamir
+heuristic](https://en.wikipedia.org/wiki/Fiat%E2%80%93Shamir_heuristic). Both
+the prover and verifier use the transcript to deterministically generate
+*challenge variables* based on the public inputs and proof data.
+
+Another way to think about the transcript is as a state machine where the state
+is a single data buffer. Every time a challenge is requested, it hashes the
+buffer replaces the contents of the buffer with the hash, and returns a value
+derived from the hash. The transcript can also be updated with abitrary data by
+appending the update to the buffer.
+
+Our transcript implements this concept with the following functions:
+
+- `new_transcript`: returns a new transcript whose buffer is 32 bytes of `0`
+  values.
+- `update_with_f`: accepts a single \\(\mathbb{F}_r\\) value, converts it to a
+  big-endian byte array, and appends it to the buffer.
+- `update_with_g1`: accepts a single \\(\mathbb{G}_1\\) point, converts its
+  \\(x\\) and \\(y\\) points to big-endian byte arrays, and appends them to the
+  buffer in the aforementioned order.
+- `update_with_g2`: accepts a single \\(\mathbb{G}_2\\) point, converts its
+  \\(x_0\\), \\(x_1\\), \\(y_0\\), and \\(y_1\\) points into big-endian byte
+  arrays, and appends them to the buffer in the aforementioned order.
+- `get_challenge`: hashes the buffer with Keccak256, replaces the buffer with
+  the hash, converts the hash into a \\(\mathbb{F}_r\\) element (treating it
+  as a big-endian buffer), and returns the \\(\mathbb{F}_r\\) element.
diff --git a/docs/src/gas_costs.md b/docs/src/gas_costs.md
new file mode 100644
index 0000000..e103cc7
--- /dev/null
+++ b/docs/src/gas_costs.md
@@ -0,0 +1,11 @@
+# Gas costs
+
+An insertion (via `insertIdentity()` costs around 68k gas.
+
+`broadcastSignal()`, which includes proof verification, costs around 355k gas.
+
+By contrast, a Tornado Cash deposit (which involves inserting a leaf to a
+Merkle tree) costs [907787
+gas](https://etherscan.io/tx/0x6f60a4aa7058dab153a859adfb139362d4bc395145528371ed90b127e528c7e7)
+and a withdrawal (which involves a Groth16 verification step) costs [327188
+gas](https://etherscan.io/tx/0xf2eb3005bf1d1866b4778d6b3686aaed64f8c6b015d2e998855598226223b613).
diff --git a/docs/src/insertion.md b/docs/src/insertion.md
new file mode 100644
index 0000000..50b5cef
--- /dev/null
+++ b/docs/src/insertion.md
@@ -0,0 +1,15 @@
+# Insertion
+
+As described in the [Cryptographic
+Specification](./cryptographic_specification.html#7-the-accumulator),
+insertions to the accumulator are easily achieved via an elliptic curve point
+multiplication and addition.
+
+To replace a value (originally $w_i$) at index \\(i\\) with $v_i$:
+
+$C_{\mathsf{new}}= C + L \cdot (v_i - w_i)$
+
+where $L = \mathsf{commit}(L_i, \mathsf{srs\\_g1})$
+
+If only insertions are allowed, $w_i$ is by definition the [nothing-up-my-sleeve
+value](./cryptographic_specification.html#2-the-nothing-up-my-sleeve-value).
diff --git a/docs/src/lagrange_basis_polynomial_commitment_tree.md b/docs/src/lagrange_basis_polynomial_commitment_tree.md
new file mode 100644
index 0000000..00f86f2
--- /dev/null
+++ b/docs/src/lagrange_basis_polynomial_commitment_tree.md
@@ -0,0 +1,17 @@
+# The Lagrange Basis Polynomial Commitment Tree
+
+The Semacaulk contract's `insertIdentity` function requires access to a valid
+commitment to the Lagrange basis polynomial at the index at which an insertion
+is made. This commitment is prohibitively expensive to compute on-chain, so 
+we instead have a Merkle root to the hashes of all of these commitments be set
+as an immutable storage variable at deployment time. The user only has to
+provide a Merkle path to said commitment, which the contract can cheaply
+verify. These commitments are deterministic and anyone can verify that the
+Merkle root to these values is valid.
+
+## Code
+
+The Rust function to compute the Lagrange basis polynomial commitments is 
+`commit_to_lagrange_bases` located in `src/accumulator.rs`. The code to compute
+the Merkle tree of the hashes of these commitments is also located in the same
+file.
diff --git a/docs/src/mechanism_of_operation.md b/docs/src/mechanism_of_operation.md
new file mode 100644
index 0000000..e0bd23b
--- /dev/null
+++ b/docs/src/mechanism_of_operation.md
@@ -0,0 +1,58 @@
+# Mechanism of Operation
+
+The goal of Semacaulk is to enable users to:
+
+1. Register their identity;
+2. Prove in zero-knowledge that they are a member of the set of registered users;
+3. Broadcast an arbitrary signal towards an external nullifier, without the
+   possibility of double-signalling.
+
+## 6.1. User identities
+
+A user's identity consists of an *identity nullifier* \\(\mathsf{id\\_nul}\\)
+and an *identity trapdoor* \\(\mathsf{id\\_trap}\\). These are secret values
+and are elements of \\(\mathbb{F}_r\\) (see [1.1](./cryptographic_specification.html#11-the-bn254-scalar-field)).
+
+An *identity commitment* \\(\mathsf{id\\_comm}\\) is the MiMC7 `multi_hash` (see [4.3](./cryptographic_specification.html#43-the-mimc7-multi_hash-algorithm))
+of \\(\mathsf{id\\_nul}\\) and \\(\mathsf{id\\_trap}\\):
+
+\\(\mathsf{id\\_comm} = \mathsf{multi\\_hash}([\mathsf{id\\_nul}, \mathsf{id\\_trap}])\\)
+
+## 6.2. External nullifiers
+
+An *external nullifier* \\(\mathsf{ext\\_nul}\\) is a \\(\mathbb{F}_r\\) field
+element which represents a topic. A signal can only be broadcast towards each
+external nullifier once and only once.
+
+## 6.3. Nullifier hashes
+
+A nullifier hash is the MiMC7 `multi_hash` of
+\\(\mathsf{id\\_nul}\\) and \\(\mathsf{ext\\_nul}\\):
+
+\\(\mathsf{nul\\_hash} = \mathsf{multi\\_hash}([\mathsf{id\\_nul}, \mathsf{ext\\_nul}])\\)
+
+## 6.4. Insertions
+
+An *insertion* is the act of updating the on-chain accumulator with a user's
+identity commitment. This is done by invoking the `insertIdentity()` function
+of the Semacaulk smart contract.
+
+## 6.5. Broadcasting a signal
+
+When a user *broadcasts a signal*, they generate a proof that they know the
+secret identity nullifier and identity trapdoor behind their identity
+commitment, and then submit said proof to the Semacaulk smart contract's
+`broadcastSignal()` function.
+
+Tied to this proof is the hash of a *signal* and the user's desired external
+nullifier. The contract (not the user) hashes the user-provided signal using
+Keccak256 and right-shifts the result by 8 bits to derive
+\\(\\mathsf{sig\\_hash}\\), which is used as one of the public inputs to the
+verifier.
+
+### 6.6. Preventing double-signalling
+
+The Semacaulk smart contract maintains a mapping of nullifier hashes. Each
+nullifier hash is unique to the user and an external nullifier. If the
+`broadcastSignal()` function finds that a nullifier hash has already been seen,
+it rejects the transaction, thus preventing double-signalling.
diff --git a/docs/src/overview.md b/docs/src/overview.md
new file mode 100644
index 0000000..74deca0
--- /dev/null
+++ b/docs/src/overview.md
@@ -0,0 +1,58 @@
+# Overview
+
+Semacaulk is a zero-knowledge set membership protocol that works on Ethereum.
+
+Semacaulk allows a user to *commit* to an identity, represented by two secret
+values: an identity nullifier and an identity trapdoor. Next, any user who
+knows their secret values can generate a proof that they had previously
+committed to said identity, without revealing which member of the set they
+were. Moreover, when they submit such a proof, they can broadcast an arbitrary
+*signal* against an *external nullifier*, but only do so once per external
+nullifier. This enables applications like mixers, whistleblowing, and simple
+private voting systems. This is the same basic functionality as the [Semaphore
+Protocol](https://github.com/semaphore-protocol/semaphore).
+
+The source code for Semacaulk can be found
+[here](https://github.com/geometryresearch/semacaulk).
+
+## Differences from Semaphore
+
+Semacaulk differs from Semaphore in two key ways. First, instead of
+accumulating identity commitments in a Merkle tree, it updates a KZG
+commitment. This operations involves BN254 point multiplication and addition,
+rather than expensive zk-friendly hash operations. Secondly, the underlying
+proof system is a polynomial interactive oracle proof that combines [Caulk+
+lookups](https://eprint.iacr.org/2022/957) and a [multipoint opening
+argument](https://zcash.github.io/halo2/design/proving-system/multipoint-opening.html).
+
+Thanks to these techniques, on-chain insertions are far cheaper in Semacaulk
+(around 68k gas) while the gas cost of verification (356k gas) is comparable to
+that of Semaphore. Moreover, proof generation comes in two phases - a
+[precomputation stage](precomputation_and_updates.html) and a proof generation
+stage. The total time taken is comparable to Groth16 proof generation for a
+Semaphore circuit that supports the same number of insertions, but more
+imporantly, precomputation can be performed long in advance and efficiently
+updated, which imparts more flexibility which may lead to higher
+user-friendliness.
+
+## Motivation
+
+We intend Semacaulk to demonstrate the use of Caulk+ techniques for membership
+proofs in a gas-efficient manner to enable privacy-related applications. We
+believe these techniques, as are other new proving systems and lookup
+arguments, can be highly useful, and we hope that Semacaulk shows how to
+practically use them.
+
+We highly welcome and strongly encourage collaboration with projects who wish
+to build upon Semacaulk.
+
+Note that the techniques used in Semacaulk do not have to involve an end-to-end
+custom prover such as used here. We have done this only because we wanted to
+experiment with improving prover efficiency further. With only small changes,
+the same gas-efficient membership proof construction can be used with more
+generic and expressive SNARK-based programs.
+
+## Security
+
+The code base has not been audited. We do not recommend its use in production
+until a thorough audit has been performed.
diff --git a/docs/src/performance_benchmarks.md b/docs/src/performance_benchmarks.md
new file mode 100644
index 0000000..76cf73a
--- /dev/null
+++ b/docs/src/performance_benchmarks.md
@@ -0,0 +1,17 @@
+# Performance and Benchmarks
+
+These benchmarks were performed on an Intel(R) Core(TM) i7-8565U CPU @ 1.80GHz
+machine with 24 GB RAM. They represent the time taken for a native Rust binary
+(built for `release`) to perform the precomputation and proof generation steps.
+
+To reproduce these benchamarks, run the `demo` binary following [these instructions](./quick_start.html).
+
+## Benchmarks
+
+| Maximum capacity | Precomputation (ms)  | Proof generation (ms) | Precomputation + proving | SRS size (uncompressed hex) (MB) |
+|-|-|-|-|-|
+| `2 ** 11 = 2048` | `103` | `63` | `166` | `0.78` |
+| `2 ** 12 = 4096` | `183` | `51` | `234` | `1.6` |
+| `2 ** 14 = 16384` | `668` | `53` | `721` | `6.1` |
+| `2 ** 16 = 65536` | `2126` | `50` | `2176` | `25` |
+| `2 ** 20 = 1048576` | `24333` | `42` | `24375` | `387` |
diff --git a/docs/src/precomputation_and_updates.md b/docs/src/precomputation_and_updates.md
new file mode 100644
index 0000000..96e5827
--- /dev/null
+++ b/docs/src/precomputation_and_updates.md
@@ -0,0 +1,112 @@
+# Precomputation and updates
+
+Caulk employs a precomputation step in order to make the use of it sublinear in
+the group size. This allows neatly separating the membership proof part of
+Semacaulk from the nullifier computation, while allowing to blind the
+precomputed membership proof differently at each use.
+
+When a group is updated, precomputation is needed again, so there are a few
+options as to how to avoid many precomputations in frequently updated groups.
+These include storing a history of valid group commitments or batching
+insertions and updating the precomputation after some predefined time slot.
+This also opens the possibility to use a centralised, but verifiable, service
+to compute these for them, since a unique feature of the precomputation in
+Caulk is that a batch can be computed even more cheaply. There are, of course,
+privacy implications when using a service, but these can also be mitigated
+using several techniques and trade-offs.
+
+Additionally, the precomputation done in Caulk is amenable to efficient updates
+when the group changes, justifying a higher cost for the initial
+precomputation.
+
+## Precomputed data
+
+Precomputed data consists of the following:
+
+1. \\(\mathsf{mimc\\_cts}\\)
+2. \\(\mathsf{mimc\\_cts\\_coset\\_evals}\\)
+3. \\(\mathsf{zh\\_inverse\\_coset\\_evals}\\)
+4. \\(\mathsf{q\\_mimc}\\) 
+5. \\(\mathsf{q\\_mimc\\_coset\\_evals}\\) 
+6. \\(\mathsf{l0\\_coset\\_evals}\\) 
+7. \\(\mathsf{w_1\\_mapping}\\) 
+7. \\([{\mathsf{W}_1}^{(i)}]_2\\) for all indices \\(i \in I\\)
+8. \\([{\mathsf{W}_2}^{(i)}]_2\\) for all indices \\(i \in I\\)
+
+The only parts of the precomputed data which rely on the secret index \\(i\\),
+which denotes the secret position of the prover's identity commitment in the
+accumulator, are \\([{\mathsf{W}_1}^{(i)}]_2\\) and \\([{\mathsf{W}_2}^{(i)}]_2\\).
+
+The Caulk+ paper defines:
+
+- \\({\mathsf{W}_1}^{(i)} = (C(X) - v_i) / (X - \omega^i)\\)
+- \\({\mathsf{W}_2}^{(i)} = Z_H(X) / (X - \omega^i)\\)
+
+## Updating commitments to \\(\mathsf{W}_1^{(i)}\\)
+
+For many of Semacaulk's use cases, users insert new items into the accumulator,
+and do not update existing items. As such, this section will only discuss
+how to update commitments to \\(\mathsf{W}_1^{(i)}\\) when the accumulator
+changes at an index \\(j\\) which is different from that of the user's entry
+\\(i\\).
+
+We can efficiently update \\([{\mathsf{W}_1}^{(i)}]_2\\) using the technique
+described in [TADBFK20, section 3.4.2](https://eprint.iacr.org/2020/527.pdf),
+where \\(i \neq j\\). An implementation of this approach can be found in the
+[`quotient-pir`](https://github.com/geometryresearch/quotient-pir) repository.
+Additionally, a proof of concept of precomputation-as-a-service can be found in
+the
+[`semacaulk-precompute`](https://github.com/geometryresearch/semacaulk-precompute)
+repository.
+
+## Updating commitments to \\(\mathsf{W}_2^{(i)}\\)
+
+For use cases where users do not update their own entries (i.e. \\(i \neq j\\)),
+there is no need to update the precomputed commitments to
+\\(\mathsf{W}_2^{(i)}\\).
+
+<!--
+### \\(\mathsf{mimc\\_cts}\\)
+
+A polynomial over the multiplicative subgroup which evaluates to the MiMC7
+round constants at each root of unity. The subgroup size is the number of MiMC7
+rounds defined in
+[4](./cryptographic_specification.html#4-the-mimc7-hash-function).
+
+### \\(\mathsf{mimc\\_cts\\_coset\\_evals}\\)
+
+We first compute a polynomial which evaluates, at each root of unity in the
+subgroup domain, to a vector (of the size of the subgroup) consisting of the
+evaluations of the MiMC7 round constants, padded by dummy values. Next, we
+perform an FFT over the coset of the extended domain on the coefficients of
+this polynomial to obtain \\(\mathsf{mimc\\_cts\\_coset\\_evals}\\).
+
+### \\(\mathsf{zh\\_inverse\\_coset\\_evals}\\)
+
+A vector of \\(\mathbb{F}_r\\) elements that are the field inversions of the
+(coefficients of the vanishing polynomial over the coset??? TODO)
+
+### \\(\mathsf{q\\_mimc}\\) 
+
+A polynomial whose evaluations at the roots of unity over the subgroup domain
+of size 128 are \\(n = 91\\) `1` values, followed by zeroes. It represents the
+\\(\mathsf{q\\_mimc}\\) [selector column](./circuit_and_gates.html).
+
+### \\(\mathsf{q\\_mimc\\_coset\\_evals}\\) 
+
+A vector of \\(\mathbb{F}_r\\) elements that are the evaluations of the
+\\(\\mathsf{q\\_mimc}\\) polynomial coefficients over the coset?? (TODO) 
+
+### \\(\mathsf{l0\\_coset\\_evals}\\) 
+
+Where \\(L_0\\) is the 0th Lagrange basis polynomial over the subgroup
+evaluation domain, this is a vector of its evaluations over the coset (?? TODO)
+
+### \\({\mathsf{W}_1}^{i}\\) 
+
+As defined in the [Caulk+ paper, section 3](https://eprint.iacr.org/2022/957.pdf).
+
+### \\({\mathsf{W}_2}^{i}\\) 
+
+As defined in the [Caulk+ paper, section 3](https://eprint.iacr.org/2022/957.pdf).
+-->
diff --git a/docs/src/proof_generation.md b/docs/src/proof_generation.md
new file mode 100644
index 0000000..4067337
--- /dev/null
+++ b/docs/src/proof_generation.md
@@ -0,0 +1,260 @@
+# Proof generation
+
+## 4.6.1. Assignment Round
+
+Given the public and private inputs, the prover generates the assignment table
+(see [4.3](./circuit_and_gates.html)). Each column is represented as a
+polynomial over the multiplicative subgroup.
+
+- \\(\mathsf{w}_0\\)
+- \\(\mathsf{w}_1\\)
+- \\(\mathsf{w}_2\\)
+- \\(\mathsf{key}\\)
+
+The prover then computes KZG commitments to each of the above polynomials:
+
+- \\([\mathsf{w}_0]_1\\)
+- \\([\mathsf{w}_1]_1\\)
+- \\([\mathsf{w}_2]_1\\)
+- \\([\mathsf{key}]_1\\)
+
+The prover also computes:
+
+\\(A = \mathsf{w}_1 + \mathsf{w}_1(\gamma^{91}X) + 2 \cdot \mathsf{key}\\)
+
+where \\(\mathsf{w}_1(\gamma^{91}X)\\) is \\(\mathsf{w}_1\\) shifted by the
+\\(n\\)th root of unity in the subgroup domain
+([9.1](cryptographic_specification.html#91-the-subgroup-domain)).
+
+Next, the prover adds the public inputs to the transcript in this order:
+
+1. \\(\mathsf{ext\\_nul}\\)
+2. \\(\mathsf{nul\\_hash}\\)
+3. \\(\mathsf{sig\\_hash}\\)
+
+The prover then extracts the challenge \\(v\\), which is used in the next
+round.
+
+## 4.6.2. Quotient round
+
+The prover generates a quotient polynomial \\(q\\) by dividing
+a numerator — a powers-of-\\(v\\)-separated linear combination of gate
+polynomials — with the vanishing polynomial \\(Z_H\\).
+
+\\(q(X) = \mathsf{numerator} / Z_H\\) where
+
+\\(\mathsf{numerator} =\\)
+
+\\(\mathsf{q\\_mimc}((\mathsf{w}_0 + \mathsf{cts})^7 - \mathsf{w}_0(\gamma X)) + \\)
+
+\\(v \cdot \mathsf{q\\_mimc}((w_1 + \mathsf{key} + \mathsf{cts})^7 - w_1(\gamma X)) +\\)
+
+\\(v^2 \cdot \mathsf{q\\_mimc}((\mathsf{w}_2 + \mathsf{key} + \mathsf{cts})^7 - \mathsf{w}_2(\gamma X)) +\\)
+
+\\(v^3 \cdot \mathsf{q\\_mimc}(\mathsf{key} - \mathsf{key}(\gamma X)) +\\)
+
+\\(v^4 \cdot L_0(\mathsf{key} - \mathsf{w}_0 - \mathsf{w}_0(\gamma ^{91}X)) +\\)
+
+\\(v^5 \cdot L_0(\mathsf{nul\\_hash} - \mathsf{w}_2 - \mathsf{w}_2(\gamma ^{91}X) - 2 \cdot \mathsf{key}) +\\)
+
+\\(v^6 \cdot L_0 \cdot (\mathsf{w}_2 - \mathsf{ext\\_nul})\\)
+
+These equations correspond to the gates defined in
+[4.3](circuit_and_gates.html#gates).
+
+\\(\mathsf{w}_0(\gamma X)\\) refers to \\(\mathsf{w}_0\\) shifted (or
+"rotated") forward by one.
+
+\\(\mathsf{w}_0(\gamma ^{91}X)\\) refers to \\(\mathsf{w}_0\\) shifted forward
+by 91, which is the number of MiMC7 rounds defined in
+[4.1](./cryptographic_specification.html#41-the-mimc7-round-constants).
+
+The prover then commits to \\(q\\) to obtain \\([q]_1\\).
+
+## 4.6.3. First Caulk+ round
+
+The prover computes:
+
+- \\(\mathsf{z}_i\\)
+- \\(\mathsf{c}_i\\)
+- \\(u'\\)
+
+and their commitments:
+
+- \\([\mathsf{z}_i]_1\\)
+- \\([\mathsf{c}_i]_1\\)
+- \\([u']_1\\)
+
+according to [page 6 of the Caulk+
+paper](https://eprint.iacr.org/2022/957.pdf).
+
+The prover then updates the transcript with \\([q]_1\\) and the above values,
+and extracts the challenge values \\(\chi_1\\) and \\(\chi_2\\), which are
+used in the next round. \\(\chi_1\\) is also used in the opening round.
+
+## 4.6.4. Second Caulk+ round
+
+The prover computes:
+
+- \\(\mathsf{h}\\)
+- \\(\mathsf{w}\\)
+
+according to the Round 2 steps from [page 6 of the Caulk+
+paper](https://eprint.iacr.org/2022/957.pdf), and commits to them:
+
+- \\([\mathsf{h}]_1\\)
+- \\([\mathsf{w}]_2\\)
+
+The prover then extracts the challenge \\(\alpha\\), which is used in the next
+round.
+
+## 4.6.5. Opening round
+
+This section is a work in progress; in the meantime, see [this
+document](https://hackmd.io/D-bL6-oNSbSej7Ao_-9PLA) for the multiopen argument.
+Also see [this document](https://hackmd.io/D-bL6-oNSbSej7Ao_-9PLA) which
+describes the argument adapted for Semacaulk.
+
+The prover computes:
+
+- \\(\omega\\): the root of unity with index 1 (starting from zero) of the
+  subgroup domain
+  ((9.1)[./cryptographic_specification.html#91-the-subgroup-domain]).
+- \\(\omega^n\\): the root of unity with index \\(n\\) (starting from 0) of the
+  subgroup domain.
+
+The prover computes the polynomials:
+
+<!--\\(\mathsf{p}_1 = \mathsf{zi} + \mathsf{ci} \cdot \chi_1\\)-->
+
+<!--\\(\mathsf{p}_2 = \mathsf{zi} \cdot \mathsf{u'}(\alpha) + \chi_1 \cdot \mathsf{ci}(\mathsf{u'}(\alpha))\\)-->
+
+- \\(\mathsf{p}_1\\)
+- \\(\mathsf{p}_2\\)
+
+The commitments:
+
+- \\([\mathsf{p}_1]_1\\)
+- \\([\mathsf{p}_2]_1\\)
+
+The openings:
+
+- \\(\mathsf{w}_0(\alpha)\\)
+- \\(\mathsf{w}_0(\omega\alpha)\\)
+- \\(\mathsf{w}_0(\omega^n \alpha)\\)
+- \\(\mathsf{w}_1(\alpha)\\)
+- \\(\mathsf{w}_1(\omega\alpha)\\)
+- \\(\mathsf{w}_1(\omega^n \alpha)\\)
+- \\(\mathsf{w}_2(\alpha)\\)
+- \\(\mathsf{w}_2(\omega\alpha)\\)
+- \\(\mathsf{w}_2(\omega^n \alpha)\\)
+- \\(\mathsf{key}(\alpha)\\)
+- \\(\mathsf{key}(\omega\alpha)\\)
+- \\(\mathsf{q\\_mimc}(\alpha)\\)
+- \\(\mathsf{mimc\\_cts}(\alpha)\\)
+- \\(\mathsf{q}(\alpha)\\)
+- \\(\mathsf{u'}_1(\alpha)\\)
+- \\(\mathsf{p}_1(\mathsf{u'}_1(\alpha))\\)
+- \\(\mathsf{p}_2(\alpha)\\)
+
+The prover adds the above openings to the transcript in the stated order.
+
+## 4.6.6. Multiopen argument round
+
+The steps in this are based on the Halo2 [multipoint opening
+argument](https://zcash.github.io/halo2/design/proving-system/multipoint-opening.html).
+
+The prover computes the vanishing polynomials:
+
+- \\(\mathsf{z}_1 = x - \mathsf{u'}_1(\alpha)\\)
+- \\(\mathsf{z}_2 = x - \alpha\\)
+- \\(\mathsf{z}_3 = \\mathsf{z}_2 \cdot (x - \omega\alpha)\\)
+- \\(\mathsf{z}_4 = \\mathsf{z}_3 \cdot (x - \omega^n \alpha)\\)
+
+The prover extracts the challenge values \\(x_1\\), \\(x_2\\), \\(x_3\\), and
+\\(x_4\\).
+
+The prover computes the polynomials:
+
+- \\(\mathsf{q}_1 = \mathsf{p}_1\\)
+- \\(\mathsf{q}_2 = \mathsf{q\\_mimc} + 
+    \\mathsf{mimc\\_cts} \cdot x_1 + 
+    \\mathsf{q} \cdot {x_1}^{2} + 
+    \mathsf{u'} * {x_1}^{3} + 
+    \mathsf{p}_2 \cdot {x_1}^{4}\\)
+- \\(\mathsf{q}_3 = \mathsf{key}\\)
+- \\(\mathsf{q}_4 = \mathsf{w}_0 + \mathsf{w}_1 \cdot x_1 + \mathsf{w}_2 \cdot {x_1} ^ 2\\)
+- \\(\mathsf{f}_1 = \mathsf{q}_1 / \mathsf{z}_1\\)
+- \\(\mathsf{f}_2 = \mathsf{q}_2 / \mathsf{z}_2\\)
+- \\(\mathsf{f}_3 = \mathsf{q}_3 / \mathsf{z}_3\\)
+- \\(\mathsf{f}_4 = \mathsf{q}_4 / \mathsf{z}_4\\)
+- \\(\mathsf{f} = \mathsf{f}_1 +
+    \mathsf{f}_2 \cdot x_2 +
+    \mathsf{f}_3 \cdot {x_2}^2 +
+    \mathsf{f}_4 \cdot {x_2}^3\\)
+- \\(\mathsf{final} = \mathsf{f} +
+    \mathsf{q}_1 \cdot x_4 +
+    \mathsf{q}_2 \cdot {x_4}^2 +
+    \mathsf{q}_3 \cdot {x_4}^3 +
+    \mathsf{q}_4 \cdot {x_4}^4\\)
+
+The prover computes the openings:
+
+- \\(\mathsf{q}_1(x_3)\\)
+- \\(\mathsf{q}_2(x_3)\\)
+- \\(\mathsf{q}_3(x_3)\\)
+- \\(\mathsf{q}_4(x_3)\\)
+
+The prover computes the commitments:
+
+- \\([\mathsf{f}]_1\\)
+
+Finally, the prover computes a KZG opening proof:
+
+- \\(\pi_\mathsf{final} = \mathsf{open}(\mathsf{srs\\_g1}, \mathsf{final},
+  x_3)\\)
+
+## 4.6.7. The proof
+
+The final proof consists of:
+
+- The multiopen proof
+    - \\(\mathsf{q1\\_opening}\\)
+    - \\(\mathsf{q2\\_opening}\\)
+    - \\(\mathsf{q3\\_opening}\\)
+    - \\(\mathsf{q4\\_opening}\\)
+    - \\(\mathsf{f\\_cm}\\)
+    - \\(\mathsf{final\\_\pi}\\)
+- The openings
+    - \\(\mathsf{q\\_mimc}\\)
+    - \\(\mathsf{mimc\\_cts}\\)
+    - \\(\mathsf{quotient}\\)
+    - \\(\mathsf{u\\_prime}\\)
+    - \\(\mathsf{p1}\\)
+    - \\(\mathsf{p2}\\)
+    - \\(\mathsf{w0}_0\\)
+    - \\(\mathsf{w0}_1\\)
+    - \\(\mathsf{w0}_2\\)
+    - \\(\mathsf{w1}_0\\)
+    - \\(\mathsf{w1}_1\\)
+    - \\(\mathsf{w1}_2\\)
+    - \\(\mathsf{w2}_0\\)
+    - \\(\mathsf{w2}_1\\)
+    - \\(\mathsf{w2}_2\\)
+    - \\(\mathsf{key}_0\\)
+    - \\(\mathsf{key}_1\\)
+- The commitments
+    - \\([\mathsf{w}_0]_1\\)
+    - \\([\mathsf{w}_1]_1\\)
+    - \\([\mathsf{w}_2]_1\\)
+    - \\([\mathsf{key}]_1\\)
+    - \\([\mathsf{mimc\\_cts}]_1\\)
+    - \\([\mathsf{quotient}]_1\\)
+    - \\([\mathsf{u\\_prime}]_1\\)
+    - \\([\mathsf{zi}]_1\\)
+    - \\([\mathsf{ci}]_1\\)
+    - \\([\mathsf{p1}]_1\\)
+    - \\([\mathsf{p2}]_1\\)
+    - \\([\mathsf{q\\_mimc}]_1\\)
+    - \\([\mathsf{h}]_1\\)
+    - \\([\mathsf{w}]_2\\)
diff --git a/docs/src/quick_start.md b/docs/src/quick_start.md
new file mode 100644
index 0000000..f06aa5e
--- /dev/null
+++ b/docs/src/quick_start.md
@@ -0,0 +1,38 @@
+# Quick start
+
+1. Install Rust using [these
+   instructions](https://www.rust-lang.org/learn/get-started).
+
+2. Install Foundry using [these
+   instructions](https://github.com/foundry-rs/foundry#installation).
+
+3. Clone this repository.
+
+```bash
+git clone https://github.com/geometryresearch/semacaulk.git && \
+cd semacaulk
+```
+
+4. Build the contracts
+
+```bash
+./build_contracts.sh
+```
+
+5. Run tests
+
+```bash
+cargo test
+```
+
+6. Build and run the demo:
+
+```bash
+cargo build --release && \
+./target/release/demo 11 11.ptau
+```
+
+Note that the Powers of Tau `11.ptau` file supports up to 2048 leaf
+insertions. To support a larger capacity, see the [Trusted Setup - Processing
+the points](./trusted_setup.html#processing-the-points) section for
+instructions on how to do so.
diff --git a/docs/src/specification.md b/docs/src/specification.md
new file mode 100644
index 0000000..33e6104
--- /dev/null
+++ b/docs/src/specification.md
@@ -0,0 +1 @@
+# Specification
diff --git a/docs/src/system_invariants.md b/docs/src/system_invariants.md
new file mode 100644
index 0000000..08de99c
--- /dev/null
+++ b/docs/src/system_invariants.md
@@ -0,0 +1,42 @@
+# System invariants
+
+An [invariant](https://mathworld.wolfram.com/Invariant.html) is a property of a
+system which remains unmodified even after operations or transformations are
+applied to it. The authors of Semacaulk intend the following to be the
+invariants of Semacaulk:
+
+1. **Privacy**: No-one but the user who knows the value of the identity
+   nullifier and identity trapdoor behind an identity commitment may generate a
+   valid proof of set membership of the identity commitment in the accumulator.
+
+2. **Safe NUMS value**: No-one should be able to produce a valid proof of set
+   membership for the default nothing-up-my-sleeve value.
+
+3. **Proof non-malleability**: Proofs are visible once submitted to the mempool,
+   but no-one should be able to modify an existing proof, change it such that
+   it is associated with a different signal, and remain valid.
+
+4. **Zero-knowledge**: given a valid proof, no-one should be able to determine
+   the index of the identity commitment the identity nullifier, or the identity
+   trapdor associated with the proof.
+
+Other invariants which have to do with the internal consistency and correctness
+of the system are:
+
+5. All identity commitments must be less than the BN254 scalar field size.
+
+6. Every identity commitment in the accumulator must have been added at some
+   point in the past, except for the NUMS values.
+
+7. Any identity commitment besides the NUMS value may be added to the
+   accumulator, unless it is full.
+
+8. The NUMS value cannot be added to the accumulator.
+
+9. There can be no valid proof associated with a NUMS value as the identity
+   commitment.
+
+10. All nullifier hashes must be less than the BN254 scalar field size.
+
+11. It should only be possible to generate a proof for a valid user, and
+    impossible to generate a proof for an invalid user.
diff --git a/docs/src/trusted_setup.md b/docs/src/trusted_setup.md
new file mode 100644
index 0000000..35ee7ae
--- /dev/null
+++ b/docs/src/trusted_setup.md
@@ -0,0 +1,29 @@
+# Trusted Setup
+
+Semacaulk requires a [securely run trusted
+setup](https://eprint.iacr.org/2017/1050.pdf). Specifically, for a capacity of
+\\(2^n\\) elements, it requires \\(2^n + 1\\) \\({g_1}^{\tau}\\) points and
+\\(2^n\\) \\({g_2}^{\tau}\\) points where \\(\tau\\) is highly unlikely to be
+known but \\({g_1}^{\tau}\\) and \\({g_2}^{\tau}\\) can be generated via a
+multi-party ceremony. As long as one participant does not reveal and destroys
+the secret so-called toxic waste that they  use, the entire ceremony is secure.
+
+For compatibility with Ethereum, Semacaulk is built on the BN254 curve. As
+such, the output of the [Perpetual Powers of
+Tau](https://github.com/privacy-scaling-explorations/perpetualpowersoftau)
+ceremony can be used. The outputs of this ceremony include up to \\(2^{28}\\)
+\\({g_1}^{\tau}\\) and \\({g_2}^{\tau}\\) points. If Semacaulk is to be used on
+a different elliptic curve, a different trusted setup must be used.
+
+For the sake of convenience, we recommend the trusted setup output from Hermez
+Network, which consist of the 54th contribution of Perpetual Powers of Tau (PPOT) with
+a random beacon. These files can be downloaded from [this
+page](https://github.com/iden3/snarkjs#7-prepare-phase-2). (You may also use
+the latest contribution to PPOT, but at the time of writing, a tool to parse
+and convert it has not yet been written.)
+
+Note that the [Aztec Ignition ceremony
+output](https://github.com/AztecProtocol/ignition-verification/blob/master/Transcript_spec.md)
+is not sufficient for Semacaulk as only provides 1 `tauG2` point, while
+Semacaulk requires as many `tauG2` points as the maximum desired capacity of
+the accumulator. 
diff --git a/docs/src/verification.md b/docs/src/verification.md
new file mode 100644
index 0000000..b8c19ee
--- /dev/null
+++ b/docs/src/verification.md
@@ -0,0 +1,47 @@
+# Proof verification
+
+At a high level, the verifier does three main steps to verify a proof
+([4.6.6](proof_generation.html#466-the-proof)):
+
+## 4.7.1. Check the gate openings
+
+Given the opening values which the prover claims to be evaluations of the
+column polynomials which correspond to the circuit, the verifier computes the
+linear combination of the evaluation of the openings based on each gate
+equations separated by the \\(v\\) challenge values. This linear combination
+must equal the product of the quotient opening and the evaluation of the
+vanishing polynomial, or the verifier will return false.
+
+## 4.7.2. Compute the multiopen argument's `final_poly` and `final_poly_eval` values
+
+Leveraging the homomorphic properties of KZG commitments, the verifier
+reconstructs a commitment to the \\(\mathsf{final}_\pi\\) polynomial generated
+in the
+[prover's multiopen argument round](./proof_generation.html#466-multiopen-argument-round).
+
+The verifier also
+reconstructs \\(\mathsf{final\\_poly\\_eval}\\) which is the evaluation of
+\\(\mathsf{final}\\) at the \\(x_3\\) challenge.
+
+## 4.7.3. Perform pairing checks
+
+A three-part pairing product is performed and the verifier returns true only if
+the result is 1.
+
+\\(A * B * C == 1\\)
+
+where:
+
+\\(A = e(\mathsf{a}_1 + \mathsf{a}_2 + \mathsf{a}_3, [1]_2)\\)
+
+\\(\mathsf{a}_1 = C - [\mathsf{ci}]_1\\)
+
+\\(\mathsf{a}_2 = \chi_2(\mathsf{srs\\_g1}[t] - [1]_1)\\)
+
+$\mathsf{a}_3 = (\pi_\mathsf{final} \cdot x_3 - \mathsf{final\_poly\_eval} + [\mathsf{final}]_1) \cdot s$
+
+\\(B = e(-[\mathsf{zi}]_1, [\mathsf{w}]_2)\\)
+
+\\(C = e(-[\mathsf{final}_\pi]_1 \cdot s, [1]_2 \cdot \tau)\\)
+
+and \\(s\\) is a separator challenge extracted from the transcript.
diff --git a/lagrangeComms_11 b/lagrangeComms_11
deleted file mode 100644
index ef6123e..0000000
--- a/lagrangeComms_11
+++ /dev/null
@@ -1,2048 +0,0 @@
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diff --git a/src/client/main.rs b/src/client/main.rs
new file mode 100644
index 0000000..1018b0c
--- /dev/null
+++ b/src/client/main.rs
@@ -0,0 +1,747 @@
+use ark_bn254::{Bn254, Fq, Fr};
+use ark_ff::PrimeField;
+use ark_poly::{
+    univariate::DensePolynomial, EvaluationDomain, GeneralEvaluationDomain, UVPolynomial,
+};
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Read};
+use ark_std::{test_rng, Zero};
+use clap::{arg, command, Parser, Subcommand};
+use clap_num::number_range;
+use ethers::contract::abigen;
+use ethers::core::k256::ecdsa::SigningKey;
+use ethers::middleware::SignerMiddleware;
+use ethers::prelude::Wallet;
+use ethers::providers::{Http, Middleware, Provider, StreamExt};
+use ethers::signers::{LocalWallet, Signer};
+use semacaulk::prover::prover::{Prover, WitnessInput};
+use semacaulk::{
+    accumulator::{compute_lagrange_tree, compute_zero_leaf, Accumulator},
+    bn_solidity_utils::{f_to_u256, u256_to_f, f_to_hex},
+    contracts::compute_signal_hash,
+    keccak_tree::flatten_proof,
+    layouter::Layouter,
+    mimc7::init_mimc7,
+    prover::{Proof as SemacaulkProof, ProverPrecomputedData, PublicData},
+    setup::{g2_str_to_g2, setup},
+    verifier::Verifier as SemacaulkVerifier,
+};
+use std::convert::TryFrom;
+use std::process;
+use std::string::String;
+use std::sync::Arc;
+use std::time::Duration;
+
+/*
+RPC: https://rpc2.sepolia.org
+Address: 0xaaaa553ECd8C7cFBcA9396A5746956ef738BeEd4
+Private key: cf3a4fe3eaa7533fd3a5b19f874a0ff67749a926b80d4074 cc3b1c634b536c47 (remove the space)
+*/
+
+#[derive(Debug, PartialEq)]
+pub enum Error {
+    InvalidSk,
+    InvalidLog2Capacity,
+    InvalidIdNulOrTrap,
+}
+
+#[derive(Debug, Parser)] // requires `derive` feature
+#[command(name = "client")]
+#[command(about = "A Semacaulk client", long_about = None)]
+struct Cli {
+    #[command(subcommand)]
+    command: Commands,
+}
+
+fn log_2_capacity_range(s: &str) -> Result<u8, String> {
+    number_range(s, 10, 28)
+}
+
+#[derive(Debug, Subcommand)]
+enum Commands {
+    /// Deploy a Semacaulk contract
+    Deploy {
+        /// The Ethereum node URL
+        #[arg(short, long, required = false, default_value = "http://127.0.0.1:8545")]
+        rpc: String,
+
+        /// The deployer's Etheruem private key
+        #[arg(
+            short,
+            long,
+            required = false,
+            default_value = "ac0974bec39a17e36ba4a6b4d238ff944bacb478cbed5efcae784d7bf4f2ff80"
+        )]
+        sk: String,
+
+        /// The powers of tau (PTAU) file containing a phase 1 trusted setup output
+        #[arg(short, long, required = true)]
+        ptau: String,
+
+        /// The capacity of the accumulator expressed in log_2 (e.g. log_2(1024) = 10)
+        #[arg(short, long, required = false, default_value = "10", value_parser=log_2_capacity_range)]
+        log_2_capacity: u8,
+    },
+    /// Insert an identity into an existing Semacaulk contract
+    Insert {
+        /// The Ethereum node URL
+        #[arg(short, long, required = false, default_value = "http://127.0.0.1:8545")]
+        rpc: String,
+
+        /// The deployer's Etheruem private key
+        #[arg(
+            short,
+            long,
+            required = false,
+            default_value = "ac0974bec39a17e36ba4a6b4d238ff944bacb478cbed5efcae784d7bf4f2ff80"
+        )]
+        sk: String,
+
+        /// The powers of tau (PTAU) file containing a phase 1 trusted setup output
+        #[arg(short, long, required = true)]
+        ptau: String,
+
+        /// The Semacaulk contract
+        #[arg(short, long, required = true)]
+        contract: String,
+
+        /// The identity nullifier, in hexadecimal
+        #[arg(long = "id_nul", short = 'n', required = true)]
+        id_nul: String,
+
+        /// The identity trapdoor, in hexadecimal
+        #[arg(long = "id_trap", short = 't', required = true)]
+        id_trap: String,
+
+        /// The capacity of the accumulator expressed in log_2 (e.g. log_2(1024) = 10)
+        #[arg(short, long, required = false, default_value = "10", value_parser=log_2_capacity_range)]
+        log_2_capacity: u8,
+    },
+    /// Insert an identity into an existing Semacaulk contract
+    Prove {
+        /// The Ethereum node URL
+        #[arg(short, long, required = false, default_value = "http://127.0.0.1:8545")]
+        rpc: String,
+
+        /// The powers of tau (PTAU) file containing a phase 1 trusted setup output
+        #[arg(short, long, required = true)]
+        ptau: String,
+
+        /// The Semacaulk contract
+        #[arg(short, long, required = true)]
+        contract: String,
+
+        /// The index of the value in the accumulator
+        #[arg(short, long, required = false)]
+        index: usize,
+
+        /// The external_nullifier nullifier, in hexadecimal
+        #[arg(long = "ext_nul", short = 'e', required = true)]
+        ext_nul: String,
+
+        /// The identity nullifier, in hexadecimal
+        #[arg(long = "id_nul", short = 'n', required = true)]
+        id_nul: String,
+
+        /// The identity trapdoor, in hexadecimal
+        #[arg(long = "id_trap", short = 't', required = true)]
+        id_trap: String,
+
+        /// The identity trapdoor, in hexadecimal
+        #[arg(long = "signal", short, required = true)]
+        signal: String,
+
+        /// The capacity of the accumulator expressed in log_2 (e.g. log_2(1024) = 10)
+        #[arg(short, long, required = false, default_value = "10", value_parser=log_2_capacity_range)]
+        log_2_capacity: u8,
+
+        /// If specified, use this semacaulk_precompute endpoint to privately retrieve precomputed data
+        #[arg(short, long, required = false)]
+        semacaulk_precompute_endpoint: Option<String>,
+    },
+    BroadcastSignal {
+        /// The Ethereum node URL
+        #[arg(short, long, required = false, default_value = "http://127.0.0.1:8545")]
+        rpc: String,
+
+        /// The deployer's Etheruem private key
+        #[arg(
+            short,
+            long,
+            required = false,
+            default_value = "ac0974bec39a17e36ba4a6b4d238ff944bacb478cbed5efcae784d7bf4f2ff80"
+        )]
+        sk: String,
+
+        /// The Semacaulk contract
+        #[arg(short, long, required = true)]
+        contract: String,
+
+        /// The identity trapdoor, in hexadecimal
+        #[arg(long = "signal", short, required = true)]
+        signal: String,
+
+        /// The nullifier hash, in hexadecimal
+        #[arg(long = "nul_hash", short = 'h', required = true)]
+        nul_hash: String,
+
+        /// The external_nullifier nullifier, in hexadecimal
+        #[arg(long = "ext_nul", short = 'e', required = true)]
+        ext_nul: String,
+
+        /// The serialised proof
+        #[arg(long = "proof", short, required = true)]
+        proof: String,
+    },
+}
+
+#[tokio::main]
+async fn main() {
+    let args = Cli::parse();
+    let result = match args.command {
+        Commands::Deploy {
+            rpc,
+            sk,
+            ptau,
+            log_2_capacity,
+        } => deploy(&rpc, &sk, &ptau, log_2_capacity).await,
+        Commands::Insert {
+            rpc,
+            sk,
+            ptau,
+            contract,
+            id_nul,
+            id_trap,
+            log_2_capacity,
+        } => {
+            insert(
+                &rpc,
+                &sk,
+                &ptau,
+                &contract,
+                &id_nul,
+                &id_trap,
+                log_2_capacity,
+            )
+            .await
+        }
+        Commands::Prove {
+            rpc,
+            ptau,
+            contract,
+            index,
+            ext_nul,
+            id_nul,
+            id_trap,
+            signal,
+            semacaulk_precompute_endpoint,
+            log_2_capacity,
+        } => {
+            prove(
+                &rpc,
+                &ptau,
+                &contract,
+                index,
+                &ext_nul,
+                &id_nul,
+                &id_trap,
+                &signal,
+                semacaulk_precompute_endpoint,
+                log_2_capacity,
+            )
+            .await
+        }
+        Commands::BroadcastSignal {
+            rpc,
+            sk,
+            contract,
+            signal,
+            nul_hash,
+            ext_nul,
+            proof,
+        } => broadcast_signal(&rpc, &sk, &contract, &signal, &nul_hash, &ext_nul, &proof).await,
+    };
+
+    if result.is_err() {
+        #[allow(clippy::unnecessary_unwrap)]
+        match result.unwrap_err() {
+            Error::InvalidLog2Capacity => {
+                println!("--log2_capacity should be between 10 and 28 (inclusive).")
+            }
+            Error::InvalidSk => println!("--sk should be a valid hexadecimal value."),
+            Error::InvalidIdNulOrTrap => println!("-n or -t should be a valid hexadecimal value."),
+        };
+        process::exit(1);
+    }
+}
+
+abigen!(SemacaulkContract, "./src/contracts/Semacaulk.json");
+
+type SemacaulkContract = semacaulk_contract::SemacaulkContract<
+    SignerMiddleware<
+        ethers::providers::Provider<Http>,
+        ethers::signers::Wallet<ethers::core::k256::ecdsa::SigningKey>,
+    >,
+>;
+
+fn parse_sk(s: &str) -> Result<String, Error> {
+    let mut bytes = s.as_bytes();
+
+    if s.starts_with("0x") {
+        bytes = &bytes[2..];
+    }
+
+    let s = String::from_utf8(bytes.to_vec()).unwrap();
+
+    let hex = hex::decode(&s);
+    if hex.is_err() {
+        return Err(Error::InvalidSk);
+    }
+    Ok(s)
+}
+
+fn get_provider(rpc: &str) -> Provider<Http> {
+    Provider::<Http>::try_from(rpc)
+        .unwrap()
+        .interval(Duration::from_millis(10u64))
+}
+
+fn create_wallet(sk: &str) -> Result<LocalWallet, Error> {
+    let wallet = sk.parse::<LocalWallet>();
+    if wallet.is_err() {
+        return Err(Error::InvalidSk);
+    }
+    Ok(wallet.unwrap())
+}
+
+pub type EthersClient = Arc<SignerMiddleware<Provider<Http>, Wallet<SigningKey>>>;
+
+async fn create_client(rpc: &str, sk: &str) -> Result<EthersClient, Error> {
+    let provider = get_provider(rpc);
+    let wallet = create_wallet(sk)?;
+    let chain_id: u64 = provider.get_chainid().await.unwrap().try_into().unwrap();
+    let client = Arc::new(SignerMiddleware::new(
+        provider,
+        wallet.with_chain_id(chain_id),
+    ));
+    Ok(client)
+}
+
+fn parse_id_nul_or_trap<F: PrimeField>(s: &str) -> Result<F, Error> {
+    let mut bytes = s.as_bytes();
+    if s.starts_with("0x") {
+        if s.len() > 66 {
+            return Err(Error::InvalidIdNulOrTrap);
+        }
+
+        bytes = &bytes[2..];
+    } else if s.len() > 64 {
+        return Err(Error::InvalidIdNulOrTrap);
+    }
+
+    let hex_str = std::str::from_utf8(bytes);
+    if hex_str.is_err() {
+        return Err(Error::InvalidIdNulOrTrap);
+    }
+    let hex_str = hex_str.unwrap();
+    let mut h = hex_str.to_string();
+    while h.len() < 64 {
+        h = format!("0{}", &h);
+    }
+    let hex_str = h;
+    let hex_buf = hex::decode(hex_str).unwrap();
+    let hex_buf: Vec<u8> = hex_buf.iter().copied().rev().collect();
+
+    Ok(F::read(hex_buf.as_slice()).unwrap())
+}
+
+use semacaulk::contracts::format::proof_for_semacaulk::{format_proof, ProofForSemacaulk};
+async fn broadcast_signal(
+    rpc: &str,
+    sk: &str,
+    contract: &str,
+    signal: &str,
+    nul_hash: &str,
+    ext_nul: &str,
+    proof: &str,
+) -> Result<(), Error> {
+    let ext_nul = parse_id_nul_or_trap::<Fr>(ext_nul)?;
+    let nul_hash = parse_id_nul_or_trap::<Fr>(nul_hash)?;
+
+    let client = create_client(rpc, &parse_sk(sk)?).await?;
+
+    let a = str_to_ethers_address(contract);
+    let semacaulk_contract = SemacaulkContract::new(a, client);
+    let proof =
+        SemacaulkProof::<Bn254>::deserialize(hex::decode(proof).unwrap().as_slice()).unwrap();
+
+    let result = semacaulk_contract
+        .broadcast_signal(
+            ethers::types::Bytes::from(String::from(signal).as_bytes().to_vec()),
+            p_to_p(&format_proof(&proof)),
+            f_to_u256(nul_hash),
+            f_to_u256(ext_nul),
+        )
+        .send()
+        .await
+        .unwrap()
+        .await
+        .unwrap()
+        .expect("no receipt found");
+
+    let tx_hash = result.transaction_hash;
+    println!("Transaction hash:\n{:?}", tx_hash);
+    Ok(())
+}
+
+#[allow(clippy::too_many_arguments)]
+async fn prove(
+    rpc: &str,
+    ptau: &str,
+    contract: &str,
+    index: usize,
+    ext_nul: &str,
+    id_nul: &str,
+    id_trap: &str,
+    signal: &str,
+    semacaulk_precompute_endpoint: Option<String>,
+    log_2_capacity: u8,
+) -> Result<(), Error> {
+    let ext_nul = parse_id_nul_or_trap::<Fr>(ext_nul)?;
+    let id_nul = parse_id_nul_or_trap::<Fr>(id_nul)?;
+    let id_trap = parse_id_nul_or_trap::<Fr>(id_trap)?;
+
+    let table_size = 2u64.pow(log_2_capacity as u32) as usize;
+    let (pk, lagrange_comms) = setup(log_2_capacity as usize, ptau);
+
+    let zero = compute_zero_leaf::<Fr>();
+    let mut acc = Accumulator::<Bn254>::new(zero, &lagrange_comms);
+
+    // Use a dummy secret key; we shouldn't be signing any txes anywaya
+    let sk = "0000000000000000000000000000000000000000000000000000000000000001";
+    let client = create_client(rpc, &parse_sk(sk)?).await?;
+    let c = remove_address_prefix(String::from(contract));
+    let address = hex::decode(c).unwrap();
+    let a = ethers::types::H160::from_slice(address.as_slice());
+    let semacaulk_contract = SemacaulkContract::new(a, client);
+    let events = semacaulk_contract
+        .event::<InsertIdentityFilter>()
+        .from_block(0);
+    let num_leaves = semacaulk_contract.get_current_index().call().await.unwrap();
+    let mut stream = events.stream().await.unwrap().take(num_leaves.as_usize());
+
+    let mut identity_commitments: Vec<Fr> = vec![zero; table_size];
+    let mut i = 0;
+    while let Some(Ok(f)) = stream.next().await {
+        let id_comm = u256_to_f(f.identity_commitment);
+        identity_commitments[i] = id_comm;
+        acc.update(i, id_comm);
+        i += 1;
+    }
+
+    let mimc7 = init_mimc7::<Fr>();
+
+    let leaf = mimc7.multi_hash(&[id_nul, id_trap], Fr::zero());
+    assert_eq!(identity_commitments[index], leaf);
+
+    let acc_on_chain = semacaulk_contract.get_accumulator().call().await.unwrap();
+    assert_eq!(u256_to_f::<Fq>(acc_on_chain.x), acc.point.x);
+    assert_eq!(u256_to_f::<Fq>(acc_on_chain.y), acc.point.y);
+
+    let nullifier_hash = mimc7.multi_hash(&[id_nul, ext_nul], Fr::zero());
+
+    let mut rng = test_rng();
+
+    let assignment = Layouter::assign(id_nul, id_trap, ext_nul, &mimc7.cts, &mut rng);
+
+    let domain = GeneralEvaluationDomain::<Fr>::new(table_size).unwrap();
+    let c = DensePolynomial::from_coefficients_slice(&domain.ifft(&identity_commitments));
+
+    let mut precomputed = ProverPrecomputedData::precompute_fixed(&mimc7.cts);
+    precomputed.precompute_w2(&pk, &[index], table_size);
+
+    if semacaulk_precompute_endpoint.is_some() {
+        let mut endpoint = semacaulk_precompute_endpoint.unwrap();
+        while endpoint.ends_with('/') {
+            endpoint.pop();
+        }
+
+        // Fetch precomputed data
+        println!("Fetching precomputed data from the Blyss proxy at {endpoint}...");
+        let url = format!("{endpoint}/{index}");
+        let mut res = reqwest::blocking::get(url).unwrap();
+        let mut body = String::new();
+        res.read_to_string(&mut body).unwrap();
+        let w1 = g2_str_to_g2(&body);
+
+        precomputed.update_w1(index, w1);
+    } else {
+        precomputed.precompute_w1(&pk, &[index], &c, table_size);
+    }
+
+    let witness = WitnessInput {
+        identity_nullifier: id_nul,
+        identity_trapdoor: id_trap,
+        identity_commitment: identity_commitments[index],
+        index,
+    };
+
+    let signal_hash = compute_signal_hash(signal);
+    let signal_hash_f: Fr = u256_to_f(signal_hash);
+
+    let public_input = PublicData::<Bn254> {
+        accumulator: acc.point,
+        external_nullifier: ext_nul,
+        nullifier_hash,
+        signal_hash: signal_hash_f,
+    };
+
+    let proof: SemacaulkProof<Bn254> = Prover::prove(
+        &pk,
+        &witness,
+        &assignment,
+        &public_input,
+        &precomputed,
+        &mut rng,
+        table_size,
+    );
+
+    let is_valid = SemacaulkVerifier::verify(
+        &proof,
+        pk.srs_g1[table_size],
+        pk.srs_g2[1],
+        acc.point,
+        &public_input,
+    );
+
+    assert!(is_valid);
+    // Serialise and print proof
+    let mut serialised_proof = vec![];
+    let _ = proof.serialize(&mut serialised_proof);
+    let proof_hex = hex::encode(serialised_proof.as_slice());
+    println!("Nullifier hash:\n{}", f_to_hex(nullifier_hash));
+    println!("Serialised proof:\n{}", proof_hex);
+    Ok(())
+}
+
+pub fn remove_address_prefix(addr: String) -> String {
+    if addr.starts_with("0x") {
+        return addr.chars().skip(2).collect::<String>();
+    }
+    addr
+}
+
+pub fn str_to_ethers_address(addr: &str) -> ethers::types::H160 {
+    let c = remove_address_prefix(String::from(addr));
+    let address = hex::decode(c).unwrap();
+    let a = ethers::types::H160::from_slice(address.as_slice());
+    a
+}
+
+async fn insert(
+    rpc: &str,
+    sk: &str,
+    ptau: &str,
+    contract: &str,
+    id_nul: &str,
+    id_trap: &str,
+    log_2_capacity: u8,
+) -> Result<(), Error> {
+    let id_nul = parse_id_nul_or_trap::<Fr>(id_nul)?;
+    let id_trap = parse_id_nul_or_trap::<Fr>(id_trap)?;
+
+    let (_pk, lagrange_comms) = setup(log_2_capacity as usize, ptau);
+
+    let client = create_client(rpc, &parse_sk(sk)?).await?;
+
+    let a = str_to_ethers_address(contract);
+    let semacaulk_contract = SemacaulkContract::new(a, client);
+
+    // Get the index to insert to
+    let index: usize = semacaulk_contract
+        .get_current_index()
+        .call()
+        .await
+        .unwrap()
+        .as_u64() as usize;
+
+    let mimc7 = init_mimc7::<Fr>();
+    let new_leaf = mimc7.multi_hash(&[id_nul, id_trap], Fr::zero());
+
+    // Construct the tree of commitments to the Lagrange bases
+    let tree = compute_lagrange_tree::<Bn254>(&lagrange_comms);
+
+    let proof = tree.proof(index).unwrap();
+    let flattened_proof = flatten_proof(&proof);
+    let l_i = lagrange_comms[index];
+    let l_i_x = f_to_u256(l_i.x);
+    let l_i_y = f_to_u256(l_i.y);
+
+    // Insert the leaf on chain
+    let result = semacaulk_contract
+        .insert_identity(f_to_u256(new_leaf), l_i_x, l_i_y, flattened_proof)
+        .send()
+        .await
+        .unwrap()
+        .await
+        .unwrap()
+        .expect("no receipt found");
+
+    let tx_hash = result.transaction_hash;
+    let event_index = result.logs[0].topics[1];
+    println!("Transaction hash:\n{:?}", tx_hash);
+    println!("Identity index:\n{:?}", event_index);
+
+    Ok(())
+}
+
+async fn deploy(rpc: &str, sk: &str, ptau: &str, log_2_capacity: u8) -> Result<(), Error> {
+    if !(10..=28).contains(&log_2_capacity) {
+        return Err(Error::InvalidLog2Capacity);
+    }
+    let client = create_client(rpc, &parse_sk(sk)?).await?;
+
+    let (_pk, lagrange_comms) = setup(log_2_capacity as usize, ptau);
+
+    let zero = compute_zero_leaf::<Fr>();
+    let acc = Accumulator::<Bn254>::new(zero, &lagrange_comms);
+    let empty_accumulator_x = f_to_u256::<Fq>(acc.point.x);
+    let empty_accumulator_y = f_to_u256::<Fq>(acc.point.y);
+    let tree = compute_lagrange_tree::<Bn254>(&lagrange_comms);
+    let root = tree.root();
+
+    // Deploy contract
+    let semacaulk_contract =
+        SemacaulkContract::deploy(client, (root, empty_accumulator_x, empty_accumulator_y))
+            .unwrap()
+            .send()
+            .await
+            .unwrap();
+    println!("{:?}", semacaulk_contract.address());
+
+    Ok(())
+}
+
+fn p_to_p(p: &ProofForSemacaulk) -> Proof {
+    let m = MultiopenProof {
+        q_1_opening: p.multiopen_proof.q_1_opening,
+        q_2_opening: p.multiopen_proof.q_2_opening,
+        q_3_opening: p.multiopen_proof.q_3_opening,
+        q_4_opening: p.multiopen_proof.q_4_opening,
+        f_cm: G1Point {
+            x: p.multiopen_proof.f_cm.x,
+            y: p.multiopen_proof.f_cm.y,
+        },
+        final_poly_proof: G1Point {
+            x: p.multiopen_proof.final_poly_proof.x,
+            y: p.multiopen_proof.final_poly_proof.y,
+        },
+    };
+
+    let o = Openings {
+        q_mimc: p.openings.q_mimc,
+        mimc_cts: p.openings.mimc_cts,
+        quotient: p.openings.quotient,
+        u_prime: p.openings.u_prime,
+        p_1: p.openings.p_1,
+        p_2: p.openings.p_2,
+        w_0_0: p.openings.w_0_0,
+        w_0_1: p.openings.w_0_1,
+        w_0_2: p.openings.w_0_2,
+        w_1_0: p.openings.w_1_0,
+        w_1_1: p.openings.w_1_1,
+        w_1_2: p.openings.w_1_2,
+        w_2_0: p.openings.w_2_0,
+        w_2_1: p.openings.w_2_1,
+        w_2_2: p.openings.w_2_2,
+        key_0: p.openings.key_0,
+        key_1: p.openings.key_1,
+    };
+
+    let c = Commitments {
+        w_0: G1Point {
+            x: p.commitments.w_0.x,
+            y: p.commitments.w_0.y,
+        },
+        w_1: G1Point {
+            x: p.commitments.w_1.x,
+            y: p.commitments.w_1.y,
+        },
+        w_2: G1Point {
+            x: p.commitments.w_2.x,
+            y: p.commitments.w_2.y,
+        },
+        key: G1Point {
+            x: p.commitments.key.x,
+            y: p.commitments.key.y,
+        },
+        mimc_cts: G1Point {
+            x: p.commitments.mimc_cts.x,
+            y: p.commitments.mimc_cts.y,
+        },
+        quotient: G1Point {
+            x: p.commitments.quotient.x,
+            y: p.commitments.quotient.y,
+        },
+        u_prime: G1Point {
+            x: p.commitments.u_prime.x,
+            y: p.commitments.u_prime.y,
+        },
+        zi: G1Point {
+            x: p.commitments.zi.x,
+            y: p.commitments.zi.y,
+        },
+        ci: G1Point {
+            x: p.commitments.ci.x,
+            y: p.commitments.ci.y,
+        },
+        p_1: G1Point {
+            x: p.commitments.p_1.x,
+            y: p.commitments.p_1.y,
+        },
+        p_2: G1Point {
+            x: p.commitments.p_2.x,
+            y: p.commitments.p_2.y,
+        },
+        q_mimc: G1Point {
+            x: p.commitments.q_mimc.x,
+            y: p.commitments.q_mimc.y,
+        },
+        h: G1Point {
+            x: p.commitments.h.x,
+            y: p.commitments.h.y,
+        },
+        w: G2Point {
+            x_0: p.commitments.w.x_0,
+            x_1: p.commitments.w.x_1,
+            y_0: p.commitments.w.y_0,
+            y_1: p.commitments.w.y_1,
+        },
+    };
+
+    Proof {
+        multiopen_proof: m,
+        commitments: c,
+        openings: o,
+    }
+}
+
+#[test]
+pub fn test_parse_id_nul_or_trap() {
+    let s = String::from("0x1");
+    assert_eq!(parse_id_nul_or_trap::<Fr>(&s).unwrap(), Fr::from(1));
+
+    let s = String::from("0x01");
+    assert_eq!(parse_id_nul_or_trap::<Fr>(&s).unwrap(), Fr::from(1));
+
+    let s = String::from("0x0000000000000000000000000000000000000000000000000000000000000001");
+    assert_eq!(parse_id_nul_or_trap::<Fr>(&s).unwrap(), Fr::from(1));
+
+    let s = String::from("0x0101");
+    assert_eq!(parse_id_nul_or_trap::<Fr>(&s).unwrap(), Fr::from(257));
+
+    let s = String::from("0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa");
+    assert_eq!(
+        parse_id_nul_or_trap::<Fr>(&s).unwrap_err(),
+        Error::InvalidIdNulOrTrap
+    );
+}
diff --git a/src/contracts/Semacaulk.json b/src/contracts/Semacaulk.json
new file mode 100644
index 0000000..d97d442
--- /dev/null
+++ b/src/contracts/Semacaulk.json
@@ -0,0 +1,6621 @@
+{
+  "abi": [
+    {
+      "inputs": [
+        {
+          "internalType": "bytes32",
+          "name": "_lagrangeTreeRoot",
+          "type": "bytes32"
+        },
+        {
+          "internalType": "uint256",
+          "name": "_accumulatorX",
+          "type": "uint256"
+        },
+        {
+          "internalType": "uint256",
+          "name": "_accumulatorY",
+          "type": "uint256"
+        }
+      ],
+      "stateMutability": "nonpayable",
+      "type": "constructor"
+    },
+    {
+      "inputs": [
+        {
+          "internalType": "uint256",
+          "name": "_identityCommitment",
+          "type": "uint256"
+        }
+      ],
+      "name": "InvalidIdentityCommitment",
+      "type": "error"
+    },
+    {
+      "inputs": [],
+      "name": "InvalidProof",
+      "type": "error"
+    },
+    {
+      "inputs": [
+        {
+          "internalType": "uint256",
+          "name": "_nullifierHash",
+          "type": "uint256"
+        }
+      ],
+      "name": "NullifierHashAlreadySeen",
+      "type": "error"
+    },
+    {
+      "inputs": [
+        {
+          "internalType": "bytes32",
+          "name": "_generatedRoot",
+          "type": "bytes32"
+        }
+      ],
+      "name": "RootMismatch",
+      "type": "error"
+    },
+    {
+      "anonymous": false,
+      "inputs": [
+        {
+          "indexed": true,
+          "internalType": "uint256",
+          "name": "_signalHash",
+          "type": "uint256"
+        },
+        {
+          "indexed": true,
+          "internalType": "uint256",
+          "name": "_externalNullifier",
+          "type": "uint256"
+        }
+      ],
+      "name": "BroadcastSignal",
+      "type": "event"
+    },
+    {
+      "anonymous": false,
+      "inputs": [
+        {
+          "indexed": true,
+          "internalType": "uint256",
+          "name": "_index",
+          "type": "uint256"
+        },
+        {
+          "indexed": true,
+          "internalType": "uint256",
+          "name": "_identityCommitment",
+          "type": "uint256"
+        }
+      ],
+      "name": "InsertIdentity",
+      "type": "event"
+    },
+    {
+      "inputs": [
+        {
+          "internalType": "bytes",
+          "name": "_signal",
+          "type": "bytes"
+        },
+        {
+          "components": [
+            {
+              "components": [
+                {
+                  "internalType": "uint256",
+                  "name": "q1_opening",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "q2_opening",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "q3_opening",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "q4_opening",
+                  "type": "uint256"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "f_cm",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "final_poly_proof",
+                  "type": "tuple"
+                }
+              ],
+              "internalType": "struct Types.MultiopenProof",
+              "name": "multiopenProof",
+              "type": "tuple"
+            },
+            {
+              "components": [
+                {
+                  "internalType": "uint256",
+                  "name": "q_mimc",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "mimc_cts",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "quotient",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "u_prime",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "p1",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "p2",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w0_0",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w0_1",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w0_2",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w1_0",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w1_1",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w1_2",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w2_0",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w2_1",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w2_2",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "key_0",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "key_1",
+                  "type": "uint256"
+                }
+              ],
+              "internalType": "struct Types.Openings",
+              "name": "openings",
+              "type": "tuple"
+            },
+            {
+              "components": [
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "w0",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "w1",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "w2",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "key",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "mimc_cts",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "quotient",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "u_prime",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "zi",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "ci",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "p1",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "p2",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "q_mimc",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "h",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "x1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y1",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G2Point",
+                  "name": "w",
+                  "type": "tuple"
+                }
+              ],
+              "internalType": "struct Types.Commitments",
+              "name": "commitments",
+              "type": "tuple"
+            }
+          ],
+          "internalType": "struct Types.Proof",
+          "name": "_proof",
+          "type": "tuple"
+        },
+        {
+          "internalType": "uint256",
+          "name": "_nullifierHash",
+          "type": "uint256"
+        },
+        {
+          "internalType": "uint256",
+          "name": "_externalNullifier",
+          "type": "uint256"
+        }
+      ],
+      "name": "broadcastSignal",
+      "outputs": [],
+      "stateMutability": "nonpayable",
+      "type": "function"
+    },
+    {
+      "inputs": [
+        {
+          "internalType": "uint256",
+          "name": "_index",
+          "type": "uint256"
+        },
+        {
+          "internalType": "bytes32",
+          "name": "_leaf",
+          "type": "bytes32"
+        },
+        {
+          "internalType": "bytes32[]",
+          "name": "_proof",
+          "type": "bytes32[]"
+        }
+      ],
+      "name": "genRootFromPath",
+      "outputs": [
+        {
+          "internalType": "bytes32",
+          "name": "",
+          "type": "bytes32"
+        }
+      ],
+      "stateMutability": "pure",
+      "type": "function"
+    },
+    {
+      "inputs": [],
+      "name": "getAccumulator",
+      "outputs": [
+        {
+          "components": [
+            {
+              "internalType": "uint256",
+              "name": "x",
+              "type": "uint256"
+            },
+            {
+              "internalType": "uint256",
+              "name": "y",
+              "type": "uint256"
+            }
+          ],
+          "internalType": "struct Types.G1Point",
+          "name": "",
+          "type": "tuple"
+        }
+      ],
+      "stateMutability": "view",
+      "type": "function"
+    },
+    {
+      "inputs": [],
+      "name": "getCurrentIndex",
+      "outputs": [
+        {
+          "internalType": "uint256",
+          "name": "",
+          "type": "uint256"
+        }
+      ],
+      "stateMutability": "view",
+      "type": "function"
+    },
+    {
+      "inputs": [
+        {
+          "internalType": "uint256",
+          "name": "",
+          "type": "uint256"
+        }
+      ],
+      "name": "identityCommitmentHistory",
+      "outputs": [
+        {
+          "internalType": "bool",
+          "name": "",
+          "type": "bool"
+        }
+      ],
+      "stateMutability": "view",
+      "type": "function"
+    },
+    {
+      "inputs": [
+        {
+          "internalType": "uint256",
+          "name": "_identityCommitment",
+          "type": "uint256"
+        },
+        {
+          "internalType": "uint256",
+          "name": "_lagrangeLeafX",
+          "type": "uint256"
+        },
+        {
+          "internalType": "uint256",
+          "name": "_lagrangeLeafY",
+          "type": "uint256"
+        },
+        {
+          "internalType": "bytes32[]",
+          "name": "_lagrangeMerkleProof",
+          "type": "bytes32[]"
+        }
+      ],
+      "name": "insertIdentity",
+      "outputs": [],
+      "stateMutability": "nonpayable",
+      "type": "function"
+    },
+    {
+      "inputs": [],
+      "name": "lagrangeTreeRoot",
+      "outputs": [
+        {
+          "internalType": "bytes32",
+          "name": "",
+          "type": "bytes32"
+        }
+      ],
+      "stateMutability": "view",
+      "type": "function"
+    },
+    {
+      "inputs": [
+        {
+          "internalType": "uint256",
+          "name": "",
+          "type": "uint256"
+        }
+      ],
+      "name": "nullifierHashHistory",
+      "outputs": [
+        {
+          "internalType": "bool",
+          "name": "",
+          "type": "bool"
+        }
+      ],
+      "stateMutability": "view",
+      "type": "function"
+    },
+    {
+      "inputs": [
+        {
+          "components": [
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+              "components": [
+                {
+                  "internalType": "uint256",
+                  "name": "q1_opening",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "q2_opening",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "q3_opening",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "q4_opening",
+                  "type": "uint256"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "f_cm",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "final_poly_proof",
+                  "type": "tuple"
+                }
+              ],
+              "internalType": "struct Types.MultiopenProof",
+              "name": "multiopenProof",
+              "type": "tuple"
+            },
+            {
+              "components": [
+                {
+                  "internalType": "uint256",
+                  "name": "q_mimc",
+                  "type": "uint256"
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+                {
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+                  "name": "mimc_cts",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "quotient",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "u_prime",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "p1",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "p2",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w0_0",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w0_1",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w0_2",
+                  "type": "uint256"
+                },
+                {
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+                  "name": "w1_0",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w1_1",
+                  "type": "uint256"
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+                {
+                  "internalType": "uint256",
+                  "name": "w1_2",
+                  "type": "uint256"
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+                {
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+                  "name": "w2_0",
+                  "type": "uint256"
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+                {
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+                  "name": "w2_1",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w2_2",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "key_0",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "key_1",
+                  "type": "uint256"
+                }
+              ],
+              "internalType": "struct Types.Openings",
+              "name": "openings",
+              "type": "tuple"
+            },
+            {
+              "components": [
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "w0",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
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+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
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+                  "internalType": "struct Types.G1Point",
+                  "name": "w1",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
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+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
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+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
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+                  "internalType": "struct Types.G1Point",
+                  "name": "w2",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
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+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
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+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
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+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "key",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
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+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
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+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "mimc_cts",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
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+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "quotient",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "u_prime",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
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+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "zi",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
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+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "ci",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
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+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
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+                  "name": "p1",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
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+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
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+                  ],
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+                  "name": "p2",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
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+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "q_mimc",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
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+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "h",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
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+                      "internalType": "uint256",
+                      "name": "x0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "x1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y1",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G2Point",
+                  "name": "w",
+                  "type": "tuple"
+                }
+              ],
+              "internalType": "struct Types.Commitments",
+              "name": "commitments",
+              "type": "tuple"
+            }
+          ],
+          "internalType": "struct Types.Proof",
+          "name": "proof",
+          "type": "tuple"
+        },
+        {
+          "components": [
+            {
+              "internalType": "uint256",
+              "name": "x",
+              "type": "uint256"
+            },
+            {
+              "internalType": "uint256",
+              "name": "y",
+              "type": "uint256"
+            }
+          ],
+          "internalType": "struct Types.G1Point",
+          "name": "accumulator",
+          "type": "tuple"
+        },
+        {
+          "internalType": "uint256[3]",
+          "name": "publicInputs",
+          "type": "uint256[3]"
+        }
+      ],
+      "name": "verify",
+      "outputs": [
+        {
+          "internalType": "bool",
+          "name": "",
+          "type": "bool"
+        }
+      ],
+      "stateMutability": "view",
+      "type": "function"
+    }
+  ],
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+    "linkReferences": {}
+  },
+  "methodIdentifiers": {
+    "broadcastSignal(bytes,((uint256,uint256,uint256,uint256,(uint256,uint256),(uint256,uint256)),(uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256),((uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256,uint256,uint256))),uint256,uint256)": "26e738a2",
+    "genRootFromPath(uint256,bytes32,bytes32[])": "cec677b8",
+    "getAccumulator()": "ff40807b",
+    "getCurrentIndex()": "0d9005ae",
+    "identityCommitmentHistory(uint256)": "7a6a061d",
+    "insertIdentity(uint256,uint256,uint256,bytes32[])": "98ac1f81",
+    "lagrangeTreeRoot()": "f2524d96",
+    "nullifierHashHistory(uint256)": "c4cd5596",
+    "verify(((uint256,uint256,uint256,uint256,(uint256,uint256),(uint256,uint256)),(uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256),((uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256,uint256,uint256))),(uint256,uint256),uint256[3])": "b3da592b"
+  },
+  "rawMetadata": 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+  "metadata": {
+    "compiler": {
+      "version": "0.8.17+commit.8df45f5f"
+    },
+    "language": "Solidity",
+    "output": {
+      "abi": [
+        {
+          "inputs": [
+            {
+              "internalType": "bytes32",
+              "name": "_lagrangeTreeRoot",
+              "type": "bytes32"
+            },
+            {
+              "internalType": "uint256",
+              "name": "_accumulatorX",
+              "type": "uint256"
+            },
+            {
+              "internalType": "uint256",
+              "name": "_accumulatorY",
+              "type": "uint256"
+            }
+          ],
+          "stateMutability": "nonpayable",
+          "type": "constructor"
+        },
+        {
+          "inputs": [
+            {
+              "internalType": "uint256",
+              "name": "_identityCommitment",
+              "type": "uint256"
+            }
+          ],
+          "type": "error",
+          "name": "InvalidIdentityCommitment"
+        },
+        {
+          "inputs": [],
+          "type": "error",
+          "name": "InvalidProof"
+        },
+        {
+          "inputs": [
+            {
+              "internalType": "uint256",
+              "name": "_nullifierHash",
+              "type": "uint256"
+            }
+          ],
+          "type": "error",
+          "name": "NullifierHashAlreadySeen"
+        },
+        {
+          "inputs": [
+            {
+              "internalType": "bytes32",
+              "name": "_generatedRoot",
+              "type": "bytes32"
+            }
+          ],
+          "type": "error",
+          "name": "RootMismatch"
+        },
+        {
+          "inputs": [
+            {
+              "internalType": "uint256",
+              "name": "_signalHash",
+              "type": "uint256",
+              "indexed": true
+            },
+            {
+              "internalType": "uint256",
+              "name": "_externalNullifier",
+              "type": "uint256",
+              "indexed": true
+            }
+          ],
+          "type": "event",
+          "name": "BroadcastSignal",
+          "anonymous": false
+        },
+        {
+          "inputs": [
+            {
+              "internalType": "uint256",
+              "name": "_index",
+              "type": "uint256",
+              "indexed": true
+            },
+            {
+              "internalType": "uint256",
+              "name": "_identityCommitment",
+              "type": "uint256",
+              "indexed": true
+            }
+          ],
+          "type": "event",
+          "name": "InsertIdentity",
+          "anonymous": false
+        },
+        {
+          "inputs": [
+            {
+              "internalType": "bytes",
+              "name": "_signal",
+              "type": "bytes"
+            },
+            {
+              "internalType": "struct Types.Proof",
+              "name": "_proof",
+              "type": "tuple",
+              "components": [
+                {
+                  "internalType": "struct Types.MultiopenProof",
+                  "name": "multiopenProof",
+                  "type": "tuple",
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "q1_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "q2_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "q3_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "q4_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "f_cm",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "final_poly_proof",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    }
+                  ]
+                },
+                {
+                  "internalType": "struct Types.Openings",
+                  "name": "openings",
+                  "type": "tuple",
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "q_mimc",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "mimc_cts",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "quotient",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "u_prime",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "p1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "p2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w0_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w0_1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w0_2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w1_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w1_1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w1_2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w2_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w2_1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w2_2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "key_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "key_1",
+                      "type": "uint256"
+                    }
+                  ]
+                },
+                {
+                  "internalType": "struct Types.Commitments",
+                  "name": "commitments",
+                  "type": "tuple",
+                  "components": [
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "w0",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "w1",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "w2",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "key",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "mimc_cts",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "quotient",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "u_prime",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "zi",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "ci",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "p1",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "p2",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "q_mimc",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "h",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G2Point",
+                      "name": "w",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x0",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "x1",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y0",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y1",
+                          "type": "uint256"
+                        }
+                      ]
+                    }
+                  ]
+                }
+              ]
+            },
+            {
+              "internalType": "uint256",
+              "name": "_nullifierHash",
+              "type": "uint256"
+            },
+            {
+              "internalType": "uint256",
+              "name": "_externalNullifier",
+              "type": "uint256"
+            }
+          ],
+          "stateMutability": "nonpayable",
+          "type": "function",
+          "name": "broadcastSignal"
+        },
+        {
+          "inputs": [
+            {
+              "internalType": "uint256",
+              "name": "_index",
+              "type": "uint256"
+            },
+            {
+              "internalType": "bytes32",
+              "name": "_leaf",
+              "type": "bytes32"
+            },
+            {
+              "internalType": "bytes32[]",
+              "name": "_proof",
+              "type": "bytes32[]"
+            }
+          ],
+          "stateMutability": "pure",
+          "type": "function",
+          "name": "genRootFromPath",
+          "outputs": [
+            {
+              "internalType": "bytes32",
+              "name": "",
+              "type": "bytes32"
+            }
+          ]
+        },
+        {
+          "inputs": [],
+          "stateMutability": "view",
+          "type": "function",
+          "name": "getAccumulator",
+          "outputs": [
+            {
+              "internalType": "struct Types.G1Point",
+              "name": "",
+              "type": "tuple",
+              "components": [
+                {
+                  "internalType": "uint256",
+                  "name": "x",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "y",
+                  "type": "uint256"
+                }
+              ]
+            }
+          ]
+        },
+        {
+          "inputs": [],
+          "stateMutability": "view",
+          "type": "function",
+          "name": "getCurrentIndex",
+          "outputs": [
+            {
+              "internalType": "uint256",
+              "name": "",
+              "type": "uint256"
+            }
+          ]
+        },
+        {
+          "inputs": [
+            {
+              "internalType": "uint256",
+              "name": "",
+              "type": "uint256"
+            }
+          ],
+          "stateMutability": "view",
+          "type": "function",
+          "name": "identityCommitmentHistory",
+          "outputs": [
+            {
+              "internalType": "bool",
+              "name": "",
+              "type": "bool"
+            }
+          ]
+        },
+        {
+          "inputs": [
+            {
+              "internalType": "uint256",
+              "name": "_identityCommitment",
+              "type": "uint256"
+            },
+            {
+              "internalType": "uint256",
+              "name": "_lagrangeLeafX",
+              "type": "uint256"
+            },
+            {
+              "internalType": "uint256",
+              "name": "_lagrangeLeafY",
+              "type": "uint256"
+            },
+            {
+              "internalType": "bytes32[]",
+              "name": "_lagrangeMerkleProof",
+              "type": "bytes32[]"
+            }
+          ],
+          "stateMutability": "nonpayable",
+          "type": "function",
+          "name": "insertIdentity"
+        },
+        {
+          "inputs": [],
+          "stateMutability": "view",
+          "type": "function",
+          "name": "lagrangeTreeRoot",
+          "outputs": [
+            {
+              "internalType": "bytes32",
+              "name": "",
+              "type": "bytes32"
+            }
+          ]
+        },
+        {
+          "inputs": [
+            {
+              "internalType": "uint256",
+              "name": "",
+              "type": "uint256"
+            }
+          ],
+          "stateMutability": "view",
+          "type": "function",
+          "name": "nullifierHashHistory",
+          "outputs": [
+            {
+              "internalType": "bool",
+              "name": "",
+              "type": "bool"
+            }
+          ]
+        },
+        {
+          "inputs": [
+            {
+              "internalType": "struct Types.Proof",
+              "name": "proof",
+              "type": "tuple",
+              "components": [
+                {
+                  "internalType": "struct Types.MultiopenProof",
+                  "name": "multiopenProof",
+                  "type": "tuple",
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "q1_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "q2_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "q3_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "q4_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "f_cm",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "final_poly_proof",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    }
+                  ]
+                },
+                {
+                  "internalType": "struct Types.Openings",
+                  "name": "openings",
+                  "type": "tuple",
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "q_mimc",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "mimc_cts",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "quotient",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "u_prime",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "p1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "p2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w0_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w0_1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w0_2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w1_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w1_1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w1_2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w2_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w2_1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w2_2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "key_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "key_1",
+                      "type": "uint256"
+                    }
+                  ]
+                },
+                {
+                  "internalType": "struct Types.Commitments",
+                  "name": "commitments",
+                  "type": "tuple",
+                  "components": [
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "w0",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "w1",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "w2",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "key",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "mimc_cts",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "quotient",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "u_prime",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "zi",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "ci",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "p1",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "p2",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "q_mimc",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "h",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G2Point",
+                      "name": "w",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
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+                        "typeString": "function (uint256,uint256)"
+                      }
+                    },
+                    "id": 25432,
+                    "isConstant": false,
+                    "isLValue": false,
+                    "isPure": false,
+                    "kind": "functionCall",
+                    "lValueRequested": false,
+                    "nameLocations": [],
+                    "names": [],
+                    "nodeType": "FunctionCall",
+                    "src": "4487:47:20",
+                    "tryCall": false,
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_tuple$__$",
+                      "typeString": "tuple()"
+                    }
+                  },
+                  "id": 25433,
+                  "nodeType": "EmitStatement",
+                  "src": "4482:52:20"
+                }
+              ]
+            },
+            "functionSelector": "26e738a2",
+            "implemented": true,
+            "kind": "function",
+            "modifiers": [],
+            "name": "broadcastSignal",
+            "nameLocation": "3574:15:20",
+            "parameters": {
+              "id": 25365,
+              "nodeType": "ParameterList",
+              "parameters": [
+                {
+                  "constant": false,
+                  "id": 25357,
+                  "mutability": "mutable",
+                  "name": "_signal",
+                  "nameLocation": "3612:7:20",
+                  "nodeType": "VariableDeclaration",
+                  "scope": 25435,
+                  "src": "3599:20:20",
+                  "stateVariable": false,
+                  "storageLocation": "memory",
+                  "typeDescriptions": {
+                    "typeIdentifier": "t_bytes_memory_ptr",
+                    "typeString": "bytes"
+                  },
+                  "typeName": {
+                    "id": 25356,
+                    "name": "bytes",
+                    "nodeType": "ElementaryTypeName",
+                    "src": "3599:5:20",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_bytes_storage_ptr",
+                      "typeString": "bytes"
+                    }
+                  },
+                  "visibility": "internal"
+                },
+                {
+                  "constant": false,
+                  "id": 25360,
+                  "mutability": "mutable",
+                  "name": "_proof",
+                  "nameLocation": "3648:6:20",
+                  "nodeType": "VariableDeclaration",
+                  "scope": 25435,
+                  "src": "3629:25:20",
+                  "stateVariable": false,
+                  "storageLocation": "memory",
+                  "typeDescriptions": {
+                    "typeIdentifier": "t_struct$_Proof_$26182_memory_ptr",
+                    "typeString": "struct Types.Proof"
+                  },
+                  "typeName": {
+                    "id": 25359,
+                    "nodeType": "UserDefinedTypeName",
+                    "pathNode": {
+                      "id": 25358,
+                      "name": "Types.Proof",
+                      "nameLocations": [
+                        "3629:5:20",
+                        "3635:5:20"
+                      ],
+                      "nodeType": "IdentifierPath",
+                      "referencedDeclaration": 26182,
+                      "src": "3629:11:20"
+                    },
+                    "referencedDeclaration": 26182,
+                    "src": "3629:11:20",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_struct$_Proof_$26182_storage_ptr",
+                      "typeString": "struct Types.Proof"
+                    }
+                  },
+                  "visibility": "internal"
+                },
+                {
+                  "constant": false,
+                  "id": 25362,
+                  "mutability": "mutable",
+                  "name": "_nullifierHash",
+                  "nameLocation": "3672:14:20",
+                  "nodeType": "VariableDeclaration",
+                  "scope": 25435,
+                  "src": "3664:22:20",
+                  "stateVariable": false,
+                  "storageLocation": "default",
+                  "typeDescriptions": {
+                    "typeIdentifier": "t_uint256",
+                    "typeString": "uint256"
+                  },
+                  "typeName": {
+                    "id": 25361,
+                    "name": "uint256",
+                    "nodeType": "ElementaryTypeName",
+                    "src": "3664:7:20",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_uint256",
+                      "typeString": "uint256"
+                    }
+                  },
+                  "visibility": "internal"
+                },
+                {
+                  "constant": false,
+                  "id": 25364,
+                  "mutability": "mutable",
+                  "name": "_externalNullifier",
+                  "nameLocation": "3704:18:20",
+                  "nodeType": "VariableDeclaration",
+                  "scope": 25435,
+                  "src": "3696:26:20",
+                  "stateVariable": false,
+                  "storageLocation": "default",
+                  "typeDescriptions": {
+                    "typeIdentifier": "t_uint256",
+                    "typeString": "uint256"
+                  },
+                  "typeName": {
+                    "id": 25363,
+                    "name": "uint256",
+                    "nodeType": "ElementaryTypeName",
+                    "src": "3696:7:20",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_uint256",
+                      "typeString": "uint256"
+                    }
+                  },
+                  "visibility": "internal"
+                }
+              ],
+              "src": "3589:139:20"
+            },
+            "returnParameters": {
+              "id": 25366,
+              "nodeType": "ParameterList",
+              "parameters": [],
+              "src": "3736:0:20"
+            },
+            "scope": 25470,
+            "stateMutability": "nonpayable",
+            "virtual": false,
+            "visibility": "public"
+          },
+          {
+            "id": 25452,
+            "nodeType": "FunctionDefinition",
+            "src": "4730:130:20",
+            "nodes": [],
+            "body": {
+              "id": 25451,
+              "nodeType": "Block",
+              "src": "4804:56:20",
+              "nodes": [],
+              "statements": [
+                {
+                  "expression": {
+                    "commonType": {
+                      "typeIdentifier": "t_uint256",
+                      "typeString": "uint256"
+                    },
+                    "id": 25449,
+                    "isConstant": false,
+                    "isLValue": false,
+                    "isPure": false,
+                    "lValueRequested": false,
+                    "leftExpression": {
+                      "arguments": [
+                        {
+                          "arguments": [
+                            {
+                              "id": 25445,
+                              "name": "_signal",
+                              "nodeType": "Identifier",
+                              "overloadedDeclarations": [],
+                              "referencedDeclaration": 25437,
+                              "src": "4839:7:20",
+                              "typeDescriptions": {
+                                "typeIdentifier": "t_bytes_memory_ptr",
+                                "typeString": "bytes memory"
+                              }
+                            }
+                          ],
+                          "expression": {
+                            "argumentTypes": [
+                              {
+                                "typeIdentifier": "t_bytes_memory_ptr",
+                                "typeString": "bytes memory"
+                              }
+                            ],
+                            "id": 25444,
+                            "name": "keccak256",
+                            "nodeType": "Identifier",
+                            "overloadedDeclarations": [],
+                            "referencedDeclaration": -8,
+                            "src": "4829:9:20",
+                            "typeDescriptions": {
+                              "typeIdentifier": "t_function_keccak256_pure$_t_bytes_memory_ptr_$returns$_t_bytes32_$",
+                              "typeString": "function (bytes memory) pure returns (bytes32)"
+                            }
+                          },
+                          "id": 25446,
+                          "isConstant": false,
+                          "isLValue": false,
+                          "isPure": false,
+                          "kind": "functionCall",
+                          "lValueRequested": false,
+                          "nameLocations": [],
+                          "names": [],
+                          "nodeType": "FunctionCall",
+                          "src": "4829:18:20",
+                          "tryCall": false,
+                          "typeDescriptions": {
+                            "typeIdentifier": "t_bytes32",
+                            "typeString": "bytes32"
+                          }
+                        }
+                      ],
+                      "expression": {
+                        "argumentTypes": [
+                          {
+                            "typeIdentifier": "t_bytes32",
+                            "typeString": "bytes32"
+                          }
+                        ],
+                        "id": 25443,
+                        "isConstant": false,
+                        "isLValue": false,
+                        "isPure": true,
+                        "lValueRequested": false,
+                        "nodeType": "ElementaryTypeNameExpression",
+                        "src": "4821:7:20",
+                        "typeDescriptions": {
+                          "typeIdentifier": "t_type$_t_uint256_$",
+                          "typeString": "type(uint256)"
+                        },
+                        "typeName": {
+                          "id": 25442,
+                          "name": "uint256",
+                          "nodeType": "ElementaryTypeName",
+                          "src": "4821:7:20",
+                          "typeDescriptions": {}
+                        }
+                      },
+                      "id": 25447,
+                      "isConstant": false,
+                      "isLValue": false,
+                      "isPure": false,
+                      "kind": "typeConversion",
+                      "lValueRequested": false,
+                      "nameLocations": [],
+                      "names": [],
+                      "nodeType": "FunctionCall",
+                      "src": "4821:27:20",
+                      "tryCall": false,
+                      "typeDescriptions": {
+                        "typeIdentifier": "t_uint256",
+                        "typeString": "uint256"
+                      }
+                    },
+                    "nodeType": "BinaryOperation",
+                    "operator": ">>",
+                    "rightExpression": {
+                      "hexValue": "38",
+                      "id": 25448,
+                      "isConstant": false,
+                      "isLValue": false,
+                      "isPure": true,
+                      "kind": "number",
+                      "lValueRequested": false,
+                      "nodeType": "Literal",
+                      "src": "4852:1:20",
+                      "typeDescriptions": {
+                        "typeIdentifier": "t_rational_8_by_1",
+                        "typeString": "int_const 8"
+                      },
+                      "value": "8"
+                    },
+                    "src": "4821:32:20",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_uint256",
+                      "typeString": "uint256"
+                    }
+                  },
+                  "functionReturnParameters": 25441,
+                  "id": 25450,
+                  "nodeType": "Return",
+                  "src": "4814:39:20"
+                }
+              ]
+            },
+            "implemented": true,
+            "kind": "function",
+            "modifiers": [],
+            "name": "hashSignal",
+            "nameLocation": "4739:10:20",
+            "parameters": {
+              "id": 25438,
+              "nodeType": "ParameterList",
+              "parameters": [
+                {
+                  "constant": false,
+                  "id": 25437,
+                  "mutability": "mutable",
+                  "name": "_signal",
+                  "nameLocation": "4763:7:20",
+                  "nodeType": "VariableDeclaration",
+                  "scope": 25452,
+                  "src": "4750:20:20",
+                  "stateVariable": false,
+                  "storageLocation": "memory",
+                  "typeDescriptions": {
+                    "typeIdentifier": "t_bytes_memory_ptr",
+                    "typeString": "bytes"
+                  },
+                  "typeName": {
+                    "id": 25436,
+                    "name": "bytes",
+                    "nodeType": "ElementaryTypeName",
+                    "src": "4750:5:20",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_bytes_storage_ptr",
+                      "typeString": "bytes"
+                    }
+                  },
+                  "visibility": "internal"
+                }
+              ],
+              "src": "4749:22:20"
+            },
+            "returnParameters": {
+              "id": 25441,
+              "nodeType": "ParameterList",
+              "parameters": [
+                {
+                  "constant": false,
+                  "id": 25440,
+                  "mutability": "mutable",
+                  "name": "",
+                  "nameLocation": "-1:-1:-1",
+                  "nodeType": "VariableDeclaration",
+                  "scope": 25452,
+                  "src": "4795:7:20",
+                  "stateVariable": false,
+                  "storageLocation": "default",
+                  "typeDescriptions": {
+                    "typeIdentifier": "t_uint256",
+                    "typeString": "uint256"
+                  },
+                  "typeName": {
+                    "id": 25439,
+                    "name": "uint256",
+                    "nodeType": "ElementaryTypeName",
+                    "src": "4795:7:20",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_uint256",
+                      "typeString": "uint256"
+                    }
+                  },
+                  "visibility": "internal"
+                }
+              ],
+              "src": "4794:9:20"
+            },
+            "scope": 25470,
+            "stateMutability": "pure",
+            "virtual": false,
+            "visibility": "internal"
+          },
+          {
+            "id": 25460,
+            "nodeType": "FunctionDefinition",
+            "src": "4866:93:20",
+            "nodes": [],
+            "body": {
+              "id": 25459,
+              "nodeType": "Block",
+              "src": "4923:36:20",
+              "nodes": [],
+              "statements": [
+                {
+                  "expression": {
+                    "id": 25457,
+                    "name": "currentIndex",
+                    "nodeType": "Identifier",
+                    "overloadedDeclarations": [],
+                    "referencedDeclaration": 25162,
+                    "src": "4940:12:20",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_uint256",
+                      "typeString": "uint256"
+                    }
+                  },
+                  "functionReturnParameters": 25456,
+                  "id": 25458,
+                  "nodeType": "Return",
+                  "src": "4933:19:20"
+                }
+              ]
+            },
+            "functionSelector": "0d9005ae",
+            "implemented": true,
+            "kind": "function",
+            "modifiers": [],
+            "name": "getCurrentIndex",
+            "nameLocation": "4875:15:20",
+            "parameters": {
+              "id": 25453,
+              "nodeType": "ParameterList",
+              "parameters": [],
+              "src": "4890:2:20"
+            },
+            "returnParameters": {
+              "id": 25456,
+              "nodeType": "ParameterList",
+              "parameters": [
+                {
+                  "constant": false,
+                  "id": 25455,
+                  "mutability": "mutable",
+                  "name": "",
+                  "nameLocation": "-1:-1:-1",
+                  "nodeType": "VariableDeclaration",
+                  "scope": 25460,
+                  "src": "4914:7:20",
+                  "stateVariable": false,
+                  "storageLocation": "default",
+                  "typeDescriptions": {
+                    "typeIdentifier": "t_uint256",
+                    "typeString": "uint256"
+                  },
+                  "typeName": {
+                    "id": 25454,
+                    "name": "uint256",
+                    "nodeType": "ElementaryTypeName",
+                    "src": "4914:7:20",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_uint256",
+                      "typeString": "uint256"
+                    }
+                  },
+                  "visibility": "internal"
+                }
+              ],
+              "src": "4913:9:20"
+            },
+            "scope": 25470,
+            "stateMutability": "view",
+            "virtual": false,
+            "visibility": "public"
+          },
+          {
+            "id": 25469,
+            "nodeType": "FunctionDefinition",
+            "src": "4965:104:20",
+            "nodes": [],
+            "body": {
+              "id": 25468,
+              "nodeType": "Block",
+              "src": "5034:35:20",
+              "nodes": [],
+              "statements": [
+                {
+                  "expression": {
+                    "id": 25466,
+                    "name": "accumulator",
+                    "nodeType": "Identifier",
+                    "overloadedDeclarations": [],
+                    "referencedDeclaration": 25165,
+                    "src": "5051:11:20",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_struct$_G1Point_$25971_storage",
+                      "typeString": "struct Types.G1Point storage ref"
+                    }
+                  },
+                  "functionReturnParameters": 25465,
+                  "id": 25467,
+                  "nodeType": "Return",
+                  "src": "5044:18:20"
+                }
+              ]
+            },
+            "functionSelector": "ff40807b",
+            "implemented": true,
+            "kind": "function",
+            "modifiers": [],
+            "name": "getAccumulator",
+            "nameLocation": "4974:14:20",
+            "parameters": {
+              "id": 25461,
+              "nodeType": "ParameterList",
+              "parameters": [],
+              "src": "4988:2:20"
+            },
+            "returnParameters": {
+              "id": 25465,
+              "nodeType": "ParameterList",
+              "parameters": [
+                {
+                  "constant": false,
+                  "id": 25464,
+                  "mutability": "mutable",
+                  "name": "",
+                  "nameLocation": "-1:-1:-1",
+                  "nodeType": "VariableDeclaration",
+                  "scope": 25469,
+                  "src": "5012:20:20",
+                  "stateVariable": false,
+                  "storageLocation": "memory",
+                  "typeDescriptions": {
+                    "typeIdentifier": "t_struct$_G1Point_$25971_memory_ptr",
+                    "typeString": "struct Types.G1Point"
+                  },
+                  "typeName": {
+                    "id": 25463,
+                    "nodeType": "UserDefinedTypeName",
+                    "pathNode": {
+                      "id": 25462,
+                      "name": "Types.G1Point",
+                      "nameLocations": [
+                        "5012:5:20",
+                        "5018:7:20"
+                      ],
+                      "nodeType": "IdentifierPath",
+                      "referencedDeclaration": 25971,
+                      "src": "5012:13:20"
+                    },
+                    "referencedDeclaration": 25971,
+                    "src": "5012:13:20",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_struct$_G1Point_$25971_storage_ptr",
+                      "typeString": "struct Types.G1Point"
+                    }
+                  },
+                  "visibility": "internal"
+                }
+              ],
+              "src": "5011:22:20"
+            },
+            "scope": 25470,
+            "stateMutability": "view",
+            "virtual": false,
+            "visibility": "public"
+          }
+        ],
+        "abstract": false,
+        "baseContracts": [
+          {
+            "baseName": {
+              "id": 25153,
+              "name": "KeccakMT",
+              "nameLocations": [
+                "340:8:20"
+              ],
+              "nodeType": "IdentifierPath",
+              "referencedDeclaration": 25090,
+              "src": "340:8:20"
+            },
+            "id": 25154,
+            "nodeType": "InheritanceSpecifier",
+            "src": "340:8:20"
+          },
+          {
+            "baseName": {
+              "id": 25155,
+              "name": "BN254",
+              "nameLocations": [
+                "350:5:20"
+              ],
+              "nodeType": "IdentifierPath",
+              "referencedDeclaration": 24968,
+              "src": "350:5:20"
+            },
+            "id": 25156,
+            "nodeType": "InheritanceSpecifier",
+            "src": "350:5:20"
+          },
+          {
+            "baseName": {
+              "id": 25157,
+              "name": "Verifier",
+              "nameLocations": [
+                "357:8:20"
+              ],
+              "nodeType": "IdentifierPath",
+              "referencedDeclaration": 26738,
+              "src": "357:8:20"
+            },
+            "id": 25158,
+            "nodeType": "InheritanceSpecifier",
+            "src": "357:8:20"
+          }
+        ],
+        "canonicalName": "Semacaulk",
+        "contractDependencies": [],
+        "contractKind": "contract",
+        "fullyImplemented": true,
+        "linearizedBaseContracts": [
+          25470,
+          26738,
+          24968,
+          25090
+        ],
+        "name": "Semacaulk",
+        "nameLocation": "327:9:20",
+        "scope": 25471,
+        "usedErrors": [
+          25191,
+          25195,
+          25199,
+          25201
+        ]
+      }
+    ],
+    "license": "MIT"
+  },
+  "id": 20
+}
\ No newline at end of file
diff --git a/src/contracts/Verifier.json b/src/contracts/Verifier.json
new file mode 100644
index 0000000..a003d85
--- /dev/null
+++ b/src/contracts/Verifier.json
@@ -0,0 +1,31742 @@
+{
+  "abi": [
+    {
+      "inputs": [
+        {
+          "components": [
+            {
+              "components": [
+                {
+                  "internalType": "uint256",
+                  "name": "q1_opening",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "q2_opening",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "q3_opening",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "q4_opening",
+                  "type": "uint256"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "f_cm",
+                  "type": "tuple"
+                },
+                {
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "x",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "y",
+                      "type": "uint256"
+                    }
+                  ],
+                  "internalType": "struct Types.G1Point",
+                  "name": "final_poly_proof",
+                  "type": "tuple"
+                }
+              ],
+              "internalType": "struct Types.MultiopenProof",
+              "name": "multiopenProof",
+              "type": "tuple"
+            },
+            {
+              "components": [
+                {
+                  "internalType": "uint256",
+                  "name": "q_mimc",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "mimc_cts",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "quotient",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "u_prime",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "p1",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "p2",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w0_0",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w0_1",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w0_2",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w1_0",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w1_1",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w1_2",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w2_0",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w2_1",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "w2_2",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "key_0",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "key_1",
+                  "type": "uint256"
+                }
+              ],
+              "internalType": "struct Types.Openings",
+              "name": "openings",
+              "type": "tuple"
+            },
+            {
+              "components": [
+                {
+                  "components": [
+                    {
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+                  "internalType": "struct Types.G1Point",
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+                      "name": "x",
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+                  "name": "h",
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+                      "name": "y0",
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+                      "name": "y1",
+                      "type": "uint256"
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+                  "internalType": "struct Types.G2Point",
+                  "name": "w",
+                  "type": "tuple"
+                }
+              ],
+              "internalType": "struct Types.Commitments",
+              "name": "commitments",
+              "type": "tuple"
+            }
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+          "internalType": "struct Types.Proof",
+          "name": "proof",
+          "type": "tuple"
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+        {
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+              "internalType": "uint256",
+              "name": "x",
+              "type": "uint256"
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+            {
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+              "type": "uint256"
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+          ],
+          "internalType": "struct Types.G1Point",
+          "name": "accumulator",
+          "type": "tuple"
+        },
+        {
+          "internalType": "uint256[3]",
+          "name": "publicInputs",
+          "type": "uint256[3]"
+        }
+      ],
+      "name": "verify",
+      "outputs": [
+        {
+          "internalType": "bool",
+          "name": "",
+          "type": "bool"
+        }
+      ],
+      "stateMutability": "view",
+      "type": "function"
+    }
+  ],
+  "bytecode": {
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+    "linkReferences": {}
+  },
+  "methodIdentifiers": {
+    "verify(((uint256,uint256,uint256,uint256,(uint256,uint256),(uint256,uint256)),(uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256,uint256),((uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256),(uint256,uint256,uint256,uint256))),(uint256,uint256),uint256[3])": "b3da592b"
+  },
+  "rawMetadata": "{\"compiler\":{\"version\":\"0.8.17+commit.8df45f5f\"},\"language\":\"Solidity\",\"output\":{\"abi\":[{\"inputs\":[{\"components\":[{\"components\":[{\"internalType\":\"uint256\",\"name\":\"q1_opening\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"q2_opening\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"q3_opening\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"q4_opening\",\"type\":\"uint256\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"f_cm\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"final_poly_proof\",\"type\":\"tuple\"}],\"internalType\":\"struct Types.MultiopenProof\",\"name\":\"multiopenProof\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"q_mimc\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"mimc_cts\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"quotient\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"u_prime\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"p1\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"p2\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"w0_0\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"w0_1\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"w0_2\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"w1_0\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"w1_1\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"w1_2\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"w2_0\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"w2_1\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"w2_2\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"key_0\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"key_1\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.Openings\",\"name\":\"openings\",\"type\":\"tuple\"},{\"components\":[{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"w0\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"w1\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"w2\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"key\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"mimc_cts\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"quotient\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"u_prime\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"zi\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"ci\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"p1\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"p2\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"q_mimc\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"h\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x0\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"x1\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y0\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y1\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G2Point\",\"name\":\"w\",\"type\":\"tuple\"}],\"internalType\":\"struct Types.Commitments\",\"name\":\"commitments\",\"type\":\"tuple\"}],\"internalType\":\"struct Types.Proof\",\"name\":\"proof\",\"type\":\"tuple\"},{\"components\":[{\"internalType\":\"uint256\",\"name\":\"x\",\"type\":\"uint256\"},{\"internalType\":\"uint256\",\"name\":\"y\",\"type\":\"uint256\"}],\"internalType\":\"struct Types.G1Point\",\"name\":\"accumulator\",\"type\":\"tuple\"},{\"internalType\":\"uint256[3]\",\"name\":\"publicInputs\",\"type\":\"uint256[3]\"}],\"name\":\"verify\",\"outputs\":[{\"internalType\":\"bool\",\"name\":\"\",\"type\":\"bool\"}],\"stateMutability\":\"view\",\"type\":\"function\"}],\"devdoc\":{\"kind\":\"dev\",\"methods\":{},\"version\":1},\"userdoc\":{\"kind\":\"user\",\"methods\":{},\"version\":1}},\"settings\":{\"compilationTarget\":{\"sol/Verifier.sol\":\"Verifier\"},\"evmVersion\":\"london\",\"libraries\":{},\"metadata\":{\"bytecodeHash\":\"ipfs\"},\"optimizer\":{\"enabled\":true,\"runs\":200},\"remappings\":[\":ds-test/=lib/forge-std/lib/ds-test/src/\",\":forge-std/=lib/forge-std/src/\"]},\"sources\":{\"sol/BN254.sol\":{\"keccak256\":\"0x3387e0c55cd2bdcedf8d3e5cf66a97f397e4673e8f040af92f16e6ec6b248de6\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://4fa56bc2c09b9fb96b18a3a4d5bb2734eae0f5b50229cb42bccf9bd4a58e5309\",\"dweb:/ipfs/QmQuAo1NLKqKb1cqx9x8mPxWsPY4LHjbJg5KR7feaDqkPd\"]},\"sol/Constants.sol\":{\"keccak256\":\"0x3e119809d4115dd17bd20fdb86436bd5af327127ed223801456e7a917d6054e8\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://fb67d5412ac9bdf638246fae6d7fccc6de23b36486308b578211e44847a64616\",\"dweb:/ipfs/QmQY3Ezd3RHtpofEPRRsipYjMzrgvmk5vG6hNL2bdURMxx\"]},\"sol/Lagrange.sol\":{\"keccak256\":\"0x9c4449d4146e90a99094c38dffb583c7017a2453b9254b4662d4c91387593405\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://41b3006cbd16acb0f29a008822d65381bbe779eabdf1ce86e952374fa5c75422\",\"dweb:/ipfs/QmYmjRzSEzwxJHkVSb7sZVLCARDz76Gnpdr5xnKfr2wMt2\"]},\"sol/Transcript.sol\":{\"keccak256\":\"0x376df72539581cd652d4aea09d0c18accc1ee001ee19f80fea89f3e1a7d40e18\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://0dc8d7f873f9f5d45953bea9a394073ffa2d0930280425b973fc1f8be22a9ec5\",\"dweb:/ipfs/Qmbkg6WS8Ajjr3QLe6TtrdVmyqHaLD7cr8WHjk9uGnPQW1\"]},\"sol/Types.sol\":{\"keccak256\":\"0xbc4b390b5751a05cec4078017017130740d257fa1d4e03ee21315c14876aaaef\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://d6f30ac31762d9dccdbc1e2c542af5366e4f7513467a8234dc7183f6ce1fc3cb\",\"dweb:/ipfs/QmS8YspTKQNzaAgvdZU1VF8EZSk76Zzh5pKFz1TNghBCKo\"]},\"sol/Verifier.sol\":{\"keccak256\":\"0x1a63ed69635cba15d0863bc2bce9e1c4176fc93eda4103d6077536c953365429\",\"license\":\"MIT\",\"urls\":[\"bzz-raw://92f7ed4b5f2a2d9c090d273462c983ac0759f96bb772603f84c314bb7ba29608\",\"dweb:/ipfs/QmRNLN1iW8xstb8FHixNAmdbD5UHKRqr5KNsva85ugkofC\"]}},\"version\":1}",
+  "metadata": {
+    "compiler": {
+      "version": "0.8.17+commit.8df45f5f"
+    },
+    "language": "Solidity",
+    "output": {
+      "abi": [
+        {
+          "inputs": [
+            {
+              "internalType": "struct Types.Proof",
+              "name": "proof",
+              "type": "tuple",
+              "components": [
+                {
+                  "internalType": "struct Types.MultiopenProof",
+                  "name": "multiopenProof",
+                  "type": "tuple",
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "q1_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "q2_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "q3_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "q4_opening",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "f_cm",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "final_poly_proof",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    }
+                  ]
+                },
+                {
+                  "internalType": "struct Types.Openings",
+                  "name": "openings",
+                  "type": "tuple",
+                  "components": [
+                    {
+                      "internalType": "uint256",
+                      "name": "q_mimc",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "mimc_cts",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "quotient",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "u_prime",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "p1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "p2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w0_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w0_1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w0_2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w1_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w1_1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w1_2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w2_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w2_1",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "w2_2",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "key_0",
+                      "type": "uint256"
+                    },
+                    {
+                      "internalType": "uint256",
+                      "name": "key_1",
+                      "type": "uint256"
+                    }
+                  ]
+                },
+                {
+                  "internalType": "struct Types.Commitments",
+                  "name": "commitments",
+                  "type": "tuple",
+                  "components": [
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "w0",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "w1",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "w2",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "key",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "mimc_cts",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "quotient",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "u_prime",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "zi",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "ci",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "p1",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "p2",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "q_mimc",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G1Point",
+                      "name": "h",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y",
+                          "type": "uint256"
+                        }
+                      ]
+                    },
+                    {
+                      "internalType": "struct Types.G2Point",
+                      "name": "w",
+                      "type": "tuple",
+                      "components": [
+                        {
+                          "internalType": "uint256",
+                          "name": "x0",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "x1",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y0",
+                          "type": "uint256"
+                        },
+                        {
+                          "internalType": "uint256",
+                          "name": "y1",
+                          "type": "uint256"
+                        }
+                      ]
+                    }
+                  ]
+                }
+              ]
+            },
+            {
+              "internalType": "struct Types.G1Point",
+              "name": "accumulator",
+              "type": "tuple",
+              "components": [
+                {
+                  "internalType": "uint256",
+                  "name": "x",
+                  "type": "uint256"
+                },
+                {
+                  "internalType": "uint256",
+                  "name": "y",
+                  "type": "uint256"
+                }
+              ]
+            },
+            {
+              "internalType": "uint256[3]",
+              "name": "publicInputs",
+              "type": "uint256[3]"
+            }
+          ],
+          "stateMutability": "view",
+          "type": "function",
+          "name": "verify",
+          "outputs": [
+            {
+              "internalType": "bool",
+              "name": "",
+              "type": "bool"
+            }
+          ]
+        }
+      ],
+      "devdoc": {
+        "kind": "dev",
+        "methods": {},
+        "version": 1
+      },
+      "userdoc": {
+        "kind": "user",
+        "methods": {},
+        "version": 1
+      }
+    },
+    "settings": {
+      "remappings": [
+        ":ds-test/=lib/forge-std/lib/ds-test/src/",
+        ":forge-std/=lib/forge-std/src/"
+      ],
+      "optimizer": {
+        "enabled": true,
+        "runs": 200
+      },
+      "metadata": {
+        "bytecodeHash": "ipfs"
+      },
+      "compilationTarget": {
+        "sol/Verifier.sol": "Verifier"
+      },
+      "libraries": {}
+    },
+    "sources": {
+      "sol/BN254.sol": {
+        "keccak256": "0x3387e0c55cd2bdcedf8d3e5cf66a97f397e4673e8f040af92f16e6ec6b248de6",
+        "urls": [
+          "bzz-raw://4fa56bc2c09b9fb96b18a3a4d5bb2734eae0f5b50229cb42bccf9bd4a58e5309",
+          "dweb:/ipfs/QmQuAo1NLKqKb1cqx9x8mPxWsPY4LHjbJg5KR7feaDqkPd"
+        ],
+        "license": "MIT"
+      },
+      "sol/Constants.sol": {
+        "keccak256": "0x3e119809d4115dd17bd20fdb86436bd5af327127ed223801456e7a917d6054e8",
+        "urls": [
+          "bzz-raw://fb67d5412ac9bdf638246fae6d7fccc6de23b36486308b578211e44847a64616",
+          "dweb:/ipfs/QmQY3Ezd3RHtpofEPRRsipYjMzrgvmk5vG6hNL2bdURMxx"
+        ],
+        "license": "MIT"
+      },
+      "sol/Lagrange.sol": {
+        "keccak256": "0x9c4449d4146e90a99094c38dffb583c7017a2453b9254b4662d4c91387593405",
+        "urls": [
+          "bzz-raw://41b3006cbd16acb0f29a008822d65381bbe779eabdf1ce86e952374fa5c75422",
+          "dweb:/ipfs/QmYmjRzSEzwxJHkVSb7sZVLCARDz76Gnpdr5xnKfr2wMt2"
+        ],
+        "license": "MIT"
+      },
+      "sol/Transcript.sol": {
+        "keccak256": "0x376df72539581cd652d4aea09d0c18accc1ee001ee19f80fea89f3e1a7d40e18",
+        "urls": [
+          "bzz-raw://0dc8d7f873f9f5d45953bea9a394073ffa2d0930280425b973fc1f8be22a9ec5",
+          "dweb:/ipfs/Qmbkg6WS8Ajjr3QLe6TtrdVmyqHaLD7cr8WHjk9uGnPQW1"
+        ],
+        "license": "MIT"
+      },
+      "sol/Types.sol": {
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+                                  "nodeType": "YulLiteral",
+                                  "src": "41518:4:23",
+                                  "type": "",
+                                  "value": "0xe0"
+                                }
+                              ],
+                              "functionName": {
+                                "name": "add",
+                                "nodeType": "YulIdentifier",
+                                "src": "41505:3:23"
+                              },
+                              "nodeType": "YulFunctionCall",
+                              "src": "41505:18:23"
+                            },
+                            {
+                              "arguments": [
+                                {
+                                  "arguments": [
+                                    {
+                                      "name": "mPtr",
+                                      "nodeType": "YulIdentifier",
+                                      "src": "41535:4:23"
+                                    },
+                                    {
+                                      "kind": "number",
+                                      "nodeType": "YulLiteral",
+                                      "src": "41541:6:23",
+                                      "type": "",
+                                      "value": "0x0360"
+                                    }
+                                  ],
+                                  "functionName": {
+                                    "name": "add",
+                                    "nodeType": "YulIdentifier",
+                                    "src": "41531:3:23"
+                                  },
+                                  "nodeType": "YulFunctionCall",
+                                  "src": "41531:17:23"
+                                }
+                              ],
+                              "functionName": {
+                                "name": "mload",
+                                "nodeType": "YulIdentifier",
+                                "src": "41525:5:23"
+                              },
+                              "nodeType": "YulFunctionCall",
+                              "src": "41525:24:23"
+                            }
+                          ],
+                          "functionName": {
+                            "name": "mstore",
+                            "nodeType": "YulIdentifier",
+                            "src": "41498:6:23"
+                          },
+                          "nodeType": "YulFunctionCall",
+                          "src": "41498:52:23"
+                        },
+                        "nodeType": "YulExpressionStatement",
+                        "src": "41498:52:23"
+                      }
+                    ]
+                  },
+                  "evmVersion": "london",
+                  "externalReferences": [
+                    {
+                      "declaration": 26714,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "38677:6:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26714,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "38718:6:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26714,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "38973:6:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26714,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "40008:6:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26714,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "40406:6:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26729,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "38773:1:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26729,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "39124:1:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26729,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "39608:1:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26729,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "39652:1:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26729,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "40196:1:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26729,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "40431:1:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26729,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "40912:1:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26726,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "41012:7:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26726,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "41083:7:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26726,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "41154:7:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26726,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "41225:7:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26726,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "41296:7:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26726,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "41367:7:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26726,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "41438:7:23",
+                      "valueSize": 1
+                    },
+                    {
+                      "declaration": 26726,
+                      "isOffset": false,
+                      "isSlot": false,
+                      "src": "41509:7:23",
+                      "valueSize": 1
+                    }
+                  ],
+                  "id": 26733,
+                  "nodeType": "InlineAssembly",
+                  "src": "37179:4387:23"
+                },
+                {
+                  "expression": {
+                    "id": 26734,
+                    "name": "results",
+                    "nodeType": "Identifier",
+                    "overloadedDeclarations": [],
+                    "referencedDeclaration": 26726,
+                    "src": "41583:7:23",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_array$_t_uint256_$8_memory_ptr",
+                      "typeString": "uint256[8] memory"
+                    }
+                  },
+                  "functionReturnParameters": 26720,
+                  "id": 26735,
+                  "nodeType": "Return",
+                  "src": "41576:14:23"
+                }
+              ]
+            },
+            "implemented": true,
+            "kind": "function",
+            "modifiers": [],
+            "name": "batchInvert",
+            "nameLocation": "37001:11:23",
+            "parameters": {
+              "id": 26715,
+              "nodeType": "ParameterList",
+              "parameters": [
+                {
+                  "constant": false,
+                  "id": 26714,
+                  "mutability": "mutable",
+                  "name": "inputs",
+                  "nameLocation": "37040:6:23",
+                  "nodeType": "VariableDeclaration",
+                  "scope": 26737,
+                  "src": "37022:24:23",
+                  "stateVariable": false,
+                  "storageLocation": "memory",
+                  "typeDescriptions": {
+                    "typeIdentifier": "t_array$_t_uint256_$8_memory_ptr",
+                    "typeString": "uint256[8]"
+                  },
+                  "typeName": {
+                    "baseType": {
+                      "id": 26711,
+                      "name": "uint256",
+                      "nodeType": "ElementaryTypeName",
+                      "src": "37022:7:23",
+                      "typeDescriptions": {
+                        "typeIdentifier": "t_uint256",
+                        "typeString": "uint256"
+                      }
+                    },
+                    "id": 26713,
+                    "length": {
+                      "hexValue": "38",
+                      "id": 26712,
+                      "isConstant": false,
+                      "isLValue": false,
+                      "isPure": true,
+                      "kind": "number",
+                      "lValueRequested": false,
+                      "nodeType": "Literal",
+                      "src": "37030:1:23",
+                      "typeDescriptions": {
+                        "typeIdentifier": "t_rational_8_by_1",
+                        "typeString": "int_const 8"
+                      },
+                      "value": "8"
+                    },
+                    "nodeType": "ArrayTypeName",
+                    "src": "37022:10:23",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_array$_t_uint256_$8_storage_ptr",
+                      "typeString": "uint256[8]"
+                    }
+                  },
+                  "visibility": "internal"
+                }
+              ],
+              "src": "37012:40:23"
+            },
+            "returnParameters": {
+              "id": 26720,
+              "nodeType": "ParameterList",
+              "parameters": [
+                {
+                  "constant": false,
+                  "id": 26719,
+                  "mutability": "mutable",
+                  "name": "",
+                  "nameLocation": "-1:-1:-1",
+                  "nodeType": "VariableDeclaration",
+                  "scope": 26737,
+                  "src": "37076:17:23",
+                  "stateVariable": false,
+                  "storageLocation": "memory",
+                  "typeDescriptions": {
+                    "typeIdentifier": "t_array$_t_uint256_$8_memory_ptr",
+                    "typeString": "uint256[8]"
+                  },
+                  "typeName": {
+                    "baseType": {
+                      "id": 26716,
+                      "name": "uint256",
+                      "nodeType": "ElementaryTypeName",
+                      "src": "37076:7:23",
+                      "typeDescriptions": {
+                        "typeIdentifier": "t_uint256",
+                        "typeString": "uint256"
+                      }
+                    },
+                    "id": 26718,
+                    "length": {
+                      "hexValue": "38",
+                      "id": 26717,
+                      "isConstant": false,
+                      "isLValue": false,
+                      "isPure": true,
+                      "kind": "number",
+                      "lValueRequested": false,
+                      "nodeType": "Literal",
+                      "src": "37084:1:23",
+                      "typeDescriptions": {
+                        "typeIdentifier": "t_rational_8_by_1",
+                        "typeString": "int_const 8"
+                      },
+                      "value": "8"
+                    },
+                    "nodeType": "ArrayTypeName",
+                    "src": "37076:10:23",
+                    "typeDescriptions": {
+                      "typeIdentifier": "t_array$_t_uint256_$8_storage_ptr",
+                      "typeString": "uint256[8]"
+                    }
+                  },
+                  "visibility": "internal"
+                }
+              ],
+              "src": "37075:19:23"
+            },
+            "scope": 26738,
+            "stateMutability": "view",
+            "virtual": false,
+            "visibility": "internal"
+          }
+        ],
+        "abstract": false,
+        "baseContracts": [
+          {
+            "baseName": {
+              "id": 26196,
+              "name": "BN254",
+              "nameLocations": [
+                "296:5:23"
+              ],
+              "nodeType": "IdentifierPath",
+              "referencedDeclaration": 24968,
+              "src": "296:5:23"
+            },
+            "id": 26197,
+            "nodeType": "InheritanceSpecifier",
+            "src": "296:5:23"
+          }
+        ],
+        "canonicalName": "Verifier",
+        "contractDependencies": [],
+        "contractKind": "contract",
+        "fullyImplemented": true,
+        "linearizedBaseContracts": [
+          26738,
+          24968
+        ],
+        "name": "Verifier",
+        "nameLocation": "284:8:23",
+        "scope": 26739,
+        "usedErrors": []
+      }
+    ],
+    "license": "MIT"
+  },
+  "id": 23
+}
\ No newline at end of file
diff --git a/src/contracts/format/proof_for_semacaulk.rs b/src/contracts/format/proof_for_semacaulk.rs
index 100ea17..2479735 100644
--- a/src/contracts/format/proof_for_semacaulk.rs
+++ b/src/contracts/format/proof_for_semacaulk.rs
@@ -4,10 +4,7 @@ use crate::prover::{Commitments as RustCommitments, Openings as RustOpenings, Pr
 use ark_bn254::{Bn254, G1Affine, G2Affine};
 use ethers::prelude::abigen;
 
-abigen!(
-    SemacaulkContract,
-    "./src/contracts/out/Semacaulk.sol/Semacaulk.json"
-);
+abigen!(SemacaulkContract, "./src/contracts/Semacaulk.json");
 
 pub type ProofForSemacaulk = Proof;
 
@@ -44,7 +41,7 @@ pub fn format_commitments(commitments: &RustCommitments<Bn254>) -> Commitments {
         w_1: g1_affine_to_g1point(&commitments.w1),
         w_2: g1_affine_to_g1point(&commitments.w2),
         key: g1_affine_to_g1point(&commitments.key),
-        c: g1_affine_to_g1point(&commitments.c),
+        mimc_cts: g1_affine_to_g1point(&commitments.mimc_cts),
         quotient: g1_affine_to_g1point(&commitments.quotient),
         u_prime: g1_affine_to_g1point(&commitments.u_prime),
         zi: g1_affine_to_g1point(&commitments.zi),
@@ -60,7 +57,7 @@ pub fn format_commitments(commitments: &RustCommitments<Bn254>) -> Commitments {
 pub fn format_openings(openings: &RustOpenings<Bn254>) -> Openings {
     Openings {
         q_mimc: f_to_u256(openings.q_mimc),
-        c: f_to_u256(openings.c),
+        mimc_cts: f_to_u256(openings.mimc_cts),
         quotient: f_to_u256(openings.quotient),
         u_prime: f_to_u256(openings.u_prime),
         p_1: f_to_u256(openings.p1),
diff --git a/src/contracts/format/proof_for_verifier.rs b/src/contracts/format/proof_for_verifier.rs
index e4ecc5b..0f9cd0e 100644
--- a/src/contracts/format/proof_for_verifier.rs
+++ b/src/contracts/format/proof_for_verifier.rs
@@ -4,7 +4,7 @@ use crate::prover::{Commitments as RustCommitments, Openings as RustOpenings, Pr
 use ark_bn254::{Bn254, G1Affine, G2Affine};
 use ethers::prelude::abigen;
 
-abigen!(Verifier, "./src/contracts/out/Verifier.sol/Verifier.json");
+abigen!(Verifier, "./src/contracts/Verifier.json");
 
 pub type ProofForVerifier = Proof;
 
@@ -41,7 +41,7 @@ pub fn format_commitments(commitments: &RustCommitments<Bn254>) -> Commitments {
         w_1: g1_affine_to_g1point(&commitments.w1),
         w_2: g1_affine_to_g1point(&commitments.w2),
         key: g1_affine_to_g1point(&commitments.key),
-        c: g1_affine_to_g1point(&commitments.c),
+        mimc_cts: g1_affine_to_g1point(&commitments.mimc_cts),
         quotient: g1_affine_to_g1point(&commitments.quotient),
         u_prime: g1_affine_to_g1point(&commitments.u_prime),
         zi: g1_affine_to_g1point(&commitments.zi),
@@ -57,7 +57,7 @@ pub fn format_commitments(commitments: &RustCommitments<Bn254>) -> Commitments {
 pub fn format_openings(openings: &RustOpenings<Bn254>) -> Openings {
     Openings {
         q_mimc: f_to_u256(openings.q_mimc),
-        c: f_to_u256(openings.c),
+        mimc_cts: f_to_u256(openings.mimc_cts),
         quotient: f_to_u256(openings.quotient),
         u_prime: f_to_u256(openings.u_prime),
         p_1: f_to_u256(openings.p1),
diff --git a/src/contracts/sol/Constants.sol b/src/contracts/sol/Constants.sol
index de8ee93..1521f1c 100644
--- a/src/contracts/sol/Constants.sol
+++ b/src/contracts/sol/Constants.sol
@@ -13,7 +13,11 @@ library Constants {
     // Compute this value with Fr::from(128).inverse().unwrap()
     uint256 constant DOMAIN_SIZE_INV = 0x300385D5FB6F3CE964DFA52B147E55AC6DE38077E8C5FDB0215A31A8C8200001;
     uint256 constant LOG2_DOMAIN_SIZE = 7;
+
+    // The 1st root of unity (counting from 0) of the subgroup domain.
     uint256 constant OMEGA = 0x16E73DFDAD310991DF5CE19CE85943E01DCB5564B6F24C799D0E470CBA9D1811;
+
+    // The nth root of unity (counting from 0) of the subgroup domain.
     uint256 constant OMEGA_N = 0x1332CB377D53B9C681AFA4DC09F66BC37E3F2F33DEB33D9B40BD245C971B2447;
 
     // These values should be replaced with new ones from a trusted setup.
@@ -25,43 +29,32 @@ library Constants {
     // Using the Hermez Network phase 1 SRS (the 54th contribution of Perpetual
     // Powers of Tau plus a random beacon)
 
+    // For a table size of 2 ^ 10:
+    uint256 constant SRS_G1_T_X = 0x17A40BF6B2A82570FED3BEDB71E3DDF36680B431FFB3641FEC94F5478D34DCCC;
+    uint256 constant SRS_G1_T_Y = 0x050852202323C504AAB1AE596553781B3DC87CC6793D731D054C7D751E82AF0A;
+
     // For a table size of 2 ^ 11:
-    uint256 constant SRS_G1_T_X = 0x195B22E5A84C5D5A70E8FAEA64DB9BFE8EB57577CFEB3A7798F5470C60B99BED;
-    uint256 constant SRS_G1_T_Y = 0x15D250AF555DC3DBF386C1BBDD00D9AB2B6908120041BC75F496A6FBE051A494;
-    uint256 constant SRS_G2_1_X_0 = 0x26186A2D65EE4D2F9C9A5B91F86597D35F192CD120CAF7E935D8443D1938E23D;
-    uint256 constant SRS_G2_1_X_1 = 0x30441FD1B5D3370482C42152A8899027716989A6996C2535BC9F7FEE8AAEF79E;
-    uint256 constant SRS_G2_1_Y_0 = 0x1970EA81DD6992ADFBC571EFFB03503ADBBB6A857F578403C6C40E22D65B3C02;
-    uint256 constant SRS_G2_1_Y_1 = 0x054793348F12C0CF5622C340573CB277586319DE359AB9389778F689786B1E48;
+    //uint256 constant SRS_G1_T_X = 0x195B22E5A84C5D5A70E8FAEA64DB9BFE8EB57577CFEB3A7798F5470C60B99BED;
+    //uint256 constant SRS_G1_T_Y = 0x15D250AF555DC3DBF386C1BBDD00D9AB2B6908120041BC75F496A6FBE051A494;
 
     // For a table size of 2 ** 12:
     //uint256 constant SRS_G1_T_X = 0x160220880FDFD72FA9C1D4B6477B5AC9BF0310BE9C5C491F3F52EFD8573A2A14;
     //uint256 constant SRS_G1_T_Y = 0x094E210CAF49A96E4433927B1D17309B7724958FACADE891C041CDC196E4BCB8;
-    //uint256 constant SRS_G2_1_X_0 = 0x26186A2D65EE4D2F9C9A5B91F86597D35F192CD120CAF7E935D8443D1938E23D;
-    //uint256 constant SRS_G2_1_X_1 = 0x30441FD1B5D3370482C42152A8899027716989A6996C2535BC9F7FEE8AAEF79E;
-    //uint256 constant SRS_G2_1_Y_0 = 0x1970EA81DD6992ADFBC571EFFB03503ADBBB6A857F578403C6C40E22D65B3C02;
-    //uint256 constant SRS_G2_1_Y_1 = 0x054793348F12C0CF5622C340573CB277586319DE359AB9389778F689786B1E48;
 
     // For a table size of 2 ** 14:
     //uint256 constant SRS_G1_T_X = 0x1820CAC999202BEBA571F32647CA77E38AA8AA2C6286857D68CAAA0C8F6EA688;
     //uint256 constant SRS_G1_T_Y = 0x1F93BBD6833793937E7971F0D99FDC98521C1869870763F17F0730850C476F69;
-    //uint256 constant SRS_G2_1_X_0 = 0x26186A2D65EE4D2F9C9A5B91F86597D35F192CD120CAF7E935D8443D1938E23D;
-    //uint256 constant SRS_G2_1_X_1 = 0x30441FD1B5D3370482C42152A8899027716989A6996C2535BC9F7FEE8AAEF79E;
-    //uint256 constant SRS_G2_1_Y_0 = 0x1970EA81DD6992ADFBC571EFFB03503ADBBB6A857F578403C6C40E22D65B3C02;
-    //uint256 constant SRS_G2_1_Y_1 = 0x054793348F12C0CF5622C340573CB277586319DE359AB9389778F689786B1E48;
 
     // For a table size of 2 ** 16:
     //uint256 constant SRS_G1_T_X = 0x0E4753DD9EC507F7B9A3DB6069A6686872963B01D260378F4619E3166CA1481A;
     //uint256 constant SRS_G1_T_Y = 0x08DEAB995B28148852575D6BDB33AE1B5719861E09EC2FA4B6D295A74110BFCF;
-    //uint256 constant SRS_G2_1_X_0 = 0x26186A2D65EE4D2F9C9A5B91F86597D35F192CD120CAF7E935D8443D1938E23D;
-    //uint256 constant SRS_G2_1_X_1 = 0x30441FD1B5D3370482C42152A8899027716989A6996C2535BC9F7FEE8AAEF79E;
-    //uint256 constant SRS_G2_1_Y_0 = 0x1970EA81DD6992ADFBC571EFFB03503ADBBB6A857F578403C6C40E22D65B3C02;
-    //uint256 constant SRS_G2_1_Y_1 = 0x054793348F12C0CF5622C340573CB277586319DE359AB9389778F689786B1E48;
 
     // For a table size of 2 ^ 20:
     //uint256 constant SRS_G1_T_X = 0x28ECE6AC832172CE0174B269049E9BF74F739090D042E277AFADB9B047937885;
     //uint256 constant SRS_G1_T_Y = 0x2C408B09EA45E3DC700AD3830D57080CA519AF5EDCABFCEB47EB64E08BB75D79;
-    //uint256 constant SRS_G2_1_X_0 = 0x26186A2D65EE4D2F9C9A5B91F86597D35F192CD120CAF7E935D8443D1938E23D;
-    //uint256 constant SRS_G2_1_X_1 = 0x30441FD1B5D3370482C42152A8899027716989A6996C2535BC9F7FEE8AAEF79E;
-    //uint256 constant SRS_G2_1_Y_0 = 0x1970EA81DD6992ADFBC571EFFB03503ADBBB6A857F578403C6C40E22D65B3C02;
-    //uint256 constant SRS_G2_1_Y_1 = 0x054793348F12C0CF5622C340573CB277586319DE359AB9389778F689786B1E48;
+
+    uint256 constant SRS_G2_1_X_0 = 0x26186A2D65EE4D2F9C9A5B91F86597D35F192CD120CAF7E935D8443D1938E23D;
+    uint256 constant SRS_G2_1_X_1 = 0x30441FD1B5D3370482C42152A8899027716989A6996C2535BC9F7FEE8AAEF79E;
+    uint256 constant SRS_G2_1_Y_0 = 0x1970EA81DD6992ADFBC571EFFB03503ADBBB6A857F578403C6C40E22D65B3C02;
+    uint256 constant SRS_G2_1_Y_1 = 0x054793348F12C0CF5622C340573CB277586319DE359AB9389778F689786B1E48;
 }
diff --git a/src/contracts/sol/Semacaulk.sol b/src/contracts/sol/Semacaulk.sol
index 827e446..2141b20 100644
--- a/src/contracts/sol/Semacaulk.sol
+++ b/src/contracts/sol/Semacaulk.sol
@@ -30,8 +30,10 @@ contract Semacaulk is KeccakMT, BN254, Verifier {
         uint256(keccak256(abi.encodePacked('Semacaulk'))) % Constants.PRIME_R;
 
     mapping (uint256 => bool) public nullifierHashHistory;
+    mapping (uint256 => bool) public identityCommitmentHistory;
 
     // Custom errors
+    error InvalidIdentityCommitment(uint256 _identityCommitment);
     error RootMismatch(bytes32 _generatedRoot);
     error NullifierHashAlreadySeen(uint256 _nullifierHash);
     error InvalidProof();
@@ -58,6 +60,13 @@ contract Semacaulk is KeccakMT, BN254, Verifier {
         uint256 _lagrangeLeafY,
         bytes32[] memory _lagrangeMerkleProof
     ) public {
+        if (
+            _identityCommitment > Constants.PRIME_R ||
+            _identityCommitment == NOTHING_UP_MY_SLEEVE_ZERO
+        ) {
+            revert InvalidIdentityCommitment({ _identityCommitment: _identityCommitment });
+        }
+
         uint256 index = currentIndex;
         bytes32 lagrangeLeaf = keccak256(abi.encodePacked(_lagrangeLeafX, _lagrangeLeafY));
 
@@ -92,7 +101,7 @@ contract Semacaulk is KeccakMT, BN254, Verifier {
 
     function broadcastSignal(
         bytes memory _signal,
-        Types.Proof memory proof,
+        Types.Proof memory _proof,
         uint256 _nullifierHash,
         uint256 _externalNullifier
     ) public {
@@ -109,7 +118,7 @@ contract Semacaulk is KeccakMT, BN254, Verifier {
         publicInputs[2] = signalHash;
 
         // Verify the proof and revert if it is invalid
-        bool isValid = verify(proof, getAccumulator(), publicInputs);
+        bool isValid = verify(_proof, getAccumulator(), publicInputs);
         if (!isValid) {
             revert InvalidProof();
         }
diff --git a/src/contracts/sol/Transcript.sol b/src/contracts/sol/Transcript.sol
index b132941..0c0a7fc 100644
--- a/src/contracts/sol/Transcript.sol
+++ b/src/contracts/sol/Transcript.sol
@@ -47,9 +47,10 @@ library TranscriptLibrary {
         return bytes32(x);
     }
 
-    function updateWithU256(Transcript memory self, uint256 value) internal pure {
+    function updateWithF(Transcript memory self, uint256 value) internal pure {
         bytes memory dataPtr = self.data;
         assembly {
+            let v := mod(value, PRIME_R)
             // update length of transcript data
             let array_length := mload(dataPtr)
             mstore(dataPtr, add(0x20, array_length))
@@ -71,14 +72,19 @@ library TranscriptLibrary {
         }
     }
 
-    function round1(
+    function round0PublicInputs(
         Transcript memory transcript, 
-        Types.Proof memory proof,
         uint256[3] memory publicInputs
     ) internal pure {
-        updateWithU256(transcript, publicInputs[0]);
-        updateWithU256(transcript, publicInputs[1]);
-        updateWithU256(transcript, publicInputs[2]);
+        updateWithF(transcript, publicInputs[0]);
+        updateWithF(transcript, publicInputs[1]);
+        updateWithF(transcript, publicInputs[2]);
+    }
+
+    function round1(
+        Transcript memory transcript, 
+        Types.Proof memory proof
+    ) internal pure {
         updateWithG1(transcript, proof.commitments.w0);
         updateWithG1(transcript, proof.commitments.key);
         updateWithG1(transcript, proof.commitments.w1);
@@ -107,23 +113,23 @@ library TranscriptLibrary {
         Transcript memory transcript, 
         Types.Proof memory proof
     ) internal pure {
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.w0_0);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.w0_1);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.w0_2);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.w1_0);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.w1_1);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.w1_2);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.w2_0);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.w2_1);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.w2_2);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.key_0);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.key_1);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.q_mimc);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.c);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.quotient);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.u_prime);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.p1);
-        TranscriptLibrary.updateWithU256(transcript, proof.openings.p2);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.w0_0);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.w0_1);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.w0_2);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.w1_0);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.w1_1);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.w1_2);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.w2_0);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.w2_1);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.w2_2);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.key_0);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.key_1);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.q_mimc);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.mimc_cts);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.quotient);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.u_prime);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.p1);
+        TranscriptLibrary.updateWithF(transcript, proof.openings.p2);
     }
 
     function round5(
diff --git a/src/contracts/sol/Types.sol b/src/contracts/sol/Types.sol
index 66bcb95..05b0007 100644
--- a/src/contracts/sol/Types.sol
+++ b/src/contracts/sol/Types.sol
@@ -72,7 +72,7 @@ library Types {
         /* 0x40  */ Types.G1Point w1;
         /* 0x80  */ Types.G1Point w2;
         /* 0xc0  */ Types.G1Point key;
-        /* 0x100 */ Types.G1Point c;
+        /* 0x100 */ Types.G1Point mimc_cts;
         /* 0x140 */ Types.G1Point quotient;
         /* 0x180 */ Types.G1Point u_prime;
         /* 0x1c0 */ Types.G1Point zi;
@@ -86,7 +86,7 @@ library Types {
 
     struct Openings {
         /* 0x00  */ uint256 q_mimc;
-        /* 0x20  */ uint256 c;
+        /* 0x20  */ uint256 mimc_cts;
         /* 0x40  */ uint256 quotient;
         /* 0x60  */ uint256 u_prime;
         /* 0x80  */ uint256 p1;
diff --git a/src/contracts/sol/Verifier.sol b/src/contracts/sol/Verifier.sol
index 59b2823..fc8eda5 100644
--- a/src/contracts/sol/Verifier.sol
+++ b/src/contracts/sol/Verifier.sol
@@ -23,7 +23,8 @@ contract Verifier is BN254 {
         Types.ChallengeTranscript memory challengeTranscript;
         Types.VerifierTranscript memory verifierTranscript;
 
-        TranscriptLibrary.round1(transcript, proof, publicInputs);
+        TranscriptLibrary.round0PublicInputs(transcript, publicInputs);
+        TranscriptLibrary.round1(transcript, proof);
 
         challengeTranscript.v = TranscriptLibrary.getChallenge(transcript);
 
diff --git a/src/contracts/sol/tests/TestTranscript.sol b/src/contracts/sol/tests/TestTranscript.sol
index 0e26ebc..5776701 100644
--- a/src/contracts/sol/tests/TestTranscript.sol
+++ b/src/contracts/sol/tests/TestTranscript.sol
@@ -13,13 +13,13 @@ contract TestTranscript {
     ) public pure returns(uint256, uint256) {
         TranscriptLibrary.Transcript memory transcript = TranscriptLibrary.newTranscript();
 
-        TranscriptLibrary.updateWithU256(transcript, u1);
+        TranscriptLibrary.updateWithF(transcript, u1);
 
         TranscriptLibrary.updateWithG1(transcript, pt1);
 
         uint256 challenge_1 =  TranscriptLibrary.getChallenge(transcript);
 
-        TranscriptLibrary.updateWithU256(transcript, u2);
+        TranscriptLibrary.updateWithF(transcript, u2);
         TranscriptLibrary.updateWithG2(transcript, pt2);
 
         uint256 challenge_2 =  TranscriptLibrary.getChallenge(transcript);
diff --git a/src/contracts/tests/mod.rs b/src/contracts/tests/mod.rs
index 71e5496..3e0e7b9 100644
--- a/src/contracts/tests/mod.rs
+++ b/src/contracts/tests/mod.rs
@@ -21,6 +21,9 @@ mod crypto;
 #[cfg(test)]
 mod verifier;
 
+#[cfg(test)]
+mod transcript;
+
 pub type EthersClient = Arc<SignerMiddleware<Provider<Http>, Wallet<SigningKey>>>;
 
 pub async fn setup_eth_backend() -> (AnvilInstance, EthersClient) {
diff --git a/src/contracts/tests/semacaulk.rs b/src/contracts/tests/semacaulk.rs
index 03b1ee6..0f0d662 100644
--- a/src/contracts/tests/semacaulk.rs
+++ b/src/contracts/tests/semacaulk.rs
@@ -7,7 +7,7 @@ use crate::layouter::Layouter;
 use crate::mimc7::init_mimc7;
 use crate::prover::prover::{Prover, WitnessInput};
 use crate::prover::{Proof as SemacaulkProof, ProverPrecomputedData, ProvingKey, PublicData};
-use crate::setup::{load_lagrange_comms_from_file, load_srs_from_hex};
+use crate::setup::setup;
 use crate::verifier::Verifier as SemacaulkVerifier;
 use crate::{
     bn_solidity_utils::{f_to_u256, u256_to_f},
@@ -26,10 +26,7 @@ use ethers::core::utils::hex;
 use ethers::middleware::SignerMiddleware;
 use ethers::providers::Http;
 
-abigen!(
-    Semacaulk,
-    "./src/contracts/out/Semacaulk.sol/Semacaulk.json",
-);
+abigen!(Semacaulk, "./src/contracts/Semacaulk.json");
 
 type SemacaulkContract = semacaulk::Semacaulk<
     SignerMiddleware<
@@ -40,8 +37,8 @@ type SemacaulkContract = semacaulk::Semacaulk<
 
 pub async fn deploy_semacaulk(
     client: EthersClient,
-    srs_hex_filename: &str,
-    lagrange_comms_filename: &str,
+    log_2_table_size: usize,
+    ptau_filename: &str,
 ) -> (
     SemacaulkContract,
     Accumulator<Bn254>,
@@ -51,18 +48,16 @@ pub async fn deploy_semacaulk(
 ) {
     let zero = compute_zero_leaf::<Fr>();
 
-    // This file is generated by https://github.com/geometryresearch/export-ptau-points
-    // If you change this file, use `cargo run setup <table_size> <hex_filename> <lagrange_comms_out>`
-    // to regenerate the lagrangeCommsX file. Also remember to update Constants.sol.
-    let (srs_g1, srs_g2) = load_srs_from_hex(srs_hex_filename);
-    let lagrange_comms = load_lagrange_comms_from_file(lagrange_comms_filename);
+    let (pk, lagrange_comms) = setup(log_2_table_size, ptau_filename);
+    let srs_g1 = pk.srs_g1;
+    let srs_g2 = pk.srs_g2;
 
     let acc = Accumulator::<Bn254>::new(zero, &lagrange_comms);
     let empty_accumulator_x = f_to_u256::<Fq>(acc.point.x);
     let empty_accumulator_y = f_to_u256::<Fq>(acc.point.y);
 
     // Construct the tree of commitments to the Lagrange bases
-    let tree = compute_lagrange_tree::<Bn254>(&lagrange_comms);
+    let tree = compute_lagrange_tree::<Bn254>(&lagrange_comms.to_vec());
     let root = tree.root();
 
     // Deploy contract
@@ -85,9 +80,10 @@ pub async fn test_semacaulk_insert_and_broadcast() {
 
     // During development, remember to update Constants.sol's SRS values if you change the table
     // size!
-    let table_size = 2048;
+    let log_2_table_size = 10;
+    let table_size: usize = 1 << log_2_table_size;
 
-    let r = deploy_semacaulk(client, "./11.hex", "./lagrangeComms_11").await;
+    let r = deploy_semacaulk(client, log_2_table_size, "./11.ptau").await;
     let semacaulk_contract = r.0;
     let mut acc = r.1;
     let srs_g1 = r.2;
@@ -185,7 +181,7 @@ pub async fn test_semacaulk_insert_and_broadcast() {
     let accumulator = commit(&pk.srs_g1, &c).into_affine();
     assert_eq!(accumulator, acc.point);
 
-    let precomputed = ProverPrecomputedData::index(&pk, &mimc7.cts, index, &c, table_size);
+    let precomputed = ProverPrecomputedData::index(&pk, &mimc7.cts, &[index], &c, table_size);
 
     let witness = WitnessInput {
         identity_nullifier: identity_nullifiers[index],
@@ -274,7 +270,7 @@ fn p_to_p(p: &ProofForSemacaulk) -> Proof {
 
     let o = Openings {
         q_mimc: p.openings.q_mimc,
-        c: p.openings.c,
+        mimc_cts: p.openings.mimc_cts,
         quotient: p.openings.quotient,
         u_prime: p.openings.u_prime,
         p_1: p.openings.p_1,
@@ -309,9 +305,9 @@ fn p_to_p(p: &ProofForSemacaulk) -> Proof {
             x: p.commitments.key.x,
             y: p.commitments.key.y,
         },
-        c: G1Point {
-            x: p.commitments.c.x,
-            y: p.commitments.c.y,
+        mimc_cts: G1Point {
+            x: p.commitments.mimc_cts.x,
+            y: p.commitments.mimc_cts.y,
         },
         quotient: G1Point {
             x: p.commitments.quotient.x,
diff --git a/src/contracts/tests/transcript.rs b/src/contracts/tests/transcript.rs
index deda880..37cd995 100644
--- a/src/contracts/tests/transcript.rs
+++ b/src/contracts/tests/transcript.rs
@@ -1,23 +1,9 @@
-use std::ops::Neg;
-use ark_poly::{EvaluationDomain, GeneralEvaluationDomain};
-use ark_bn254::{Bn254, Fq12, Fr, G1Affine, G2Affine};
-use ark_ec::AffineCurve;
-use ark_ec::PairingEngine;
-use ark_ec::ProjectiveCurve;
-use ark_ff::BigInteger256;
-use ark_ff::Field;
-use ark_ff::One;
-use ark_ff::Zero;
-use ark_ff::{PrimeField, UniformRand};
-use ark_std::test_rng;
-use ethers::contract::abigen;
-use ethers::types::U256;
-use tokio::test;
 use super::setup_eth_backend;
+use crate::bn_solidity_utils::f_to_u256;
 use crate::transcript::Transcript;
-use crate::{
-    bn_solidity_utils::{f_to_u256, format_g1, format_g2},
-};
+use ark_bn254::{Fr, G1Affine, G2Affine};
+use ark_ec::AffineCurve;
+use ethers::contract::abigen;
 
 abigen!(
     TestTranscript,
@@ -46,27 +32,35 @@ pub async fn test_transcript() {
     let anvil = eth_backend.0;
     let client = eth_backend.1;
 
-    let contract = TestTranscript::deploy(client, ()).unwrap().send().await.unwrap();
+    let contract = TestTranscript::deploy(client, ())
+        .unwrap()
+        .send()
+        .await
+        .unwrap();
     let u1 = Fr::from(100);
     let u2 = Fr::from(200);
     let g1 = G1Affine::prime_subgroup_generator();
     let g2 = G2Affine::prime_subgroup_generator();
 
-    let (ch_contract_1, ch_contract_2) = contract.test_challenges(
-        f_to_u256(u1),
-        f_to_u256(u2),
-        g1_affine_to_g1point(&g1),
-        g2_affine_to_g2point(&g2),
-    ).call().await.unwrap();
+    let (ch_contract_1, ch_contract_2) = contract
+        .test_challenges(
+            f_to_u256(u1),
+            f_to_u256(u2),
+            g1_affine_to_g1point(&g1),
+            g2_affine_to_g2point(&g2),
+        )
+        .call()
+        .await
+        .unwrap();
 
     let mut transcript = Transcript::new_transcript();
 
-    transcript.update_with_u256(u1);
+    transcript.update_with_f(u1);
     transcript.update_with_g1(&g1);
 
     let challenge_1 = transcript.get_challenge();
 
-    transcript.update_with_u256(u2);
+    transcript.update_with_f(u2);
     transcript.update_with_g2(&g2);
 
     let challenge_2 = transcript.get_challenge();
diff --git a/src/contracts/tests/verifier.rs b/src/contracts/tests/verifier.rs
index b9e44a3..ad60f5e 100644
--- a/src/contracts/tests/verifier.rs
+++ b/src/contracts/tests/verifier.rs
@@ -1,14 +1,14 @@
 use super::setup_eth_backend;
 use crate::contracts::format::proof_for_verifier::{format_proof, ProofForVerifier};
 use crate::prover::prover::{Prover, WitnessInput};
-use crate::setup::load_srs_from_hex;
+use crate::setup::setup;
 use crate::verifier::Verifier as SemacaulkVerifier;
 use crate::{
     bn_solidity_utils::f_to_u256,
     kzg::commit,
     layouter::Layouter,
     mimc7::init_mimc7,
-    prover::{ProverPrecomputedData, ProvingKey, PublicData},
+    prover::{ProverPrecomputedData, PublicData},
 };
 use ark_bn254::{Bn254, Fr};
 use ark_ec::ProjectiveCurve;
@@ -29,7 +29,8 @@ abigen!(
 pub async fn test_semacaulk_verifier() {
     let mut rng = test_rng();
 
-    let table_size: usize = 2048;
+    let log_2_table_size = 11;
+    let table_size: usize = 1 << log_2_table_size;
     let domain = GeneralEvaluationDomain::<Fr>::new(table_size).unwrap();
 
     let mimc7 = init_mimc7::<Fr>();
@@ -57,13 +58,9 @@ pub async fn test_semacaulk_verifier() {
     identity_commitments[index] = identity_commitment;
     let c = DensePolynomial::from_coefficients_slice(&domain.ifft(&identity_commitments));
 
-    let (srs_g1, srs_g2) = load_srs_from_hex("./11.hex");
-    let pk = ProvingKey::<Bn254> {
-        srs_g1,
-        srs_g2: srs_g2.clone(),
-    };
+    let (pk, _) = setup(log_2_table_size, "./11.ptau");
 
-    let precomputed = ProverPrecomputedData::index(&pk, &mimc7.cts, index, &c, table_size);
+    let precomputed = ProverPrecomputedData::index(&pk, &mimc7.cts, &[index], &c, table_size);
 
     let witness = WitnessInput {
         identity_nullifier,
@@ -79,8 +76,6 @@ pub async fn test_semacaulk_verifier() {
         nullifier_hash,
         signal_hash,
     };
-    //println!("{}", pk.srs_g1[table_size].clone());
-    //println!("{}", srs_g2[1].clone());
 
     let proof = Prover::prove(
         &pk,
@@ -95,7 +90,7 @@ pub async fn test_semacaulk_verifier() {
     let is_valid = SemacaulkVerifier::verify(
         &proof,
         pk.srs_g1[table_size],
-        srs_g2[1],
+        pk.srs_g2[1],
         accumulator,
         &public_input,
     );
@@ -157,7 +152,7 @@ fn p_to_p(p: &ProofForVerifier) -> Proof {
 
     let o = Openings {
         q_mimc: p.openings.q_mimc,
-        c: p.openings.c,
+        mimc_cts: p.openings.mimc_cts,
         quotient: p.openings.quotient,
         u_prime: p.openings.u_prime,
         p_1: p.openings.p_1,
@@ -192,9 +187,9 @@ fn p_to_p(p: &ProofForVerifier) -> Proof {
             x: p.commitments.key.x,
             y: p.commitments.key.y,
         },
-        c: G1Point {
-            x: p.commitments.c.x,
-            y: p.commitments.c.y,
+        mimc_cts: G1Point {
+            x: p.commitments.mimc_cts.x,
+            y: p.commitments.mimc_cts.y,
         },
         quotient: G1Point {
             x: p.commitments.quotient.x,
diff --git a/src/demo/main.rs b/src/demo/main.rs
index baa84e2..dfdae58 100644
--- a/src/demo/main.rs
+++ b/src/demo/main.rs
@@ -7,10 +7,6 @@ use ark_std::{test_rng, Zero};
 use ethers::contract::abigen;
 use ethers::middleware::SignerMiddleware;
 use ethers::providers::Http;
-use std::env;
-use stopwatch::Stopwatch;
-//use ark_ec::ProjectiveCurve;
-//use semacaulk::kzg::commit;
 use semacaulk::accumulator::{compute_lagrange_tree, compute_zero_leaf, Accumulator};
 use semacaulk::contracts::compute_signal_hash;
 use semacaulk::contracts::format::proof_for_semacaulk::{format_proof, ProofForSemacaulk};
@@ -19,17 +15,16 @@ use semacaulk::layouter::Layouter;
 use semacaulk::mimc7::init_mimc7;
 use semacaulk::prover::prover::{Prover, WitnessInput};
 use semacaulk::prover::{Proof as SemacaulkProof, ProverPrecomputedData, ProvingKey, PublicData};
-use semacaulk::setup::{load_lagrange_comms_from_file, load_srs_from_hex};
+use semacaulk::setup::setup;
 use semacaulk::verifier::Verifier as SemacaulkVerifier;
 use semacaulk::{
     bn_solidity_utils::{f_to_u256, u256_to_f},
     keccak_tree::{flatten_proof, KeccakTree},
 };
+use std::env;
+use stopwatch::Stopwatch;
 
-abigen!(
-    SemacaulkContract,
-    "./src/contracts/out/Semacaulk.sol/Semacaulk.json",
-);
+abigen!(SemacaulkContract, "./src/contracts/Semacaulk.json");
 
 type SemacaulkContract = semacaulk_contract::SemacaulkContract<
     SignerMiddleware<
@@ -40,8 +35,8 @@ type SemacaulkContract = semacaulk_contract::SemacaulkContract<
 
 pub async fn deploy_semacaulk(
     client: EthersClient,
-    srs_hex_filename: &str,
-    lagrange_comms_filename: &str,
+    log_2_table_size: usize,
+    ptau_filename: &str,
 ) -> (
     SemacaulkContract,
     Accumulator<Bn254>,
@@ -54,15 +49,11 @@ pub async fn deploy_semacaulk(
     // This file is generated by https://github.com/geometryresearch/export-ptau-points
     // If you change this file, use `cargo run setup <table_size> <hex_filename> <lagrange_comms_out>` to regenerate the lagrangeCommsX file. Also remember to update Constants.sol.
     let sw = Stopwatch::start_new();
-    let (srs_g1, srs_g2) = load_srs_from_hex(srs_hex_filename);
-    println!("\tload_srs_from_hex() took {}ms", sw.elapsed_ms());
+    let (pk, lagrange_comms) = setup(log_2_table_size, ptau_filename);
+    let srs_g1 = pk.srs_g1;
+    let srs_g2 = pk.srs_g2;
 
-    let sw = Stopwatch::start_new();
-    let lagrange_comms = load_lagrange_comms_from_file(lagrange_comms_filename);
-    println!(
-        "\tload_lagrange_comms_from_file() took {}ms",
-        sw.elapsed_ms()
-    );
+    println!("\tsetup() took {}ms", sw.elapsed_ms());
 
     let acc = Accumulator::<Bn254>::new(zero, &lagrange_comms);
     let empty_accumulator_x = f_to_u256::<Fq>(acc.point.x);
@@ -87,16 +78,19 @@ pub async fn deploy_semacaulk(
 
 #[tokio::main]
 async fn main() {
-    // demo <log_2_table_size> <srs_hex_filename> <lagrange_comms_filename>
+    let args: Vec<String> = env::args().collect();
+    if args.len() < 2 {
+        println!("Usage: demo <log_2_table_size> <ptau_filename>");
+        return;
+    }
+    // demo <log_2_table_size> <ptau_filename>
     let _ = 1; // Change this value between builds to force the compiler to rebuild the binary properly
     let sw = Stopwatch::start_new();
     println!("Started");
 
-    let args: Vec<String> = env::args().collect();
-    assert!(args.len() > 3);
-    let log_2_table_size = &args[args.len() - 3];
-    let srs_hex_filename = &args[args.len() - 2];
-    let lagrange_comms_filename = &args[args.len() - 1];
+    assert!(args.len() > 2);
+    let log_2_table_size = &args[args.len() - 2];
+    let ptau_filename = &args[args.len() - 1];
 
     let log_2_table_size: usize = log_2_table_size.parse().unwrap();
     let table_size = 2u64.pow(log_2_table_size as u32) as usize;
@@ -108,7 +102,7 @@ async fn main() {
     let mut rng = test_rng();
     let mimc7 = init_mimc7::<Fr>();
 
-    let r = deploy_semacaulk(client, srs_hex_filename, lagrange_comms_filename).await;
+    let r = deploy_semacaulk(client, log_2_table_size, ptau_filename).await;
     println!("deploy_semacaulk() took {}ms", sw.elapsed_ms());
     let semacaulk_contract = r.0;
     let mut acc = r.1;
@@ -141,7 +135,6 @@ async fn main() {
 
         identity_nullifiers.push(identity_nullifier);
         identity_trapdoors.push(identity_trapdoor);
-        //identity_commitments.push(new_leaf);
         identity_commitments[index] = new_leaf;
 
         // Insert the leaf on chain
@@ -169,7 +162,7 @@ async fn main() {
     };
     let mut rng = test_rng();
 
-    let index = 1;
+    let index = 0;
     let nullifier_hash = mimc7.multi_hash(
         &[identity_nullifiers[index], external_nullifier],
         Fr::zero(),
@@ -187,7 +180,7 @@ async fn main() {
     let c = DensePolynomial::from_coefficients_slice(&domain.ifft(&identity_commitments));
 
     let sw = Stopwatch::start_new();
-    let precomputed = ProverPrecomputedData::index(&pk, &mimc7.cts, index, &c, table_size);
+    let precomputed = ProverPrecomputedData::index(&pk, &mimc7.cts, &[index], &c, table_size);
     println!("Precomputation took {}ms", sw.elapsed_ms());
 
     let sw = Stopwatch::start_new();
@@ -269,7 +262,7 @@ fn p_to_p(p: &ProofForSemacaulk) -> Proof {
 
     let o = Openings {
         q_mimc: p.openings.q_mimc,
-        c: p.openings.c,
+        mimc_cts: p.openings.mimc_cts,
         quotient: p.openings.quotient,
         u_prime: p.openings.u_prime,
         p_1: p.openings.p_1,
@@ -304,9 +297,9 @@ fn p_to_p(p: &ProofForSemacaulk) -> Proof {
             x: p.commitments.key.x,
             y: p.commitments.key.y,
         },
-        c: G1Point {
-            x: p.commitments.c.x,
-            y: p.commitments.c.y,
+        mimc_cts: G1Point {
+            x: p.commitments.mimc_cts.x,
+            y: p.commitments.mimc_cts.y,
         },
         quotient: G1Point {
             x: p.commitments.quotient.x,
diff --git a/src/gates/mod.rs b/src/gates/mod.rs
index a87732f..c4ff608 100644
--- a/src/gates/mod.rs
+++ b/src/gates/mod.rs
@@ -25,11 +25,11 @@ impl<F: PrimeField> Mimc7RoundGate<F> {
     }
 }
 
-pub struct KeyEquality<F: PrimeField> {
+pub struct KeyEqualityGate<F: PrimeField> {
     _f: PhantomData<F>,
 }
 
-impl<F: PrimeField> KeyEquality<F> {
+impl<F: PrimeField> KeyEqualityGate<F> {
     pub fn compute_in_coset(omega_i: usize, key: &[F], q_mimc: &[F]) -> F {
         let key_next = positive_rotation_in_coset(key, omega_i, 1, EXTENDED_DOMAIN_FACTOR);
         q_mimc[omega_i] * (key[omega_i] - key_next)
@@ -52,11 +52,11 @@ impl<F: PrimeField> KeyCopyGate<F> {
     }
 }
 
-pub struct NullifierGate<F: PrimeField> {
+pub struct NullifierHashGate<F: PrimeField> {
     _f: PhantomData<F>,
 }
 
-impl<F: PrimeField> NullifierGate<F> {
+impl<F: PrimeField> NullifierHashGate<F> {
     pub fn compute_in_coset(
         omega_i: usize,
         nullifier_external: &[F], // rename to w2?
diff --git a/src/layouter/mod.rs b/src/layouter/mod.rs
index 5143ad6..4ff2f51 100644
--- a/src/layouter/mod.rs
+++ b/src/layouter/mod.rs
@@ -77,7 +77,7 @@ impl<F: PrimeField> Layouter<F> {
         Self::blind(&mut identity_commitment_col, rng);
 
         //---------------------------------------------------------------------
-        // Assign the nullifier_external column
+        // Assign the external_nullifier column
         let mut external_nullifier_col = Vec::<F>::with_capacity(SUBGROUP_SIZE);
         external_nullifier_col.push(external_nullifier);
 
@@ -141,7 +141,7 @@ mod layouter_tests {
         let nullifier = mimc7.hash(identity_nullifier, Fr::zero());
         let identity_commitment =
             mimc7.multi_hash(&[identity_nullifier, identity_trapdoor], Fr::zero());
-        let nullifier_external =
+        let nullifier_hash =
             mimc7.multi_hash(&[identity_nullifier, external_nullifier], Fr::zero());
 
         let assignment = Layouter::assign(
@@ -197,7 +197,7 @@ mod layouter_tests {
 
         // Check that the public nullifier is calculated correctly
         assert_eq!(
-            nullifier_external,
+            nullifier_hash,
             assignment.external_nullifier[n_rounds]
                 + external_nullifier
                 + Fr::from(2u64) * assignment.key[0]
diff --git a/src/mimc7.rs b/src/mimc7.rs
index 9cc4f5b..102a590 100644
--- a/src/mimc7.rs
+++ b/src/mimc7.rs
@@ -53,15 +53,34 @@ impl<F: PrimeField> Mimc7<F> {
         r
     }
 
+    pub fn multi_hash_two(&self, arr: &[F], key: F) -> F {
+        assert_eq!(arr.len(), 2);
+        let mut r = key;
+        let h0 = self.hash(arr[0], r); // n round functions, then add key
+        r += arr[0] + h0;
+        let h1 = self.hash(arr[1], r); // n round functions, then add arr[0] + h0
+        r += arr[1] + h1;
+        r
+    }
+
     pub fn hash(&self, x: F, k: F) -> F {
-        let seven = [7u64, 0, 0, 0];
-        let mut round_digest = (x + k).pow(seven);
+        //let seven = [7u64, 0, 0, 0];
+        //let mut round_digest = (x + k).pow(seven);
+        //for i in 1..self.n_rounds {
+        //round_digest = (round_digest + self.cts[i] + k).pow(seven);
+        //}
+        let mut round_digest = self.round_function(0, x, k);
         for i in 1..self.n_rounds {
-            round_digest = (round_digest + self.cts[i] + k).pow(seven);
+            round_digest = self.round_function(i, round_digest, k);
         }
         round_digest + k
     }
 
+    fn round_function(&self, i: usize, digest: F, k: F) -> F {
+        let seven = [7u64, 0, 0, 0];
+        (digest + self.cts[i] + k).pow(seven)
+    }
+
     fn initialize_constants(seed: &str, n_rounds: usize) -> Vec<F> {
         let mut cts = Vec::<F>::with_capacity(n_rounds);
         cts.push(F::zero());
@@ -130,5 +149,8 @@ mod mimc7_tests {
                 "5233261170300319370386085858846328736737478911451874673953613863492170606314"
             )
         );
+
+        let hash2 = mimc7.multi_hash_two(&[F::from(1), F::from(2)], F::from(0));
+        assert_eq!(hash, hash2);
     }
 }
diff --git a/src/multiopen/prover.rs b/src/multiopen/prover.rs
index d4aab4d..7f58141 100644
--- a/src/multiopen/prover.rs
+++ b/src/multiopen/prover.rs
@@ -24,14 +24,14 @@ impl Prover {
         w2: &DensePolynomial<Fr>,
         key: &DensePolynomial<Fr>,
         q_mimc: &DensePolynomial<Fr>,
-        c: &DensePolynomial<Fr>,
+        mimc_cts: &DensePolynomial<Fr>,
         quotient: &DensePolynomial<Fr>,
         // caulk+ related polys
         u_prime: &DensePolynomial<Fr>,
         p1: &DensePolynomial<Fr>,
         p2: &DensePolynomial<Fr>,
         // proof specific information
-        v: Fr,
+        u_prime_opening: Fr,
         alpha: Fr,
         omega_alpha: Fr,
         omega_n_alpha: Fr,
@@ -50,7 +50,7 @@ impl Prover {
         // define qi-s
         let q1 = p1.clone();
         let q2 = q_mimc
-            + &(c * x1_powers[0])
+            + &(mimc_cts * x1_powers[0])
             + (quotient * x1_powers[1])
             + (u_prime * x1_powers[2])
             + (p2 * x1_powers[3]);
@@ -58,7 +58,7 @@ impl Prover {
         let q4 = w0 + &(w1 * x1_powers[0]) + (w2 * x1_powers[1]);
 
         // prepare vanishing polys
-        let z1 = DensePolynomial::from_coefficients_slice(&[-v, Fr::one()]);
+        let z1 = DensePolynomial::from_coefficients_slice(&[-u_prime_opening, Fr::one()]);
         let z2 = DensePolynomial::from_coefficients_slice(&[-alpha, Fr::one()]);
         let z3 = &z2 * &DensePolynomial::from_coefficients_slice(&[-omega_alpha, Fr::one()]);
         let z4 = &z3 * &DensePolynomial::from_coefficients_slice(&[-omega_n_alpha, Fr::one()]);
diff --git a/src/multiopen/verifier.rs b/src/multiopen/verifier.rs
index 822e806..9906519 100644
--- a/src/multiopen/verifier.rs
+++ b/src/multiopen/verifier.rs
@@ -157,9 +157,7 @@ impl Verifier {
             .take(4)
             .collect();
 
-        /* BEGIN: construct qi-s */
-
-        //q1
+        // q1
         let q1 = *p1;
         let q1_eval = p1_opening;
 
@@ -195,8 +193,6 @@ impl Verifier {
             w0_openings[2] + x1_powers[0] * w1_openings[2] + x1_powers[1] * w2_openings[2];
         let q4_evals = [q4_at_alpha, q4_at_omega_alpha, q4_at_omega_n_alpha];
 
-        /* END: construct qi-s */
-
         let (f1, f2, f3, f4) = Self::evaluate_fs(
             q1_eval,
             proof.q1_opening,
diff --git a/src/prover/mod.rs b/src/prover/mod.rs
index 3f51671..4b4dc61 100644
--- a/src/prover/mod.rs
+++ b/src/prover/mod.rs
@@ -17,19 +17,19 @@ pub mod precomputed;
 #[allow(clippy::module_inception)]
 pub mod prover;
 
-use crate::prover::precomputed::Precomputed;
+use crate::prover::precomputed::CaulkPlusPrecomputed;
 
 #[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
 pub struct Proof<E: PairingEngine> {
     pub(crate) multiopen_proof: MultiopenProof<E>,
-    pub(crate) openings: Openings<E>,
+    pub openings: Openings<E>,
     pub(crate) commitments: Commitments<E>,
 }
 
 #[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
 pub struct Openings<E: PairingEngine> {
-    pub(crate) q_mimc: E::Fr,
-    pub(crate) c: E::Fr,
+    pub q_mimc: E::Fr,
+    pub(crate) mimc_cts: E::Fr,
     pub(crate) quotient: E::Fr,
     pub(crate) u_prime: E::Fr,
     pub(crate) p1: E::Fr,
@@ -53,7 +53,7 @@ pub struct Commitments<E: PairingEngine> {
     pub(crate) w1: E::G1Affine,
     pub(crate) w2: E::G1Affine,
     pub(crate) key: E::G1Affine,
-    pub(crate) c: E::G1Affine,
+    pub(crate) mimc_cts: E::G1Affine,
     pub(crate) quotient: E::G1Affine,
     pub(crate) u_prime: E::G1Affine,
     pub(crate) zi: E::G1Affine,
@@ -67,23 +67,32 @@ pub struct Commitments<E: PairingEngine> {
 
 #[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
 pub struct ProverPrecomputedData<E: PairingEngine> {
-    pub(crate) c: DensePolynomial<E::Fr>, // mimc round constants poly
-    pub(crate) c_coset_evals: Vec<E::Fr>, // evaluations of mimc round constants over coset
+    pub(crate) mimc_cts: DensePolynomial<E::Fr>, // mimc round constants poly
+    pub(crate) mimc_cts_coset_evals: Vec<E::Fr>, // evaluations of mimc round constants over coset
     pub(crate) zh_inverse_coset_evals: Vec<E::Fr>, // evaluations of vanishing poly over coset
     pub(crate) q_mimc: DensePolynomial<E::Fr>,
     pub(crate) q_mimc_coset_evals: Vec<E::Fr>,
     pub(crate) l0_coset_evals: Vec<E::Fr>,
-    pub(crate) caulk_plus_precomputed: Precomputed<E>,
+    pub caulk_plus_precomputed: CaulkPlusPrecomputed<E>,
 }
 
 impl<E: PairingEngine> ProverPrecomputedData<E> {
+    /// Precompute everything (both fixed data, W1, and W2)
     pub fn index(
         pk: &ProvingKey<E>,
         mimc_round_constants: &Vec<E::Fr>,
-        index: usize,
+        indices: &[usize],
         c: &DensePolynomial<E::Fr>,
         table_size: usize,
     ) -> Self {
+        let mut p = ProverPrecomputedData::precompute_fixed(mimc_round_constants);
+        p.precompute_w1(pk, indices, c, table_size);
+        p.precompute_w2(pk, indices, table_size);
+        p
+    }
+
+    /// Precompute only fixed data
+    pub fn precompute_fixed(mimc_round_constants: &Vec<E::Fr>) -> Self {
         let domain = GeneralEvaluationDomain::<E::Fr>::new(SUBGROUP_SIZE).unwrap();
         let extended_coset_domain =
             GeneralEvaluationDomain::<E::Fr>::new(EXTENDED_DOMAIN_FACTOR * SUBGROUP_SIZE).unwrap();
@@ -93,16 +102,24 @@ impl<E: PairingEngine> ProverPrecomputedData<E> {
             compute_vanishing_poly_over_coset(extended_coset_domain, domain.size() as u64);
         ark_ff::batch_inversion(&mut zh_inverse_coset_evals);
 
-        // Compute c coset evals
+        // Compute mimc_cts coset evals
         assert_eq!(mimc_round_constants.len(), NUMBER_OF_MIMC_ROUNDS);
-        let mut c_evals = mimc_round_constants[..].to_vec();
+        let mut mimc_cts_evals = mimc_round_constants[..].to_vec();
         let mut to_append: Vec<E::Fr> = iter::repeat(E::Fr::from(DUMMY_VALUE))
-            .take(SUBGROUP_SIZE - c_evals.len())
+            .take(SUBGROUP_SIZE - mimc_cts_evals.len())
             .collect();
-        c_evals.append(&mut to_append);
+        mimc_cts_evals.append(&mut to_append);
 
-        let c_poly = DensePolynomial::from_coefficients_slice(&domain.ifft(&c_evals));
-        let c_coset_evals = extended_coset_domain.coset_fft(&c_poly);
+        // A polynomial over the multiplicative subgroup which evaluates to the MiMC7 round
+        // constants at each root of unity. The subgroup size is the number of MiMC7 rounds.
+        let mimc_cts_poly = DensePolynomial::from_coefficients_slice(&domain.ifft(&mimc_cts_evals));
+
+        // We first compute a polynomial which evaluates, at each root of unity in the subgroup
+        // domain, to a vector (of the size of the subgroup) consisting of the evaluations of the
+        // MiMC7 round constants, padded by dummy values. Next, we perform an FFT over the coset of
+        // the extended domain on the coefficients of this polynomial to obtain
+        // \\(\mathsf{mimc\\_cts\\_coset\\_evals}\\).
+        let mimc_cts_coset_evals = extended_coset_domain.coset_fft(&mimc_cts_poly);
 
         // Compute q_mimc coset evals
         let mut q_mimc_evals: Vec<E::Fr> = iter::repeat(E::Fr::one())
@@ -113,6 +130,8 @@ impl<E: PairingEngine> ProverPrecomputedData<E> {
             .collect();
         q_mimc_evals.append(&mut zeroes);
 
+        // A polynomial whose evaluations at the roots of unity over the subgroup domain of size
+        // 128 are 91 `1` values, followed by zeroes. It represents the q_mimc selector column.
         let q_mimc = DensePolynomial::from_coefficients_slice(&domain.ifft(&q_mimc_evals));
         let q_mimc_coset_evals = extended_coset_domain.coset_fft(&q_mimc);
 
@@ -124,21 +143,44 @@ impl<E: PairingEngine> ProverPrecomputedData<E> {
         let l0_coset_evals = extended_coset_domain.coset_fft(&l0);
 
         // Precompute w1 & w2 for the Caulk+ part of the proof
-        let domain_t = GeneralEvaluationDomain::new(table_size).unwrap();
-        let mut precomputed = Precomputed::<E>::empty();
-        precomputed.precompute_w1(&pk.srs_g2, &[index], c, &domain_t);
-        precomputed.precompute_w2(&pk.srs_g2, &[index], &domain_t);
+        //let domain_t = GeneralEvaluationDomain::new(table_size).unwrap();
+        let caulk_plus_precomputed = CaulkPlusPrecomputed::<E>::empty();
 
         Self {
-            c: c_poly,
-            c_coset_evals,
+            mimc_cts: mimc_cts_poly,
+            mimc_cts_coset_evals,
             zh_inverse_coset_evals,
             q_mimc,
             q_mimc_coset_evals,
             l0_coset_evals,
-            caulk_plus_precomputed: precomputed,
+            caulk_plus_precomputed,
         }
     }
+
+    /// Update one W1 commitment
+    pub fn update_w1(&mut self, index: usize, new_w1: E::G2Affine) {
+        self.caulk_plus_precomputed.w1_mapping.insert(index, new_w1);
+    }
+
+    /// Precompute the W1 commitments
+    pub fn precompute_w1(
+        &mut self,
+        pk: &ProvingKey<E>,
+        indices: &[usize],
+        c: &DensePolynomial<E::Fr>,
+        table_size: usize,
+    ) {
+        let domain_t = GeneralEvaluationDomain::new(table_size).unwrap();
+        self.caulk_plus_precomputed
+            .precompute_w1(&pk.srs_g2, indices, c, &domain_t);
+    }
+
+    /// Precompute the W2 commitments
+    pub fn precompute_w2(&mut self, pk: &ProvingKey<E>, indices: &[usize], table_size: usize) {
+        let domain_t = GeneralEvaluationDomain::new(table_size).unwrap();
+        self.caulk_plus_precomputed
+            .precompute_w2(&pk.srs_g2, indices, &domain_t);
+    }
 }
 
 pub struct ProvingKey<E: PairingEngine> {
diff --git a/src/prover/precomputed.rs b/src/prover/precomputed.rs
index 481da07..f5b8b86 100644
--- a/src/prover/precomputed.rs
+++ b/src/prover/precomputed.rs
@@ -17,18 +17,19 @@ use crate::kzg::commit;
    so we optimize precomputed data needed to store
 */
 #[derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug)]
-pub struct Precomputed<E: PairingEngine> {
-    w1_mapping: BTreeMap<usize, E::G2Affine>,
-    w2_mapping: BTreeMap<usize, E::G2Affine>,
+pub struct CaulkPlusPrecomputed<E: PairingEngine> {
+    pub(crate) w1_mapping: BTreeMap<usize, E::G2Affine>,
+    pub(crate) w2_mapping: BTreeMap<usize, E::G2Affine>,
 }
 
-impl<E: PairingEngine> Precomputed<E> {
+impl<E: PairingEngine> CaulkPlusPrecomputed<E> {
     pub fn empty() -> Self {
         Self {
             w1_mapping: BTreeMap::default(),
             w2_mapping: BTreeMap::default(),
         }
     }
+
     pub fn get_w1_i(&self, index: &usize) -> E::G2Affine {
         match self.w1_mapping.get(index) {
             Some(element) => *element,
@@ -50,12 +51,16 @@ impl<E: PairingEngine> Precomputed<E> {
         c: &DensePolynomial<E::Fr>,
         domain: &GeneralEvaluationDomain<E::Fr>,
     ) {
+        // As defined in the [Caulk+ paper, section 3](https://eprint.iacr.org/2022/957.pdf).
         for index in indices {
             let w_i = domain.element(*index);
             let mut num = c.clone();
             num[0] -= c.evaluate(&w_i);
 
+            // denom = (X - w_i)
             let denom = DensePolynomial::from_coefficients_slice(&[-w_i, E::Fr::one()]);
+
+            // w1_i = (C - c_i) / (X - w_i)
             let w1_i = &num / &denom;
             let w1_i = commit(srs, &w1_i);
             self.w1_mapping.insert(*index, w1_i.into());
@@ -68,6 +73,7 @@ impl<E: PairingEngine> Precomputed<E> {
         indices: &[usize],
         domain: &GeneralEvaluationDomain<E::Fr>,
     ) {
+        // As defined in the [Caulk+ paper, section 3](https://eprint.iacr.org/2022/957.pdf).
         let zh: DensePolynomial<_> = domain.vanishing_polynomial().into();
         for index in indices {
             let w2_i = &zh
@@ -94,9 +100,9 @@ mod precomputed_test {
     use rand::rngs::StdRng;
 
     use crate::kzg::{commit, unsafe_setup};
-    use crate::utils::construct_lagrange_basis;
+    use crate::utils::construct_lagrange_basis_polys;
 
-    use super::Precomputed;
+    use super::CaulkPlusPrecomputed;
 
     // TODO: make this as a macro
     fn to_field<F: Field>(evals: &[u64]) -> Vec<F> {
@@ -105,7 +111,7 @@ mod precomputed_test {
 
     // zH = w2 * zI
     fn compute_w2<E: PairingEngine>(
-        precomputed: &Precomputed<E>,
+        precomputed: &CaulkPlusPrecomputed<E>,
         indices: &[usize],
         domain: &GeneralEvaluationDomain<E::Fr>,
     ) -> E::G2Affine {
@@ -129,7 +135,7 @@ mod precomputed_test {
 
     // C - cI = zH * w1
     fn compute_w1<E: PairingEngine>(
-        precomputed: &Precomputed<E>,
+        precomputed: &CaulkPlusPrecomputed<E>,
         indices: &[usize],
         domain: &GeneralEvaluationDomain<E::Fr>,
     ) -> E::G2Affine {
@@ -164,7 +170,7 @@ mod precomputed_test {
 
         let indices = [1, 3, 4, 5, 7];
 
-        let mut precomputed = Precomputed::<Bn254>::empty();
+        let mut precomputed = CaulkPlusPrecomputed::<Bn254>::empty();
 
         precomputed.precompute_w2(&srs_g2, &indices, &domain);
 
@@ -191,7 +197,7 @@ mod precomputed_test {
 
         let indices = [1, 3, 4, 5, 7];
         let elems: Vec<_> = indices.iter().map(|&i| domain.element(i)).collect();
-        let t_bases = construct_lagrange_basis(&elems);
+        let t_bases = construct_lagrange_basis_polys(&elems);
 
         let c_evals = [12391, 3219031, 32131, 412331, 31231, 3213, 938532, 49802342];
         let c_evals = to_field::<F>(&c_evals);
@@ -216,7 +222,7 @@ mod precomputed_test {
         let c_commitment = commit(&srs_g1, &c);
         let ci_commitment = commit(&srs_g1, &ci);
 
-        let mut precomputed = Precomputed::<Bn254>::empty();
+        let mut precomputed = CaulkPlusPrecomputed::<Bn254>::empty();
 
         precomputed.precompute_w1(&srs_g2, &indices, &c, &domain);
 
@@ -249,7 +255,7 @@ mod precomputed_test {
 
         let indices = [1, 3, 4, 5, 7];
         let elems: Vec<_> = indices.iter().map(|&i| domain.element(i)).collect();
-        let t_bases = construct_lagrange_basis(&elems);
+        let t_bases = construct_lagrange_basis_polys(&elems);
 
         let c_evals = [12391, 3219031, 32131, 412331, 31231, 3213, 938532, 49802342];
         let c_evals = to_field::<F>(&c_evals);
@@ -267,7 +273,7 @@ mod precomputed_test {
         let c_commitment = commit(&srs_g1, &c);
         let ci_commitment = commit(&srs_g1, &ci);
 
-        let mut precomputed = Precomputed::<Bn254>::empty();
+        let mut precomputed = CaulkPlusPrecomputed::<Bn254>::empty();
 
         precomputed.precompute_w1(&srs_g2, &indices, &c, &domain);
         precomputed.precompute_w2(&srs_g2, &indices, &domain);
@@ -303,7 +309,7 @@ mod precomputed_test {
 
         let indices = [1, 3, 4, 5, 7];
         let elems: Vec<_> = indices.iter().map(|&i| domain.element(i)).collect();
-        let t_bases = construct_lagrange_basis(&elems);
+        let t_bases = construct_lagrange_basis_polys(&elems);
 
         let c_evals = [12391, 3219031, 32131, 412331, 31231, 3213, 938532, 49802342];
         let c_evals = to_field::<F>(&c_evals);
@@ -338,7 +344,7 @@ mod precomputed_test {
         let c_blinder = &DensePolynomial::from_coefficients_slice(&[r2, r3, r4]);
         let c_blinder_commitment = commit(&srs_g2, c_blinder);
 
-        let mut precomputed = Precomputed::<Bn254>::empty();
+        let mut precomputed = CaulkPlusPrecomputed::<Bn254>::empty();
 
         precomputed.precompute_w1(&srs_g2, &indices, &c, &domain);
         precomputed.precompute_w2(&srs_g2, &indices, &domain);
@@ -370,7 +376,7 @@ mod precomputed_test {
 
         let indices = [1, 3, 4, 5, 7];
         let elems: Vec<_> = indices.iter().map(|&i| domain.element(i)).collect();
-        let t_bases = construct_lagrange_basis(&elems);
+        let t_bases = construct_lagrange_basis_polys(&elems);
 
         let c_evals = [12391, 3219031, 32131, 412331, 31231, 3213, 938532, 49802342];
         let c_evals = to_field::<F>(&c_evals);
@@ -384,7 +390,7 @@ mod precomputed_test {
 
         let (_, srs_g2) = unsafe_setup::<Bn254, StdRng>(max_power, max_power, &mut rng);
 
-        let mut precomputed = Precomputed::<Bn254>::empty();
+        let mut precomputed = CaulkPlusPrecomputed::<Bn254>::empty();
 
         precomputed.precompute_w1(&srs_g2, &indices, &c, &domain);
         precomputed.precompute_w2(&srs_g2, &indices, &domain);
diff --git a/src/prover/prover.rs b/src/prover/prover.rs
index ce782fe..3b7ca86 100644
--- a/src/prover/prover.rs
+++ b/src/prover/prover.rs
@@ -13,12 +13,14 @@ use rand::RngCore;
 
 use crate::{
     constants::{EXTENDED_DOMAIN_FACTOR, NUMBER_OF_MIMC_ROUNDS, SUBGROUP_SIZE},
-    gates::{ExternalNullifierGate, KeyCopyGate, KeyEquality, Mimc7RoundGate, NullifierGate},
+    gates::{
+        ExternalNullifierGate, KeyCopyGate, KeyEqualityGate, Mimc7RoundGate, NullifierHashGate,
+    },
     kzg::commit,
     layouter::Assignment,
     multiopen::{prover::Prover as MultiopenProver, MultiopenProof},
     transcript::Transcript,
-    utils::construct_lagrange_basis,
+    utils::construct_lagrange_basis_polys,
     utils::shift_dense_poly,
 };
 
@@ -146,14 +148,13 @@ impl Prover {
 
         let (w0, key, w1, w2) = Self::assignment_round(&mut state);
 
-        transcript.round_1(
-            [&w0, &key, &w1, &w2],
-            [
-                public_input.external_nullifier,
-                public_input.nullifier_hash,
-                public_input.signal_hash,
-            ],
-        );
+        transcript.round_0_public_inputs([
+            public_input.external_nullifier,
+            public_input.nullifier_hash,
+            public_input.signal_hash,
+        ]);
+
+        transcript.round_1([&w0, &key, &w1, &w2]);
 
         let v = transcript.get_challenge();
 
@@ -186,7 +187,7 @@ impl Prover {
             key_openings_0,
             key_openings_1,
             q_mimc_opening,
-            c_opening,
+            mimc_cts_opening,
             quotient_opening,
             u_prime_opening,
             p1_opening,
@@ -198,9 +199,9 @@ impl Prover {
         //// Sanity check multiopen_proof
         //if cfg!(debug_assertions) {
         //let mut transcript = Transcript::new_transcript();
-        //transcript.update_with_u256(public_input.external_nullifier);
-        //transcript.update_with_u256(public_input.nullifier_hash);
-        //transcript.update_with_u256(public_input.signal_hash);
+        //transcript.update_with_f(public_input.external_nullifier);
+        //transcript.update_with_f(public_input.nullifier_hash);
+        //transcript.update_with_f(public_input.signal_hash);
         //transcript.update_with_g1(&w0);
         //transcript.update_with_g1(&key);
         //transcript.update_with_g1(&w1);
@@ -215,28 +216,28 @@ impl Prover {
         //transcript.update_with_g2(&w);
         //transcript.update_with_g1(&h);
         //let alpha = transcript.get_challenge();
-        //transcript.update_with_u256(w0_openings_0);
-        //transcript.update_with_u256(w0_openings_1);
-        //transcript.update_with_u256(w0_openings_2);
+        //transcript.update_with_f(w0_openings_0);
+        //transcript.update_with_f(w0_openings_1);
+        //transcript.update_with_f(w0_openings_2);
 
-        //transcript.update_with_u256(w1_openings_0);
-        //transcript.update_with_u256(w1_openings_1);
-        //transcript.update_with_u256(w1_openings_2);
+        //transcript.update_with_f(w1_openings_0);
+        //transcript.update_with_f(w1_openings_1);
+        //transcript.update_with_f(w1_openings_2);
 
-        //transcript.update_with_u256(w2_openings_0);
-        //transcript.update_with_u256(w2_openings_1);
-        //transcript.update_with_u256(w2_openings_2);
+        //transcript.update_with_f(w2_openings_0);
+        //transcript.update_with_f(w2_openings_1);
+        //transcript.update_with_f(w2_openings_2);
 
-        //transcript.update_with_u256(key_openings_0);
-        //transcript.update_with_u256(key_openings_1);
+        //transcript.update_with_f(key_openings_0);
+        //transcript.update_with_f(key_openings_1);
 
-        //transcript.update_with_u256(q_mimc_opening);
-        //transcript.update_with_u256(c_opening);
-        //transcript.update_with_u256(quotient_opening);
+        //transcript.update_with_f(q_mimc_opening);
+        //transcript.update_with_f(mimc_cts_opening);
+        //transcript.update_with_f(quotient_opening);
 
-        //transcript.update_with_u256(u_prime_opening);
-        //transcript.update_with_u256(p1_opening);
-        //transcript.update_with_u256(p2_opening);
+        //transcript.update_with_f(u_prime_opening);
+        //transcript.update_with_f(p1_opening);
+        //transcript.update_with_f(p2_opening);
 
         //let n = SUBGROUP_SIZE;
         //let domain = GeneralEvaluationDomain::new(n).unwrap();
@@ -260,7 +261,7 @@ impl Prover {
         //&q_mimc,
         //q_mimc_opening,
         //&c,
-        //c_opening,
+        //mimc_cts_opening,
         //&quotient,
         //quotient_opening,
         //&u_prime,
@@ -279,7 +280,7 @@ impl Prover {
         //}
 
         let q_mimc = commit(&state.proving_key.srs_g1, &state.precomputed.q_mimc).into_affine();
-        let c = commit(&state.proving_key.srs_g1, &state.precomputed.c).into_affine();
+        let mimc_cts = commit(&state.proving_key.srs_g1, &state.precomputed.mimc_cts).into_affine();
         let p1 = commit(&state.proving_key.srs_g1, &p1).into_affine();
         let p2 = commit(&state.proving_key.srs_g1, &p2).into_affine();
 
@@ -288,7 +289,7 @@ impl Prover {
             w1,
             w2,
             key,
-            c,
+            mimc_cts,
             quotient,
             u_prime,
             zi,
@@ -302,7 +303,7 @@ impl Prover {
 
         let openings = Openings {
             q_mimc: q_mimc_opening,
-            c: c_opening,
+            mimc_cts: mimc_cts_opening,
             quotient: quotient_opening,
             u_prime: u_prime_opening,
             p1: p1_opening,
@@ -397,7 +398,7 @@ impl Prover {
                     i,
                     &w0_coset_evals,
                     &zeroes,
-                    &state.precomputed.c_coset_evals,
+                    &state.precomputed.mimc_cts_coset_evals,
                     &state.precomputed.q_mimc_coset_evals,
                 );
 
@@ -407,7 +408,7 @@ impl Prover {
                     i,
                     &w1_coset_evals,
                     &key_coset_evals,
-                    &state.precomputed.c_coset_evals,
+                    &state.precomputed.mimc_cts_coset_evals,
                     &state.precomputed.q_mimc_coset_evals,
                 );
 
@@ -417,13 +418,13 @@ impl Prover {
                     i,
                     &w2_coset_evals,
                     &key_coset_evals,
-                    &state.precomputed.c_coset_evals,
+                    &state.precomputed.mimc_cts_coset_evals,
                     &state.precomputed.q_mimc_coset_evals,
                 );
 
             // Gate 3:
             numerator_coset_evals[i] += v_powers[3]
-                * KeyEquality::compute_in_coset(
+                * KeyEqualityGate::compute_in_coset(
                     i,
                     &key_coset_evals,
                     &state.precomputed.q_mimc_coset_evals,
@@ -440,7 +441,7 @@ impl Prover {
 
             // Gate 5:
             numerator_coset_evals[i] += v_powers[5]
-                * NullifierGate::compute_in_coset(
+                * NullifierHashGate::compute_in_coset(
                     i,
                     &w2_coset_evals,
                     &key_coset_evals,
@@ -511,7 +512,7 @@ impl Prover {
 
         // 2. compute lagrange basis polynomial t_i over w^j for j = index
         let omega = state.domain_t.element(state.witness.index);
-        let ts = construct_lagrange_basis(&[omega]);
+        let ts = construct_lagrange_basis_polys(&[omega]);
 
         // 3. define and mask zI`
         let mut zi = DensePolynomial::<E::Fr>::from_coefficients_slice(&[r1]);
@@ -669,7 +670,7 @@ impl Prover {
         let key = state.key.as_ref().unwrap();
         let quotient = state.quotient.as_ref().unwrap();
 
-        let c = &state.precomputed.c;
+        let mimc_cts = &state.precomputed.mimc_cts;
         let q_mimc = &state.precomputed.q_mimc;
 
         let zi = state.zi.as_ref().unwrap();
@@ -697,10 +698,9 @@ impl Prover {
             h_zv
         };
 
-        // compute all evaluations
-        let v = u_prime.evaluate(&alpha);
-
         // compute all openings
+        let u_prime_opening = u_prime.evaluate(&alpha);
+
         let w0_openings = [
             w0.evaluate(&alpha),
             w0.evaluate(&omega_alpha),
@@ -722,10 +722,9 @@ impl Prover {
         let key_openings = [key.evaluate(&alpha), key.evaluate(&omega_alpha)];
 
         let q_mimc_opening = q_mimc.evaluate(&alpha);
-        let c_opening = c.evaluate(&alpha);
+        let mimc_cts_opening = mimc_cts.evaluate(&alpha);
         let quotient_opening = quotient.evaluate(&alpha);
-        let u_prime_opening = v;
-        let p1_opening = p1.evaluate(&v);
+        let p1_opening = p1.evaluate(&u_prime_opening);
         let p2_opening = p2.evaluate(&alpha);
 
         assert_eq!(p2_opening, Fr::zero());
@@ -743,14 +742,14 @@ impl Prover {
             key_openings[0],
             key_openings[1],
             q_mimc_opening,
-            c_opening,
+            mimc_cts_opening,
             quotient_opening,
             u_prime_opening,
             p1_opening,
             p2_opening,
         ]);
 
-        // compute proof
+        // Compute the multiopen proof
         let m = MultiopenProver::prove(
             &state.proving_key.srs_g1,
             w0,
@@ -758,12 +757,12 @@ impl Prover {
             w2,
             key,
             q_mimc,
-            c,
+            mimc_cts,
             quotient,
             u_prime,
             &p1,
             &p2,
-            v,
+            u_prime_opening,
             alpha,
             omega_alpha,
             omega_n_alpha,
@@ -784,7 +783,7 @@ impl Prover {
             key_openings[0],
             key_openings[1],
             q_mimc_opening,
-            c_opening,
+            mimc_cts_opening,
             quotient_opening,
             u_prime_opening,
             p1_opening,
diff --git a/src/setup/main.rs b/src/setup/main.rs
index 99ea3da..e510534 100644
--- a/src/setup/main.rs
+++ b/src/setup/main.rs
@@ -1,4 +1,4 @@
-use semacaulk::bn_solidity_utils::f_to_hex_le;
+use semacaulk::bn_solidity_utils::{f_to_hex, f_to_hex_le};
 use semacaulk::setup::setup;
 use std::env;
 use std::fs::File;
@@ -6,20 +6,29 @@ use std::io::prelude::*;
 use std::io::LineWriter;
 
 /*
- * Usage: cargo run setup <table_size> <hex_filename> <lagrange_comms_out>
- * Reads the SRS G1 and G2 points from <hex_filename>, and writes the commitments to the Lagrange
+ * Usage: cargo run setup <table_size> <ptau_filename> <lagrange_comms_out>
+ * Reads the SRS G1 and G2 points from <ptau_filename>, and writes the commitments to the Lagrange
  * basis polynomials to <lagrange_comms_out>.
  */
 fn main() {
     let args: Vec<String> = env::args().collect();
+    if args.len() <= 3 {
+        println!("Usage: cargo run setup <table_size> <ptau_filename> <lagrange_comms_out>");
+        println!(
+            "Reads the SRS G1 and G2 points from <ptau_filename>, and writes the commitments to the Lagrange basis polynomials to <lagrange_comms_out>."
+        );
+        return;
+    }
     assert!(args.len() > 3);
     let log_2_table_size = &args[args.len() - 3];
-    let hex_filename = &args[args.len() - 2];
+    let ptau_filename = &args[args.len() - 2];
     let lagrange_comms_out = &args[args.len() - 1];
 
     let log_2_table_size: usize = log_2_table_size.parse().unwrap();
 
-    let (_pk, lagrange_comms) = setup(log_2_table_size, hex_filename.as_str());
+    let (pk, lagrange_comms) = setup(log_2_table_size, ptau_filename.as_str());
+    let srs_g1 = pk.srs_g1;
+    let srs_g2 = pk.srs_g2;
 
     let file = File::create(lagrange_comms_out).unwrap();
     let mut file = LineWriter::new(file);
@@ -30,4 +39,31 @@ fn main() {
         file.write_all(b"\n").unwrap();
     }
     file.flush().unwrap();
+
+    let table_size: usize = 2u64.pow(log_2_table_size as u32) as usize;
+    println!("Update Constants.sol with these values:");
+    println!(
+        "uint256 constant SRS_G1_T_X = 0x{};",
+        f_to_hex(srs_g1[table_size].x)
+    );
+    println!(
+        "uint256 constant SRS_G1_T_Y = 0x{};",
+        f_to_hex(srs_g1[table_size].y)
+    );
+    println!(
+        "uint256 constant SRS_G2_1_X_0 = 0x{};",
+        f_to_hex(srs_g2[1].x.c1)
+    );
+    println!(
+        "uint256 constant SRS_G2_1_X_1 = 0x{};",
+        f_to_hex(srs_g2[1].x.c0)
+    );
+    println!(
+        "uint256 constant SRS_G2_1_Y_0 = 0x{};",
+        f_to_hex(srs_g2[1].y.c1)
+    );
+    println!(
+        "uint256 constant SRS_G2_1_Y_1 = 0x{};",
+        f_to_hex(srs_g2[1].y.c0)
+    );
 }
diff --git a/src/setup/mod.rs b/src/setup/mod.rs
index 40bb38b..c6d7a35 100644
--- a/src/setup/mod.rs
+++ b/src/setup/mod.rs
@@ -1,5 +1,4 @@
 use crate::accumulator::commit_to_lagrange_bases;
-use crate::bn_solidity_utils::f_to_hex;
 use crate::prover::ProvingKey;
 use ark_bn254::{Bn254, Fq, Fq2, G1Affine, G2Affine};
 use ark_ff::bytes::FromBytes;
@@ -10,48 +9,16 @@ use std::path::Path;
 #[cfg(test)]
 pub mod tests;
 
-pub fn setup(
-    log_2_table_size: usize,
-    srs_hex_filename: &str,
-) -> (ProvingKey<Bn254>, Vec<G1Affine>) {
-    assert!(log_2_table_size < 28 && log_2_table_size > 0);
+pub fn setup(log_2_table_size: usize, ptau_filepath: &str) -> (ProvingKey<Bn254>, Vec<G1Affine>) {
+    assert!((10..28).contains(&log_2_table_size));
     let table_size: usize = 2u64.pow(log_2_table_size as u32) as usize;
+    let num_g1_points = table_size + 1;
+    let num_g2_points = table_size;
 
-    let (srs_g1, srs_g2) = load_srs_from_hex(srs_hex_filename);
-    println!("{}, {}", srs_g1.len(), table_size);
-    assert!(srs_g1.len() > table_size);
-    assert!(srs_g2.len() >= table_size);
+    let (srs_g1, srs_g2) =
+        ppot_rs::ptau::read(ptau_filepath, num_g1_points, num_g2_points).unwrap();
 
-    println!("Update Constants.sol with these values:");
-    println!(
-        "uint256 constant SRS_G1_T_X = 0x{};",
-        f_to_hex(srs_g1[table_size].x)
-    );
-    println!(
-        "uint256 constant SRS_G1_T_Y = 0x{};",
-        f_to_hex(srs_g1[table_size].y)
-    );
-    println!(
-        "uint256 constant SRS_G2_1_X_0 = 0x{};",
-        f_to_hex(srs_g2[1].x.c1)
-    );
-    println!(
-        "uint256 constant SRS_G2_1_X_1 = 0x{};",
-        f_to_hex(srs_g2[1].x.c0)
-    );
-    println!(
-        "uint256 constant SRS_G2_1_Y_0 = 0x{};",
-        f_to_hex(srs_g2[1].y.c1)
-    );
-    println!(
-        "uint256 constant SRS_G2_1_Y_1 = 0x{};",
-        f_to_hex(srs_g2[1].y.c0)
-    );
-
-    println!();
-    println!("Computing commitments to Lagrange basis polynomials...");
     let lagrange_comms = commit_to_lagrange_bases::<Bn254>(table_size, &srs_g1);
-
     (ProvingKey::<Bn254> { srs_g1, srs_g2 }, lagrange_comms)
 }
 
@@ -75,30 +42,6 @@ pub fn load_lagrange_comms_from_file(filename: &str) -> Vec<G1Affine> {
     lagrange_comms
 }
 
-pub fn load_srs_from_hex(filename: &str) -> (Vec<G1Affine>, Vec<G2Affine>) {
-    let mut srs_g1 = vec![];
-    let mut srs_g2 = vec![];
-    if let Ok(lines) = read_lines(filename) {
-        for line in lines {
-            let val = line.unwrap();
-            if val.len() == 128 {
-                let g1 = g1_str_to_g1(&val);
-                srs_g1.push(g1);
-            } else if val.len() == 256 {
-                let g2 = g2_str_to_g2(&val);
-                srs_g2.push(g2);
-            } else if val.is_empty() {
-                // do nothing
-            } else {
-                panic!("Invalid line detected - was this file generated correctly?");
-            }
-        }
-    }
-    assert!(!srs_g1.is_empty());
-    assert!(!srs_g2.is_empty());
-    (srs_g1, srs_g2)
-}
-
 pub fn hex_to_fq(val: &str) -> Fq {
     assert_eq!(val.len(), 64);
     let bytes_vec = hex::decode(val).unwrap();
diff --git a/src/setup/tests.rs b/src/setup/tests.rs
index 3abd9f3..7f12333 100644
--- a/src/setup/tests.rs
+++ b/src/setup/tests.rs
@@ -1,4 +1,4 @@
-use super::{g1_str_to_g1, g2_str_to_g2, load_srs_from_hex, setup};
+use super::{g1_str_to_g1, g2_str_to_g2, setup};
 
 #[test]
 pub fn test_g1() {
@@ -13,17 +13,15 @@ pub fn test_g2() {
     let g2_str = "edf692d95cbdde46ddda5ef7d422436779445c5e66006a42761e1f12efde0018c212f3aeb785e49712e7a9353349aaf1255dfb31b7bf60723a480d9293938e19aa7dfa6601cce64c7bd3430c69e7d1e38f40cb8d8071ab4aeb6d8cdba55ec8125b9722d1dcdaac55f38eb37033314bbc95330c69ad999eec75f05f58d0890609";
     let g2 = g2_str_to_g2(&String::from(g2_str));
     assert!(g2.is_on_curve());
-}
 
-#[test]
-pub fn test_load_hex() {
-    let (srs_g1, srs_g2) = load_srs_from_hex("./11.hex");
-    assert_eq!(srs_g1.len(), srs_g2.len() + 1);
+    let g2_str = "7fa3b682a9ca88c26d79614ba1983b2b9592ccff25bdeeb4f20a2b8dbafbd116267e64cba10106b2fe21069bdf1455802bec49d0d0166a675d5fc9d17ec43b0833a2d46d92dea96d2b0471181d6cd1ed8d08026bc9d358b1b1da0cb1011ee4011b90877c247ea9c4fc2312d977361e50949e426f27646d42f98ff36ae9ffe918";
+    let g2 = g2_str_to_g2(&String::from(g2_str));
+    assert!(g2.is_on_curve());
 }
 
 #[test]
 pub fn test_setup() {
-    let pk = setup(11, "./11.hex");
+    let pk = setup(11, "./11.ptau");
     assert_eq!(pk.0.srs_g1.len(), pk.0.srs_g2.len() + 1);
     assert_eq!(pk.1.len(), pk.0.srs_g2.len());
 }
diff --git a/src/tests/prover_and_verifier.rs b/src/tests/prover_and_verifier.rs
index 0805a3e..685dde0 100644
--- a/src/tests/prover_and_verifier.rs
+++ b/src/tests/prover_and_verifier.rs
@@ -1,29 +1,28 @@
 use crate::prover::prover::{Prover, WitnessInput};
-use crate::setup::load_srs_from_hex;
+use crate::setup::setup;
+use crate::utils::construct_lagrange_basis_poly;
 use crate::verifier::Verifier;
 use crate::{
     kzg::commit,
     layouter::Layouter,
     mimc7::init_mimc7,
-    prover::{ProverPrecomputedData, ProvingKey, PublicData},
+    prover::{ProverPrecomputedData, PublicData},
 };
 use ark_bn254::{Bn254, Fr};
-use ark_ec::ProjectiveCurve;
+use ark_ec::{AffineCurve, ProjectiveCurve};
 use ark_ff::{UniformRand, Zero};
 use ark_poly::{
-    univariate::DensePolynomial, EvaluationDomain, GeneralEvaluationDomain, UVPolynomial,
+    univariate::DensePolynomial, EvaluationDomain, GeneralEvaluationDomain, Polynomial,
+    UVPolynomial,
 };
-use ark_std::test_rng;
+use ark_std::{test_rng, One};
 
 #[test]
 pub fn test_prover_and_verifier() {
     let mut rng = test_rng();
-    let table_size: usize = 2048;
-    let (srs_g1, srs_g2) = load_srs_from_hex("./11.hex");
-    let pk = ProvingKey::<Bn254> {
-        srs_g1,
-        srs_g2: srs_g2.clone(),
-    };
+    let log_2_table_size = 10;
+    let table_size: usize = 1 << log_2_table_size;
+    let (pk, _) = setup(log_2_table_size, "./11.ptau");
 
     let domain = GeneralEvaluationDomain::<Fr>::new(table_size).unwrap();
 
@@ -52,7 +51,9 @@ pub fn test_prover_and_verifier() {
     identity_commitments[index] = identity_commitment;
     let c = DensePolynomial::from_coefficients_slice(&domain.ifft(&identity_commitments));
 
-    let precomputed = ProverPrecomputedData::index(&pk, &mimc7.cts, index, &c, table_size);
+    let mut precomputed = ProverPrecomputedData::precompute_fixed(&mimc7.cts);
+    precomputed.precompute_w1(&pk, &[index], &c, table_size);
+    precomputed.precompute_w2(&pk, &[index], table_size);
 
     let witness = WitnessInput {
         identity_nullifier,
@@ -82,10 +83,148 @@ pub fn test_prover_and_verifier() {
     let is_valid = Verifier::verify(
         &proof,
         pk.srs_g1[table_size],
-        srs_g2[1],
+        pk.srs_g2[1],
         accumulator,
         &public_input,
     );
 
     assert!(is_valid);
 }
+
+#[test]
+pub fn test_update_precomputed_w1() {
+    let mut rng = test_rng();
+    let log_2_table_size = 10;
+    let table_size: usize = 1 << log_2_table_size;
+    let (pk, lagrange_comms) = setup(log_2_table_size, "./11.ptau");
+    let zero = Fr::from(0);
+
+    let domain = GeneralEvaluationDomain::<Fr>::new(table_size).unwrap();
+
+    let mimc7 = init_mimc7::<Fr>();
+
+    // Alice's public and private inputs
+    let identity_nullifier = Fr::from(100u64);
+    let identity_trapdoor = Fr::from(200u64);
+    let external_nullifier = Fr::from(300u64);
+    let signal_hash = Fr::from(888u64);
+    let nullifier_hash = mimc7.multi_hash(&[identity_nullifier, external_nullifier], Fr::zero());
+    let identity_commitment =
+        mimc7.multi_hash(&[identity_nullifier, identity_trapdoor], Fr::zero());
+
+    let mut identity_commitments: Vec<_> = (0..table_size).map(|_| zero).collect();
+
+    // Alice inserts to index 0 and Bob inserts to index 1
+    let index_alice = 0;
+    let index_bob = 1;
+    identity_commitments[index_alice] = identity_commitment;
+
+    // Compute the accumulator
+    let accumulator_alice_poly =
+        DensePolynomial::from_coefficients_slice(&domain.ifft(&identity_commitments));
+
+    // Precompute
+    let mut precomputed = ProverPrecomputedData::index(
+        &pk,
+        &mimc7.cts,
+        &[index_alice, index_bob],
+        &accumulator_alice_poly,
+        table_size,
+    );
+
+    let accumulator_alice = commit(&pk.srs_g1, &accumulator_alice_poly).into_affine();
+
+    let identity_nullifier_bob = Fr::from(300u64);
+    let identity_trapdoor_bob = Fr::from(400u64);
+    let identity_commitment_bob =
+        mimc7.multi_hash(&[identity_nullifier_bob, identity_trapdoor_bob], Fr::zero());
+
+    // The identity commitment which Bob replaces
+    let original_bob = identity_commitments[index_bob];
+
+    // Check w1_alice
+    let w_old = precomputed.caulk_plus_precomputed.get_w1_i(&index_alice);
+    let w_i = domain.element(index_alice);
+    let denom = DensePolynomial::from_coefficients_slice(&[-w_i, Fr::one()]);
+    let mut num = accumulator_alice_poly.clone();
+    num[0] -= accumulator_alice_poly.evaluate(&w_i);
+    let p = &num / &denom;
+    let p_comm = commit(&pk.srs_g2, &p).into_affine();
+    assert_eq!(w_old, p_comm);
+
+    // Bob replaces the leaf at index_bob
+    identity_commitments[index_bob] = identity_commitment_bob;
+    let accumulator_bob_poly =
+        DensePolynomial::from_coefficients_slice(&domain.ifft(&identity_commitments));
+    let accumulator_bob = commit(&pk.srs_g1, &accumulator_bob_poly).into_affine();
+    assert_ne!(accumulator_alice, accumulator_bob);
+
+    // delta
+    let delta = identity_commitment_bob - original_bob;
+
+    // Check the new accumulator
+    let l_j_comm = lagrange_comms[index_bob];
+    let l_j_delta_comm = l_j_comm.mul(delta).into_affine();
+    let new_c = accumulator_alice + l_j_delta_comm;
+    assert_eq!(new_c, accumulator_bob);
+
+    // L_j(X) / (X - w_i)
+    let elems: Vec<Fr> = domain.elements().collect();
+    let l_j = construct_lagrange_basis_poly(&elems, index_bob);
+    let w_i = domain.element(index_alice);
+    let denom = DensePolynomial::from_coefficients_slice(&[-w_i, Fr::one()]);
+    let p = &l_j / &denom;
+    let p_comm = commit(&pk.srs_g2, &p).into_affine();
+
+    let delta_p_comm = p_comm.mul(delta);
+
+    let w_old = precomputed.caulk_plus_precomputed.get_w1_i(&index_alice);
+    let w_new = w_old + delta_p_comm.into();
+
+    // Use update_w1() to update Alice's precomputed data
+    precomputed.update_w1(index_alice, w_new);
+
+    // Generate proof for Alice
+    let witness = WitnessInput {
+        identity_nullifier,
+        identity_trapdoor,
+        identity_commitment,
+        index: index_alice,
+    };
+
+    let public_input = PublicData::<Bn254> {
+        accumulator: accumulator_bob,
+        external_nullifier,
+        nullifier_hash,
+        signal_hash,
+    };
+
+    let assignment = Layouter::assign(
+        identity_nullifier,
+        identity_trapdoor,
+        external_nullifier,
+        &mimc7.cts,
+        &mut rng,
+    );
+
+    let proof = Prover::prove(
+        &pk,
+        &witness,
+        &assignment,
+        &public_input,
+        &precomputed,
+        &mut rng,
+        table_size,
+    );
+
+    let is_valid = Verifier::verify(
+        &proof,
+        pk.srs_g1[table_size],
+        pk.srs_g2[1],
+        accumulator_bob,
+        &public_input,
+    );
+    assert!(is_valid);
+    /*
+     */
+}
diff --git a/src/transcript.rs b/src/transcript.rs
index 52df28a..192452d 100644
--- a/src/transcript.rs
+++ b/src/transcript.rs
@@ -21,10 +21,13 @@ impl Transcript {
         [0u8; 32]
     }
 
-    pub fn round_1(&mut self, g1_vals: [&G1Affine; 4], f_vals: [Fr; 3]) {
+    pub fn round_0_public_inputs(&mut self, f_vals: [Fr; 3]) {
         for val in f_vals {
-            self.update_with_u256(val);
+            self.update_with_f(val);
         }
+    }
+
+    pub fn round_1(&mut self, g1_vals: [&G1Affine; 4]) {
         for val in g1_vals {
             self.update_with_g1(val);
         }
@@ -43,7 +46,7 @@ impl Transcript {
 
     pub fn round_4(&mut self, f_vals: [Fr; 17]) {
         for val in f_vals {
-            self.update_with_u256(val);
+            self.update_with_f(val);
         }
     }
 
@@ -51,7 +54,7 @@ impl Transcript {
         self.update_with_g1(f_cm);
     }
 
-    pub fn update_with_u256(&mut self, x: Fr) {
+    pub fn update_with_f(&mut self, x: Fr) {
         let mut x_bytes = x.into_repr().to_bytes_be();
         self.data.append(&mut x_bytes);
     }
diff --git a/src/utils.rs b/src/utils.rs
index b7f4665..f6665dd 100644
--- a/src/utils.rs
+++ b/src/utils.rs
@@ -54,24 +54,34 @@ pub fn shift_dense_poly<F: Field>(
     DensePolynomial::from_coefficients_vec(coeffs)
 }
 
+pub fn construct_lagrange_basis_poly<F: FftField>(
+    evaluation_domain: &[F],
+    index: usize,
+) -> DensePolynomial<F> {
+    let mut l_i = DensePolynomial::from_coefficients_slice(&[F::one()]);
+    let x_i = evaluation_domain[index];
+
+    for (j, &x_j) in evaluation_domain.iter().enumerate() {
+        if j != index {
+            let xi_minus_xj_inv = (x_i - x_j).inverse().unwrap();
+            l_i = &l_i
+                * &DensePolynomial::from_coefficients_slice(&[
+                    -x_j * xi_minus_xj_inv,
+                    xi_minus_xj_inv,
+                ]);
+        }
+    }
+    l_i
+}
+
 // Compute the Lagrange basis polynomials in O(n^2) time. This is not recommended for domains of
 // size above 32.
-pub fn construct_lagrange_basis<F: FftField>(evaluation_domain: &[F]) -> Vec<DensePolynomial<F>> {
+pub fn construct_lagrange_basis_polys<F: FftField>(
+    evaluation_domain: &[F],
+) -> Vec<DensePolynomial<F>> {
     let mut bases = Vec::with_capacity(evaluation_domain.len());
     for i in 0..evaluation_domain.len() {
-        let mut l_i = DensePolynomial::from_coefficients_slice(&[F::one()]);
-        let x_i = evaluation_domain[i];
-
-        for (j, &x_j) in evaluation_domain.iter().enumerate() {
-            if j != i {
-                let xi_minus_xj_inv = (x_i - x_j).inverse().unwrap();
-                l_i = &l_i
-                    * &DensePolynomial::from_coefficients_slice(&[
-                        -x_j * xi_minus_xj_inv,
-                        xi_minus_xj_inv,
-                    ]);
-            }
-        }
+        let l_i = construct_lagrange_basis_poly(evaluation_domain, i);
 
         bases.push(l_i);
     }
@@ -113,7 +123,7 @@ pub fn is_pow_2(x: usize) -> bool {
 
 #[cfg(test)]
 mod util_tests {
-    use super::construct_lagrange_basis;
+    use super::construct_lagrange_basis_polys;
     use ark_bn254::Fr as F;
     use ark_ff::Zero;
     use ark_poly::{
@@ -126,7 +136,7 @@ mod util_tests {
         let domain = GeneralEvaluationDomain::<F>::new(domain_size).unwrap();
 
         let elems: Vec<F> = domain.elements().collect();
-        let bases = construct_lagrange_basis(&elems);
+        let bases = construct_lagrange_basis_polys(&elems);
         assert_eq!(bases.len(), domain.size());
 
         let to_field = |x: &u64| -> F { F::from(*x) };
@@ -152,13 +162,4 @@ mod util_tests {
 
         assert_eq!(f_from_bases, f_from_ifft);
     }
-
-    //#[test]
-    //fn test_lagrange_bases_speed() {
-    //let domain_size = 1024;
-    //let domain = GeneralEvaluationDomain::<F>::new(domain_size).unwrap();
-
-    //let elems: Vec<F> = domain.elements().collect();
-    //let bases = construct_lagrange_basis(&elems);
-    //}
 }
diff --git a/src/verifier/mod.rs b/src/verifier/mod.rs
index fabe168..7ad2f0b 100644
--- a/src/verifier/mod.rs
+++ b/src/verifier/mod.rs
@@ -26,15 +26,13 @@ impl Verifier {
         let mut transcript = Transcript::new_transcript();
 
         // Update transcript and derive challenges
-        transcript.round_1(
-            [
-                &proof.commitments.w0,
-                &proof.commitments.key,
-                &proof.commitments.w1,
-                &proof.commitments.w2,
-            ],
-            [external_nullifier, nullifier_hash, signal_hash],
-        );
+        transcript.round_0_public_inputs([external_nullifier, nullifier_hash, signal_hash]);
+        transcript.round_1([
+            &proof.commitments.w0,
+            &proof.commitments.key,
+            &proof.commitments.w1,
+            &proof.commitments.w2,
+        ]);
 
         let v = transcript.get_challenge();
 
@@ -63,7 +61,7 @@ impl Verifier {
         let key_openings = [proof.openings.key_0, proof.openings.key_1];
 
         let q_mimc_opening = proof.openings.q_mimc;
-        let c_opening = proof.openings.c;
+        let mimc_cts_opening = proof.openings.mimc_cts;
         let w0_openings = [
             proof.openings.w0_0,
             proof.openings.w0_1,
@@ -94,17 +92,18 @@ impl Verifier {
         // combination of the gate evaluations should equal
         let pow_7 = |x: Fr| x.pow([7, 0, 0, 0]);
 
-        // Gate 0: q_mimc_opening * ((w0_openings[0] + c_opening) ^ 7 - w0_openings[1])
-        let gate_0_eval = q_mimc_opening * (pow_7(w0_openings[0] + c_opening) - w0_openings[1]);
+        // Gate 0: q_mimc_opening * ((w0_openings[0] + mimc_cts_opening) ^ 7 - w0_openings[1])
+        let gate_0_eval =
+            q_mimc_opening * (pow_7(w0_openings[0] + mimc_cts_opening) - w0_openings[1]);
 
-        // Gate 1: q_mimc_opening * ((w1_openings[0] + key_openings[0] + c_opening) ^ 7 - w1_openings[1])
-        let gate_1_eval =
-            q_mimc_opening * (pow_7(w1_openings[0] + key_openings[0] + c_opening) - w1_openings[1]);
+        // Gate 1: q_mimc_opening * ((w1_openings[0] + key_openings[0] + mimc_cts_opening) ^ 7 - w1_openings[1])
+        let gate_1_eval = q_mimc_opening
+            * (pow_7(w1_openings[0] + key_openings[0] + mimc_cts_opening) - w1_openings[1]);
 
         // Gate 2:
-        // q_mimc_opening * ((w2_openings[0] + key_openings[0] + c_opening) ^ 7 - w2_openings[1])
-        let gate_2_eval =
-            q_mimc_opening * (pow_7(w2_openings[0] + key_openings[0] + c_opening) - w2_openings[1]);
+        // q_mimc_opening * ((w2_openings[0] + key_openings[0] + mimc_cts_opening) ^ 7 - w2_openings[1])
+        let gate_2_eval = q_mimc_opening
+            * (pow_7(w2_openings[0] + key_openings[0] + mimc_cts_opening) - w2_openings[1]);
 
         // Gate 3:
         // q_mimc_opening * (key_openings[0] - key_openings[1])
@@ -158,7 +157,7 @@ impl Verifier {
             proof.openings.key_0,
             proof.openings.key_1,
             q_mimc_opening,
-            c_opening,
+            mimc_cts_opening,
             proof.openings.quotient,
             proof.openings.u_prime,
             proof.openings.p1,
@@ -190,8 +189,8 @@ impl Verifier {
             &[proof.openings.key_0, proof.openings.key_1],
             &proof.commitments.q_mimc,
             q_mimc_opening,
-            &proof.commitments.c,
-            c_opening,
+            &proof.commitments.mimc_cts,
+            mimc_cts_opening,
             &proof.commitments.quotient,
             quotient_opening,
             &proof.commitments.u_prime,
@@ -221,13 +220,13 @@ impl Verifier {
         //
         // A: [1] is E::G2Affine::prime_subgroup_generator()
         //   A1:
-        //     C is accumulator
+        //     C is the accumulator
         //     ci is proof.commitments.ci
         //   A2:
         //     xi is hi_2
         //     (x^n - 1) is (public_input.srs_g1[common_input.domain_h.size()] + -E::G1Affine::prime_subgroup_generator())
         //   A3:
-        //   s is the separator challenge
+        //     s is the separator challenge
         //     zq is final_poly_proof.mul(x3)
         //     -y is g1.mul(final_poly_eval).neg()
         //     p is final_poly