diff --git a/compiled-contracts/ClaimCompressor.json b/compiled-contracts/ClaimCompressor.json
index f099f8ac9..1e99f81db 100644
--- a/compiled-contracts/ClaimCompressor.json
+++ b/compiled-contracts/ClaimCompressor.json
@@ -109,8 +109,8 @@
       "type": "function"
     }
   ],
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 }
diff --git a/compiled-contracts/FflonkVerifier.json b/compiled-contracts/FflonkVerifier.json
index f20d5cd04..484680628 100644
--- a/compiled-contracts/FflonkVerifier.json
+++ b/compiled-contracts/FflonkVerifier.json
@@ -28,8 +28,8 @@
       "type": "function"
     }
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   "linkReferences": {},
   "deployedLinkReferences": {}
 }
diff --git a/compiled-contracts/PolygonRollupManager.json b/compiled-contracts/PolygonRollupManager.json
index a65f1c14c..ee90e4f69 100644
--- a/compiled-contracts/PolygonRollupManager.json
+++ b/compiled-contracts/PolygonRollupManager.json
@@ -1965,8 +1965,8 @@
       "type": "function"
     }
   ],
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   "linkReferences": {},
   "deployedLinkReferences": {}
 }
diff --git a/compiled-contracts/PolygonRollupManagerMock.json b/compiled-contracts/PolygonRollupManagerMock.json
index f24b33b24..5dc98718f 100644
--- a/compiled-contracts/PolygonRollupManagerMock.json
+++ b/compiled-contracts/PolygonRollupManagerMock.json
@@ -2016,8 +2016,8 @@
       "type": "function"
     }
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   "linkReferences": {},
   "deployedLinkReferences": {}
 }
diff --git a/compiled-contracts/PolygonRollupManagerMockInternalTest.json b/compiled-contracts/PolygonRollupManagerMockInternalTest.json
index c451d1493..51771aefc 100644
--- a/compiled-contracts/PolygonRollupManagerMockInternalTest.json
+++ b/compiled-contracts/PolygonRollupManagerMockInternalTest.json
@@ -1965,8 +1965,8 @@
       "type": "function"
     }
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   "linkReferences": {},
   "deployedLinkReferences": {}
 }
diff --git a/compiled-contracts/PolygonValidiumEtrog.json b/compiled-contracts/PolygonValidiumEtrog.json
index 0a8e6a655..520a989a5 100644
--- a/compiled-contracts/PolygonValidiumEtrog.json
+++ b/compiled-contracts/PolygonValidiumEtrog.json
@@ -1304,8 +1304,8 @@
       "type": "function"
     }
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   "linkReferences": {},
   "deployedLinkReferences": {}
 }
diff --git a/compiled-contracts/PolygonZkEVMEtrog.json b/compiled-contracts/PolygonZkEVMEtrog.json
index 174b2e72e..55c1adc96 100644
--- a/compiled-contracts/PolygonZkEVMEtrog.json
+++ b/compiled-contracts/PolygonZkEVMEtrog.json
@@ -1168,8 +1168,8 @@
       "type": "function"
     }
   ],
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   "linkReferences": {},
   "deployedLinkReferences": {}
 }
diff --git a/compiled-contracts/PolygonZkEVMEtrogPrevious.json b/compiled-contracts/PolygonZkEVMEtrogPrevious.json
index f1d9486e0..ee0fabec8 100644
--- a/compiled-contracts/PolygonZkEVMEtrogPrevious.json
+++ b/compiled-contracts/PolygonZkEVMEtrogPrevious.json
@@ -1145,8 +1145,8 @@
       "type": "function"
     }
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   "linkReferences": {},
   "deployedLinkReferences": {}
 }
diff --git a/compiled-contracts/PolygonZkEVMExistentEtrog.json b/compiled-contracts/PolygonZkEVMExistentEtrog.json
index 364d6f87b..d8594c2e7 100644
--- a/compiled-contracts/PolygonZkEVMExistentEtrog.json
+++ b/compiled-contracts/PolygonZkEVMExistentEtrog.json
@@ -1245,8 +1245,8 @@
       "type": "function"
     }
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   "linkReferences": {},
   "deployedLinkReferences": {}
 }
diff --git a/contracts/verifiers/FflonkVerifier_10.sol b/contracts/verifiers/FflonkVerifier_10.sol
new file mode 100644
index 000000000..536235e08
--- /dev/null
+++ b/contracts/verifiers/FflonkVerifier_10.sol
@@ -0,0 +1,1244 @@
+// SPDX-License-Identifier: GPL-3.0
+/*
+    Copyright 2021 0KIMS association.
+
+    This file is generated with [snarkJS](https://github.com/iden3/snarkjs).
+
+    snarkJS is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    snarkJS is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with snarkJS. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+pragma solidity >=0.7.0 <0.9.0;
+
+contract FflonkVerifier_10 {
+    uint32 constant n     = 16777216; // Domain size
+
+    // Verification Key data
+    uint256 constant k1   = 2;   // Plonk k1 multiplicative factor to force distinct cosets of H
+    uint256 constant k2   = 3;   // Plonk k2 multiplicative factor to force distinct cosets of H
+
+    // OMEGAS
+    // Omega, Omega^{1/3}
+    uint256 constant w1   = 5709868443893258075976348696661355716898495876243883251619397131511003808859;
+    uint256 constant wr   = 18200100796661656210024324131237448517259556535315737226009542456080026430510;
+    // Omega_3, Omega_3^2
+    uint256 constant w3   = 21888242871839275217838484774961031246154997185409878258781734729429964517155;
+    uint256 constant w3_2 = 4407920970296243842393367215006156084916469457145843978461;
+    // Omega_4, Omega_4^2, Omega_4^3
+    uint256 constant w4   = 21888242871839275217838484774961031246007050428528088939761107053157389710902;
+    uint256 constant w4_2 = 21888242871839275222246405745257275088548364400416034343698204186575808495616;
+    uint256 constant w4_3 = 4407920970296243842541313971887945403937097133418418784715;
+    // Omega_8, Omega_8^2, Omega_8^3, Omega_8^4, Omega_8^5, Omega_8^6, Omega_8^7
+    uint256 constant w8_1 = 19540430494807482326159819597004422086093766032135589407132600596362845576832;
+    uint256 constant w8_2 = 21888242871839275217838484774961031246007050428528088939761107053157389710902;
+    uint256 constant w8_3 = 13274704216607947843011480449124596415239537050559949017414504948711435969894;
+    uint256 constant w8_4 = 21888242871839275222246405745257275088548364400416034343698204186575808495616;
+    uint256 constant w8_5 = 2347812377031792896086586148252853002454598368280444936565603590212962918785;
+    uint256 constant w8_6 = 4407920970296243842541313971887945403937097133418418784715;
+    uint256 constant w8_7 = 8613538655231327379234925296132678673308827349856085326283699237864372525723;
+
+    // Verifier preprocessed input C_0(x)·[1]_1
+    uint256 constant C0x  = 1994511655043659082795852683195380325378879257059488547998206007926469246776;
+    uint256 constant C0y  = 21654483303940956161215913593419782322836269247276039101149437960660654437463;
+
+    // Verifier preprocessed input x·[1]_2
+    uint256 constant X2x1 = 21831381940315734285607113342023901060522397560371972897001948545212302161822;
+    uint256 constant X2x2 = 17231025384763736816414546592865244497437017442647097510447326538965263639101;
+    uint256 constant X2y1 = 2388026358213174446665280700919698872609886601280537296205114254867301080648;
+    uint256 constant X2y2 = 11507326595632554467052522095592665270651932854513688777769618397986436103170;
+
+    // Scalar field size
+    uint256 constant q    = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
+    // Base field size
+    uint256 constant qf   = 21888242871839275222246405745257275088696311157297823662689037894645226208583;
+    // [1]_1
+    uint256 constant G1x  = 1;
+    uint256 constant G1y  = 2;
+    // [1]_2
+    uint256 constant G2x1 = 10857046999023057135944570762232829481370756359578518086990519993285655852781;
+    uint256 constant G2x2 = 11559732032986387107991004021392285783925812861821192530917403151452391805634;
+    uint256 constant G2y1 = 8495653923123431417604973247489272438418190587263600148770280649306958101930;
+    uint256 constant G2y2 = 4082367875863433681332203403145435568316851327593401208105741076214120093531;
+
+    // Proof calldata
+    // Byte offset of every parameter of the calldata
+    // Polynomial commitments
+    uint16 constant pC1       = 4 + 0;     // [C1]_1
+    uint16 constant pC2       = 4 + 32*2;  // [C2]_1
+    uint16 constant pW1       = 4 + 32*4;  // [W]_1
+    uint16 constant pW2       = 4 + 32*6;  // [W']_1
+    // Opening evaluations
+    uint16 constant pEval_ql  = 4 + 32*8;  // q_L(xi)
+    uint16 constant pEval_qr  = 4 + 32*9;  // q_R(xi)
+    uint16 constant pEval_qm  = 4 + 32*10; // q_M(xi)
+    uint16 constant pEval_qo  = 4 + 32*11; // q_O(xi)
+    uint16 constant pEval_qc  = 4 + 32*12; // q_C(xi)
+    uint16 constant pEval_s1  = 4 + 32*13; // S_{sigma_1}(xi)
+    uint16 constant pEval_s2  = 4 + 32*14; // S_{sigma_2}(xi)
+    uint16 constant pEval_s3  = 4 + 32*15; // S_{sigma_3}(xi)
+    uint16 constant pEval_a   = 4 + 32*16; // a(xi)
+    uint16 constant pEval_b   = 4 + 32*17; // b(xi)
+    uint16 constant pEval_c   = 4 + 32*18; // c(xi)
+    uint16 constant pEval_z   = 4 + 32*19; // z(xi)
+    uint16 constant pEval_zw  = 4 + 32*20; // z_omega(xi)
+    uint16 constant pEval_t1w = 4 + 32*21; // T_1(xi omega)
+    uint16 constant pEval_t2w = 4 + 32*22; // T_2(xi omega)
+    uint16 constant pEval_inv = 4 + 32*23; // inv(batch) sent by the prover to avoid any inverse calculation to save gas,
+                                           // we check the correctness of the inv(batch) by computing batch
+                                           // and checking inv(batch) * batch == 1
+
+    // Memory data
+    // Challenges
+    uint16 constant pAlpha   = 0;   // alpha challenge
+    uint16 constant pBeta    = 32;  // beta challenge
+    uint16 constant pGamma   = 64;  // gamma challenge
+    uint16 constant pY       = 96;  // y challenge
+    uint16 constant pXiSeed  = 128; // xi seed, from this value we compute xi = xiSeed^24
+    uint16 constant pXiSeed2 = 160; // (xi seed)^2
+    uint16 constant pXi      = 192; // xi challenge
+
+    // Roots
+    // S_0 = roots_8(xi) = { h_0, h_0w_8, h_0w_8^2, h_0w_8^3, h_0w_8^4, h_0w_8^5, h_0w_8^6, h_0w_8^7 }
+    uint16 constant pH0w8_0 = 224;
+    uint16 constant pH0w8_1 = 256;
+    uint16 constant pH0w8_2 = 288;
+    uint16 constant pH0w8_3 = 320;
+    uint16 constant pH0w8_4 = 352;
+    uint16 constant pH0w8_5 = 384;
+    uint16 constant pH0w8_6 = 416;
+    uint16 constant pH0w8_7 = 448;
+
+    // S_1 = roots_4(xi) = { h_1, h_1w_4, h_1w_4^2, h_1w_4^3 }
+    uint16 constant pH1w4_0 = 480;
+    uint16 constant pH1w4_1 = 512;
+    uint16 constant pH1w4_2 = 544;
+    uint16 constant pH1w4_3 = 576;
+
+    // S_2 = roots_3(xi) U roots_3(xi omega)
+    // roots_3(xi) = { h_2, h_2w_3, h_2w_3^2 }
+    uint16 constant pH2w3_0 = 608;
+    uint16 constant pH2w3_1 = 640;
+    uint16 constant pH2w3_2 = 672;
+    // roots_3(xi omega) = { h_3, h_3w_3, h_3w_3^2 }
+    uint16 constant pH3w3_0 = 704;
+    uint16 constant pH3w3_1 = 736;
+    uint16 constant pH3w3_2 = 768;
+
+    uint16 constant pPi     = 800; // PI(xi)
+    uint16 constant pR0     = 832; // r0(y)
+    uint16 constant pR1     = 864; // r1(y)
+    uint16 constant pR2     = 896; // r2(y)
+
+    uint16 constant pF      = 928;  // [F]_1, 64 bytes
+    uint16 constant pE      = 992;  // [E]_1, 64 bytes
+    uint16 constant pJ      = 1056; // [J]_1, 64 bytes
+
+    uint16 constant pZh     = 1184; // Z_H(xi)
+    // From this point we write all the variables that must be computed using the Montgomery batch inversion
+    uint16 constant pZhInv  = 1216; // 1/Z_H(xi)
+    uint16 constant pDenH1  = 1248; // 1/( (y-h_1w_4) (y-h_1w_4^2) (y-h_1w_4^3) (y-h_1w_4^4) )
+    uint16 constant pDenH2  = 1280; // 1/( (y-h_2w_3) (y-h_2w_3^2) (y-h_2w_3^3) (y-h_3w_3) (y-h_3w_3^2) (y-h_3w_3^3) )
+    uint16 constant pLiS0Inv = 1312; // Reserve 8 * 32 bytes to compute r_0(X)
+    uint16 constant pLiS1Inv = 1568; // Reserve 4 * 32 bytes to compute r_1(X)
+    uint16 constant pLiS2Inv = 1696; // Reserve 6 * 32 bytes to compute r_2(X)
+    // Lagrange evaluations
+    
+    uint16 constant pEval_l1 = 1888;
+    
+    
+    uint16 constant lastMem = 1920;
+     
+
+    function verifyProof(bytes32[24] calldata proof, uint256[1] calldata pubSignals) public view returns (bool) {
+        assembly {
+            // Computes the inverse of an array of values
+            // See https://vitalik.ca/general/2018/07/21/starks_part_3.html in section where explain fields operations
+            // To save the inverse to be computed on chain the prover sends the inverse as an evaluation in commits.eval_inv
+            function inverseArray(pMem) {
+
+                let pAux := mload(0x40)     // Point to the next free position
+                let acc := mload(add(pMem,pZhInv))       // Read the first element
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pDenH1)), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pDenH2)), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pLiS0Inv)), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 32))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 64))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 96))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 128))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 160))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 192))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 224))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pLiS1Inv)), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 32))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 64))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 96))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pLiS2Inv)), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 32))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 64))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 96))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 128))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 160))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pEval_l1)), q)
+                mstore(pAux, acc)
+
+
+                let inv := calldataload(pEval_inv)
+
+                // Before using the inverse sent by the prover the verifier checks inv(batch) * batch === 1
+                if iszero(eq(1, mulmod(acc, inv, q))) {
+                    mstore(0, 0)
+                    return(0,0x20)
+                }
+
+                acc := inv
+
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pEval_l1)), q)
+                mstore(add(pMem, pEval_l1), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 160))), q)
+                mstore(add(pMem, add(pLiS2Inv, 160)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 128))), q)
+                mstore(add(pMem, add(pLiS2Inv, 128)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 96))), q)
+                mstore(add(pMem, add(pLiS2Inv, 96)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 64))), q)
+                mstore(add(pMem, add(pLiS2Inv, 64)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 32))), q)
+                mstore(add(pMem, add(pLiS2Inv, 32)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pLiS2Inv)), q)
+                mstore(add(pMem, pLiS2Inv), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 96))), q)
+                mstore(add(pMem, add(pLiS1Inv, 96)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 64))), q)
+                mstore(add(pMem, add(pLiS1Inv, 64)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 32))), q)
+                mstore(add(pMem, add(pLiS1Inv, 32)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pLiS1Inv)), q)
+                mstore(add(pMem, pLiS1Inv), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 224))), q)
+                mstore(add(pMem, add(pLiS0Inv, 224)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 192))), q)
+                mstore(add(pMem, add(pLiS0Inv, 192)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 160))), q)
+                mstore(add(pMem, add(pLiS0Inv, 160)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 128))), q)
+                mstore(add(pMem, add(pLiS0Inv, 128)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 96))), q)
+                mstore(add(pMem, add(pLiS0Inv, 96)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 64))), q)
+                mstore(add(pMem, add(pLiS0Inv, 64)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 32))), q)
+                mstore(add(pMem, add(pLiS0Inv, 32)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pLiS0Inv)), q)
+                mstore(add(pMem, pLiS0Inv), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pDenH2)), q)
+                mstore(add(pMem, pDenH2), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pDenH1)), q)
+                mstore(add(pMem, pDenH1), inv)
+
+                mstore(add(pMem, pZhInv), acc)
+            }
+
+            function checkField(v) {
+                if iszero(lt(v, q)) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+            }
+
+            function checkPointBelongsToBN128Curve(p) {
+                let x := calldataload(p)
+                let y := calldataload(add(p, 32))
+
+                // Check that the point is on the curve
+                // y^2 = x^3 + 3
+                let x3_3 := addmod(mulmod(x, mulmod(x, x, qf), qf), 3, qf)
+                let y2 := mulmod(y, y, qf)
+
+                if iszero(eq(x3_3, y2)) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+            }  
+            
+            // Validate all the evaluations sent by the prover ∈ F
+            function checkInput() {
+                // Check proof commitments fullfill bn128 curve equation Y^2 = X^3 + 3
+                checkPointBelongsToBN128Curve(pC1)
+                checkPointBelongsToBN128Curve(pC2)
+                checkPointBelongsToBN128Curve(pW1)
+                checkPointBelongsToBN128Curve(pW2)
+
+                checkField(calldataload(pEval_ql))
+                checkField(calldataload(pEval_qr))
+                checkField(calldataload(pEval_qm))
+                checkField(calldataload(pEval_qo))
+                checkField(calldataload(pEval_qc))
+                checkField(calldataload(pEval_s1))
+                checkField(calldataload(pEval_s2))
+                checkField(calldataload(pEval_s3))
+                checkField(calldataload(pEval_a))
+                checkField(calldataload(pEval_b))
+                checkField(calldataload(pEval_c))
+                checkField(calldataload(pEval_z))
+                checkField(calldataload(pEval_zw))
+                checkField(calldataload(pEval_t1w))
+                checkField(calldataload(pEval_t2w))
+                checkField(calldataload(pEval_inv))
+
+                // Points are checked in the point operations precompiled smart contracts
+            }
+
+            function computeChallenges(pMem, pPublic) {
+                // Compute challenge.beta & challenge.gamma
+                mstore(add(pMem, 1920 ), C0x)
+                mstore(add(pMem, 1952 ), C0y)
+
+                mstore(add(pMem, 1984), calldataload(pPublic))
+                
+                
+
+                mstore(add(pMem, 2016 ),  calldataload(pC1))
+                mstore(add(pMem, 2048 ),  calldataload(add(pC1, 32)))
+
+                mstore(add(pMem, pBeta),  mod(keccak256(add(pMem, lastMem), 160), q))
+                mstore(add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q))
+
+                // Get xiSeed & xiSeed2
+                mstore(add(pMem, lastMem), mload(add(pMem, pGamma)))
+                mstore(add(pMem, 1952), calldataload(pC2))
+                mstore(add(pMem, 1984), calldataload(add(pC2, 32)))
+                let xiSeed := mod(keccak256(add(pMem, lastMem), 96), q)
+
+                mstore(add(pMem, pXiSeed), xiSeed)
+                mstore(add(pMem, pXiSeed2), mulmod(xiSeed, xiSeed, q))
+
+                // Compute roots.S0.h0w8
+                mstore(add(pMem, pH0w8_0), mulmod(mload(add(pMem, pXiSeed2)), mload(add(pMem, pXiSeed)), q))
+                mstore(add(pMem, pH0w8_1), mulmod(mload(add(pMem, pH0w8_0)), w8_1, q))
+                mstore(add(pMem, pH0w8_2), mulmod(mload(add(pMem, pH0w8_0)), w8_2, q))
+                mstore(add(pMem, pH0w8_3), mulmod(mload(add(pMem, pH0w8_0)), w8_3, q))
+                mstore(add(pMem, pH0w8_4), mulmod(mload(add(pMem, pH0w8_0)), w8_4, q))
+                mstore(add(pMem, pH0w8_5), mulmod(mload(add(pMem, pH0w8_0)), w8_5, q))
+                mstore(add(pMem, pH0w8_6), mulmod(mload(add(pMem, pH0w8_0)), w8_6, q))
+                mstore(add(pMem, pH0w8_7), mulmod(mload(add(pMem, pH0w8_0)), w8_7, q))
+
+                // Compute roots.S1.h1w4
+                mstore(add(pMem, pH1w4_0), mulmod(mload(add(pMem, pH0w8_0)), mload(add(pMem, pH0w8_0)), q))
+                mstore(add(pMem, pH1w4_1), mulmod(mload(add(pMem, pH1w4_0)), w4, q))
+                mstore(add(pMem, pH1w4_2), mulmod(mload(add(pMem, pH1w4_0)), w4_2, q))
+                mstore(add(pMem, pH1w4_3), mulmod(mload(add(pMem, pH1w4_0)), w4_3, q))
+
+                // Compute roots.S2.h2w3
+                mstore(add(pMem, pH2w3_0), mulmod(mload(add(pMem, pH1w4_0)), mload(add(pMem, pXiSeed2)), q))
+                mstore(add(pMem, pH2w3_1), mulmod(mload(add(pMem, pH2w3_0)), w3, q))
+                mstore(add(pMem, pH2w3_2), mulmod(mload(add(pMem, pH2w3_0)), w3_2, q))
+
+                // Compute roots.S2.h2w3
+                mstore(add(pMem, pH3w3_0), mulmod(mload(add(pMem, pH2w3_0)), wr, q))
+                mstore(add(pMem, pH3w3_1), mulmod(mload(add(pMem, pH3w3_0)), w3, q))
+                mstore(add(pMem, pH3w3_2), mulmod(mload(add(pMem, pH3w3_0)), w3_2, q))
+
+                let xin := mulmod(mulmod(mload(add(pMem, pH2w3_0)), mload(add(pMem, pH2w3_0)), q), mload(add(pMem, pH2w3_0)), q)
+                mstore(add(pMem, pXi), xin)
+
+                // Compute xi^n
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                
+                xin:= mod(add(sub(xin, 1), q), q)
+                mstore(add(pMem, pZh), xin)
+                mstore(add(pMem, pZhInv), xin)  // We will invert later together with lagrange pols
+
+                // Compute challenge.alpha
+                mstore(add(pMem, lastMem), xiSeed)
+
+                calldatacopy(add(pMem, 1952), pEval_ql, 480)
+                mstore(add(pMem, pAlpha), mod(keccak256(add(pMem, lastMem), 512), q))
+
+                // Compute challenge.y
+                mstore(add(pMem, lastMem), mload(add(pMem, pAlpha)))
+                mstore(add(pMem, 1952 ),  calldataload(pW1))
+                mstore(add(pMem, 1984 ),  calldataload(add(pW1, 32)))
+                mstore(add(pMem, pY), mod(keccak256(add(pMem, lastMem), 96), q))
+            }
+
+            function computeLiS0(pMem) {
+                let root0 := mload(add(pMem, pH0w8_0))
+                let y := mload(add(pMem, pY))
+                let den1 := 1
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                
+                den1 := mulmod(8, den1, q)
+
+                let den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 0), 8), 32))))
+                let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(0, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 1), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(1, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 2), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(2, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 3), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(3, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 4), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(4, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 128)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 5), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(5, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 160)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 6), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(6, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 192)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 7), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(7, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 224)), mulmod(den1, mulmod(den2, den3, q), q))
+            
+            }
+
+            function computeLiS1(pMem) {
+                let root0 := mload(add(pMem, pH1w4_0))
+                let y := mload(add(pMem, pY))
+                let den1 := 1
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                
+                den1 := mulmod(4, den1, q)
+
+                let den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 0), 4), 32))))
+                let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(0, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS1Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 1), 4), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(1, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS1Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 2), 4), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(2, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS1Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 3), 4), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(3, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS1Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q))            
+            }
+
+            function computeLiS2(pMem) {
+
+                let y := mload(add(pMem, pY))
+
+                let den1 := mulmod(mulmod(3,mload(add(pMem, pH2w3_0)),q), addmod(mload(add(pMem, pXi)) ,mod(sub(q, mulmod(mload(add(pMem, pXi)), w1 ,q)), q), q), q)
+
+                let den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 0), 3), 32))))
+                let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(0, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 1), 3), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(1, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 2), 3), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(2, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den1 := mulmod(mulmod(3,mload(add(pMem, pH3w3_0)),q), addmod(mulmod(mload(add(pMem, pXi)), w1 ,q),mod(sub(q, mload(add(pMem, pXi))), q), q), q)
+
+                den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 0), 3), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(0, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 1), 3), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(1, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 128)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 2), 3), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(2, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 160)), mulmod(den1, mulmod(den2, den3, q), q))
+            }
+
+            // Prepare all the denominators that must be inverted, placed them in consecutive memory addresses
+            function computeInversions(pMem) {
+                // 1/ZH(xi) used in steps 8 and 9 of the verifier to multiply by 1/Z_H(xi)
+                // Value computed during computeChallenges function and stores in pMem+pZhInv
+
+                // 1/((y - h1) (y - h1w4) (y - h1w4_2) (y - h1w4_3))
+                // used in steps 10 and 11 of the verifier
+                let y := mload(add(pMem, pY))
+                let w := addmod(y, mod(sub(q, mload(add(pMem, pH1w4_0))), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH1w4_1))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH1w4_2))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH1w4_3))), q), q), q)
+                mstore(add(pMem, pDenH1), w)
+
+                // 1/((y - h2) (y - h2w3) (y - h2w3_2) (y - h3) (y - h3w3) (y - h3w3_2))
+                w := addmod(y, mod(sub(q, mload(add(pMem, pH2w3_0))), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH2w3_1))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH2w3_2))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH3w3_0))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH3w3_1))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH3w3_2))), q), q), q)
+                mstore(add(pMem, pDenH2), w)
+
+                // Denominator needed in the verifier when computing L_i^{S0}(X)
+                computeLiS0(pMem)
+                
+                // Denominator needed in the verifier when computing L_i^{S1}(X)
+                computeLiS1(pMem)
+
+                // Denominator needed in the verifier when computing L_i^{S2}(X)
+                computeLiS2(pMem)
+
+                // L_i where i from 1 to num public inputs, needed in step 6 and 7 of the verifier to compute L_1(xi) and PI(xi)
+                w := 1
+                let xi := mload(add(pMem, pXi))
+                
+                mstore(add(pMem, pEval_l1), mulmod(n, mod(add(sub(xi, w), q), q), q))
+                
+
+                // Execute Montgomery batched inversions of the previous prepared values
+                inverseArray(pMem)            }
+
+            // Compute Lagrange polynomial evaluation L_i(xi)
+            function computeLagrange(pMem) {
+                let zh := mload(add(pMem, pZh))
+                let w := 1
+                
+                    mstore(add(pMem, pEval_l1 ), mulmod(mload(add(pMem, pEval_l1 )), zh, q))
+                    
+            }
+
+            // Compute public input polynomial evaluation PI(xi)
+            function computePi(pMem, pPub) {
+                let pi := 0
+                pi := mod(add(sub(pi, mulmod(mload(add(pMem, pEval_l1)), calldataload(pPub), q)), q), q)
+                
+                mstore(add(pMem, pPi), pi)
+            }
+
+            // Compute r0(y) by interpolating the polynomial r0(X) using 8 points (x,y)
+            // where x = {h9, h0w8, h0w8^2, h0w8^3, h0w8^4, h0w8^5, h0w8^6, h0w8^7}
+            // and   y = {C0(h0), C0(h0w8), C0(h0w8^2), C0(h0w8^3), C0(h0w8^4), C0(h0w8^5), C0(h0w8^6), C0(h0w8^7)}
+            // and computing C0(xi)
+            function computeR0(pMem) {
+                let num := 1
+                let y := mload(add(pMem, pY))
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+
+                num := addmod(num, mod(sub(q, mload(add(pMem, pXi))), q), q)
+
+                let res
+                let h0w80
+                let c0Value
+                let h0w8i
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_0))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 0))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_1))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 32))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_2))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 64))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_3))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 96))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_4))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 128))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_5))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 160))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_6))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 192))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_7))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 224))), q), q), q)
+
+
+                mstore(add(pMem, pR0), res)
+            }
+
+            // Compute r1(y) by interpolating the polynomial r1(X) using 4 points (x,y)
+            // where x = {h1, h1w4, h1w4^2, h1w4^3}
+            // and   y = {C1(h1), C1(h1w4), C1(h1w4^2), C1(h1w4^3)}
+            // and computing T0(xi)
+            function computeR1(pMem) {
+                let num := 1
+                let y := mload(add(pMem, pY))
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+
+                num := addmod(num, mod(sub(q, mload(add(pMem, pXi))), q), q)
+
+                let t0
+                let evalA := calldataload(pEval_a)
+                let evalB := calldataload(pEval_b)
+                let evalC := calldataload(pEval_c)
+
+                t0 := mulmod(calldataload(pEval_ql), evalA, q)
+                t0 := addmod(t0, mulmod(calldataload(pEval_qr), evalB, q) ,q)
+                t0 := addmod(t0, mulmod(calldataload(pEval_qm), mulmod(evalA, evalB, q), q) ,q)
+                t0 := addmod(t0, mulmod(calldataload(pEval_qo), evalC, q) ,q)
+                t0 := addmod(t0, calldataload(pEval_qc) ,q)
+                t0 := addmod(t0, mload(add(pMem, pPi)), q)
+                t0 := mulmod(t0, mload(add(pMem, pZhInv)), q)
+
+                let res
+                let c1Value
+                let h1w4
+                let square
+                c1Value := evalA
+                h1w4 := mload(add(pMem, pH1w4_0))
+
+                c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q)
+                square := mulmod(h1w4, h1w4, q)
+                c1Value := addmod(c1Value, mulmod(square, evalC, q), q)
+                c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q)
+
+                res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(0, 32)))), q), q), q)
+
+                c1Value := evalA
+                h1w4 := mload(add(pMem, pH1w4_1))
+
+                c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q)
+                square := mulmod(h1w4, h1w4, q)
+                c1Value := addmod(c1Value, mulmod(square, evalC, q), q)
+                c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q)
+
+                res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(1, 32)))), q), q), q)
+
+                c1Value := evalA
+                h1w4 := mload(add(pMem, pH1w4_2))
+
+                c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q)
+                square := mulmod(h1w4, h1w4, q)
+                c1Value := addmod(c1Value, mulmod(square, evalC, q), q)
+                c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q)
+
+                res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(2, 32)))), q), q), q)
+
+                c1Value := evalA
+                h1w4 := mload(add(pMem, pH1w4_3))
+
+                c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q)
+                square := mulmod(h1w4, h1w4, q)
+                c1Value := addmod(c1Value, mulmod(square, evalC, q), q)
+                c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q)
+
+                res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(3, 32)))), q), q), q)
+
+
+                mstore(add(pMem, pR1), res)
+            }
+
+            // Compute r2(y) by interpolating the polynomial r2(X) using 6 points (x,y)
+            // where x = {[h2, h2w3, h2w3^2], [h3, h3w3, h3w3^2]}
+            // and   y = {[C2(h2), C2(h2w3), C2(h2w3^2)], [C2(h3), C2(h3w3), C2(h3w3^2)]}
+            // and computing T1(xi) and T2(xi)
+            function computeR2(pMem) {
+                let y := mload(add(pMem, pY))
+                let num := 1
+                num := mulmod(y, num, q)
+                num := mulmod(y, num, q)
+                num := mulmod(y, num, q)
+                num := mulmod(y, num, q)
+                num := mulmod(y, num, q)
+                num := mulmod(y, num, q)
+
+                let num2 := 1
+                num2 := mulmod(y, num2, q)
+                num2 := mulmod(y, num2, q)
+                num2 := mulmod(y, num2, q)
+                num2 := mulmod(num2, addmod(mulmod(mload(add(pMem, pXi)), w1 ,q), mload(add(pMem, pXi)), q), q)
+
+                num := addmod(num, mod(sub(q, num2), q), q)
+
+                num2 := mulmod(mulmod(mload(add(pMem, pXi)), w1 ,q), mload(add(pMem, pXi)), q)
+
+                num := addmod(num, num2, q)
+
+                let t1
+                let t2
+                let betaXi := mulmod(mload(add(pMem, pBeta)), mload(add(pMem, pXi)), q)
+                let gamma := mload(add(pMem, pGamma))
+
+                t2 := addmod(calldataload( pEval_a), addmod(betaXi, gamma, q) ,q)
+                t2 := mulmod(t2,
+                            addmod(calldataload( pEval_b),
+                            addmod(mulmod(betaXi, k1, q), gamma, q) ,q), q)
+                t2 := mulmod(t2,
+                            addmod(calldataload( pEval_c),
+                            addmod(mulmod(betaXi, k2, q), gamma, q) ,q), q)
+                t2 := mulmod(t2, calldataload(pEval_z), q)
+
+                //Let's use t1 as a temporal variable to save one local
+                t1 := addmod(calldataload(pEval_a), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s1), q), gamma, q) ,q)
+                t1 := mulmod(t1,
+                      addmod(calldataload(pEval_b), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s2), q), gamma, q) ,q), q)
+                t1 := mulmod(t1,
+                      addmod(calldataload(pEval_c), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s3), q), gamma, q) ,q), q)
+                t1 := mulmod(t1, calldataload(pEval_zw), q)
+
+                t2:= addmod(t2, mod(sub(q, t1), q), q)
+                t2 := mulmod(t2, mload(add(pMem, pZhInv)), q)
+
+                // Compute T1(xi)
+                t1 := sub(calldataload(pEval_z), 1)
+                t1 := mulmod(t1, mload(add(pMem, pEval_l1)) ,q)
+                t1 := mulmod(t1, mload(add(pMem, pZhInv)) ,q)
+
+                // Let's use local variable gamma to save the result
+                gamma:=0
+                
+                let hw
+                let c2Value 
+
+                hw := mload(add(pMem, pH2w3_0))
+                c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(0, 32)))), q), q), q)
+
+                hw := mload(add(pMem, pH2w3_1))
+                c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(1, 32)))), q), q), q)
+
+                hw := mload(add(pMem, pH2w3_2))
+                c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(2, 32)))), q), q), q)
+
+                hw := mload(add(pMem, pH3w3_0))
+                c2Value := addmod(calldataload(pEval_zw), mulmod(hw, calldataload(pEval_t1w), q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(3, 32)))), q), q), q)
+
+                hw := mload(add(pMem, pH3w3_1))
+                c2Value := addmod(calldataload(pEval_zw), mulmod(hw, calldataload(pEval_t1w), q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(4, 32)))), q), q), q)
+
+                hw := mload(add(pMem, pH3w3_2))
+                c2Value := addmod(calldataload(pEval_zw), mulmod(hw, calldataload(pEval_t1w), q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(5, 32)))), q), q), q)
+
+                mstore(add(pMem, pR2), gamma)
+            }
+
+            // G1 function to accumulate a G1 value to an address
+            function g1_acc(pR, pP) {
+                let mIn := mload(0x40)
+                mstore(mIn, mload(pR))
+                mstore(add(mIn, 32), mload(add(pR, 32)))
+                mstore(add(mIn, 64), mload(pP))
+                mstore(add(mIn, 96), mload(add(pP, 32)))
+
+                let success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64)
+
+                if iszero(success) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+            }
+
+            // G1 function to multiply a G1 value to value in an address
+            function g1_mulAcc(pR, pP, s) {
+                let success
+                let mIn := mload(0x40)
+                mstore(mIn, calldataload(pP))
+                mstore(add(mIn, 32), calldataload(add(pP, 32)))
+                mstore(add(mIn, 64), s)
+
+                success := staticcall(sub(gas(), 2000), 7, mIn, 96, mIn, 64)
+
+                if iszero(success) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+
+                mstore(add(mIn, 64), mload(pR))
+                mstore(add(mIn, 96), mload(add(pR, 32)))
+
+                success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64)
+
+                if iszero(success) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+            }
+
+            // G1 function to multiply a G1 value(x,y) to value in an address
+            function g1_mulAccC(pR, x, y, s) {
+                let success
+                let mIn := mload(0x40)
+                mstore(mIn, x)
+                mstore(add(mIn, 32), y)
+                mstore(add(mIn, 64), s)
+
+                success := staticcall(sub(gas(), 2000), 7, mIn, 96, mIn, 64)
+
+                if iszero(success) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+
+                mstore(add(mIn, 64), mload(pR))
+                mstore(add(mIn, 96), mload(add(pR, 32)))
+
+                success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64)
+
+                if iszero(success) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+            }
+
+            function computeFEJ(pMem) {
+                // Prepare shared numerator between F, E and J to reuse it
+                let y := mload(add(pMem, pY))
+                let numerator := addmod(y, mod(sub(q, mload(add(pMem, pH0w8_0))), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_1))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_2))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_3))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_4))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_5))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_6))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_7))), q), q), q)
+
+                // Prepare shared quotient between F and E to reuse it
+                let quotient1 := mulmod(mload(add(pMem, pAlpha)), mulmod(numerator, mload(add(pMem, pDenH1)), q), q)
+                let quotient2 := mulmod(mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q), mulmod(numerator, mload(add(pMem, pDenH2)), q), q)
+
+                // Compute full batched polynomial commitment [F]_1
+                mstore(add(pMem, pF), C0x)
+                mstore(add(pMem, add(pF, 32)), C0y)
+                g1_mulAcc(add(pMem, pF), pC1, quotient1)
+                g1_mulAcc(add(pMem, pF), pC2, quotient2)
+
+                // Compute group-encoded batch evaluation [E]_1
+                g1_mulAccC(add(pMem, pE), G1x, G1y, addmod(mload(add(pMem, pR0)), addmod(mulmod(quotient1, mload(add(pMem, pR1)),q), mulmod(quotient2, mload(add(pMem, pR2)),q), q), q))
+
+                // Compute the full difference [J]_1
+                g1_mulAcc(add(pMem, pJ), pW1, numerator)
+            }
+
+            // Validate all evaluations with a pairing checking that e([F]_1 - [E]_1 - [J]_1 + y[W2]_1, [1]_2) == e([W']_1, [x]_2)
+            function checkPairing(pMem) -> isOk {
+                let mIn := mload(0x40)
+
+                // First pairing value
+                // Compute -E
+                mstore(add(add(pMem, pE), 32), mod(sub(qf, mload(add(add(pMem, pE), 32))), qf))
+                // Compute -J
+                mstore(add(add(pMem, pJ), 32), mod(sub(qf, mload(add(add(pMem, pJ), 32))), qf))
+                // F = F - E - J + y·W2
+                g1_acc(add(pMem, pF), add(pMem, pE))
+                g1_acc(add(pMem, pF), add(pMem, pJ))
+                g1_mulAcc(add(pMem, pF), pW2, mload(add(pMem, pY)))
+
+                mstore(mIn, mload(add(pMem, pF)))
+                mstore(add(mIn, 32), mload(add(add(pMem, pF), 32)))
+
+                // Second pairing value
+                mstore(add(mIn, 64), G2x2)
+                mstore(add(mIn, 96), G2x1)
+                mstore(add(mIn, 128), G2y2)
+                mstore(add(mIn, 160), G2y1)
+
+                // Third pairing value
+                // Compute -W2
+                mstore(add(mIn, 192), calldataload(pW2))
+                let s := calldataload(add(pW2, 32))
+                s := mod(sub(qf, s), qf)
+                mstore(add(mIn, 224), s)
+
+                // Fourth pairing value
+                mstore(add(mIn, 256), X2x2)
+                mstore(add(mIn, 288), X2x1)
+                mstore(add(mIn, 320), X2y2)
+                mstore(add(mIn, 352), X2y1)
+
+                let success := staticcall(sub(gas(), 2000), 8, mIn, 384, mIn, 0x20)
+
+                isOk := and(success, mload(mIn))
+            }
+
+            let pMem := mload(0x40)
+            mstore(0x40, add(pMem, lastMem))
+
+            // Validate that all evaluations ∈ F
+            checkInput()
+
+            // Compute the challenges: beta, gamma, xi, alpha and y ∈ F, h1w4/h2w3/h3w3 roots, xiN and zh(xi)
+            computeChallenges(pMem, pubSignals)
+
+            // To divide prime fields the Extended Euclidean Algorithm for computing modular inverses is needed.
+            // The Montgomery batch inversion algorithm allow us to compute n inverses reducing to a single one inversion.
+            // More info: https://vitalik.ca/general/2018/07/21/starks_part_3.html
+            // To avoid this single inverse computation on-chain, it has been computed in proving time and send it to the verifier.
+            // Therefore, the verifier:
+            //      1) Prepare all the denominators to inverse
+            //      2) Check the inverse sent by the prover it is what it should be
+            //      3) Compute the others inverses using the Montgomery Batched Algorithm using the inverse sent to avoid the inversion operation it does.
+            computeInversions(pMem)
+
+            // Compute Lagrange polynomial evaluations Li(xi)
+            computeLagrange(pMem)
+
+            // Compute public input polynomial evaluation PI(xi) = \sum_i^l -public_input_i·L_i(xi)
+            computePi(pMem, pubSignals)
+
+            // Computes r1(y) and r2(y)
+            computeR0(pMem)
+            computeR1(pMem)
+            computeR2(pMem)
+
+            // Compute full batched polynomial commitment [F]_1, group-encoded batch evaluation [E]_1 and the full difference [J]_1
+            computeFEJ(pMem)
+
+            // Validate all evaluations
+            let isValid := checkPairing(pMem)
+
+            mstore(0, isValid)
+            return(0, 0x20)
+        }
+    }
+}
\ No newline at end of file
diff --git a/contracts/verifiers/FflonkVerifier_11.sol b/contracts/verifiers/FflonkVerifier_11.sol
new file mode 100644
index 000000000..ab8511c1a
--- /dev/null
+++ b/contracts/verifiers/FflonkVerifier_11.sol
@@ -0,0 +1,1244 @@
+// SPDX-License-Identifier: GPL-3.0
+/*
+    Copyright 2021 0KIMS association.
+
+    This file is generated with [snarkJS](https://github.com/iden3/snarkjs).
+
+    snarkJS is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    snarkJS is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with snarkJS. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+pragma solidity >=0.7.0 <0.9.0;
+
+contract FflonkVerifier_11 {
+    uint32 constant n     = 16777216; // Domain size
+
+    // Verification Key data
+    uint256 constant k1   = 2;   // Plonk k1 multiplicative factor to force distinct cosets of H
+    uint256 constant k2   = 3;   // Plonk k2 multiplicative factor to force distinct cosets of H
+
+    // OMEGAS
+    // Omega, Omega^{1/3}
+    uint256 constant w1   = 5709868443893258075976348696661355716898495876243883251619397131511003808859;
+    uint256 constant wr   = 18200100796661656210024324131237448517259556535315737226009542456080026430510;
+    // Omega_3, Omega_3^2
+    uint256 constant w3   = 21888242871839275217838484774961031246154997185409878258781734729429964517155;
+    uint256 constant w3_2 = 4407920970296243842393367215006156084916469457145843978461;
+    // Omega_4, Omega_4^2, Omega_4^3
+    uint256 constant w4   = 21888242871839275217838484774961031246007050428528088939761107053157389710902;
+    uint256 constant w4_2 = 21888242871839275222246405745257275088548364400416034343698204186575808495616;
+    uint256 constant w4_3 = 4407920970296243842541313971887945403937097133418418784715;
+    // Omega_8, Omega_8^2, Omega_8^3, Omega_8^4, Omega_8^5, Omega_8^6, Omega_8^7
+    uint256 constant w8_1 = 19540430494807482326159819597004422086093766032135589407132600596362845576832;
+    uint256 constant w8_2 = 21888242871839275217838484774961031246007050428528088939761107053157389710902;
+    uint256 constant w8_3 = 13274704216607947843011480449124596415239537050559949017414504948711435969894;
+    uint256 constant w8_4 = 21888242871839275222246405745257275088548364400416034343698204186575808495616;
+    uint256 constant w8_5 = 2347812377031792896086586148252853002454598368280444936565603590212962918785;
+    uint256 constant w8_6 = 4407920970296243842541313971887945403937097133418418784715;
+    uint256 constant w8_7 = 8613538655231327379234925296132678673308827349856085326283699237864372525723;
+
+    // Verifier preprocessed input C_0(x)·[1]_1
+    uint256 constant C0x  = 11553294103217785023516748419184161960688215767988858039368256322332861589771;
+    uint256 constant C0y  = 10092895974211559972859178879634538990964607545177723538837209775275130760109;
+
+    // Verifier preprocessed input x·[1]_2
+    uint256 constant X2x1 = 21831381940315734285607113342023901060522397560371972897001948545212302161822;
+    uint256 constant X2x2 = 17231025384763736816414546592865244497437017442647097510447326538965263639101;
+    uint256 constant X2y1 = 2388026358213174446665280700919698872609886601280537296205114254867301080648;
+    uint256 constant X2y2 = 11507326595632554467052522095592665270651932854513688777769618397986436103170;
+
+    // Scalar field size
+    uint256 constant q    = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
+    // Base field size
+    uint256 constant qf   = 21888242871839275222246405745257275088696311157297823662689037894645226208583;
+    // [1]_1
+    uint256 constant G1x  = 1;
+    uint256 constant G1y  = 2;
+    // [1]_2
+    uint256 constant G2x1 = 10857046999023057135944570762232829481370756359578518086990519993285655852781;
+    uint256 constant G2x2 = 11559732032986387107991004021392285783925812861821192530917403151452391805634;
+    uint256 constant G2y1 = 8495653923123431417604973247489272438418190587263600148770280649306958101930;
+    uint256 constant G2y2 = 4082367875863433681332203403145435568316851327593401208105741076214120093531;
+
+    // Proof calldata
+    // Byte offset of every parameter of the calldata
+    // Polynomial commitments
+    uint16 constant pC1       = 4 + 0;     // [C1]_1
+    uint16 constant pC2       = 4 + 32*2;  // [C2]_1
+    uint16 constant pW1       = 4 + 32*4;  // [W]_1
+    uint16 constant pW2       = 4 + 32*6;  // [W']_1
+    // Opening evaluations
+    uint16 constant pEval_ql  = 4 + 32*8;  // q_L(xi)
+    uint16 constant pEval_qr  = 4 + 32*9;  // q_R(xi)
+    uint16 constant pEval_qm  = 4 + 32*10; // q_M(xi)
+    uint16 constant pEval_qo  = 4 + 32*11; // q_O(xi)
+    uint16 constant pEval_qc  = 4 + 32*12; // q_C(xi)
+    uint16 constant pEval_s1  = 4 + 32*13; // S_{sigma_1}(xi)
+    uint16 constant pEval_s2  = 4 + 32*14; // S_{sigma_2}(xi)
+    uint16 constant pEval_s3  = 4 + 32*15; // S_{sigma_3}(xi)
+    uint16 constant pEval_a   = 4 + 32*16; // a(xi)
+    uint16 constant pEval_b   = 4 + 32*17; // b(xi)
+    uint16 constant pEval_c   = 4 + 32*18; // c(xi)
+    uint16 constant pEval_z   = 4 + 32*19; // z(xi)
+    uint16 constant pEval_zw  = 4 + 32*20; // z_omega(xi)
+    uint16 constant pEval_t1w = 4 + 32*21; // T_1(xi omega)
+    uint16 constant pEval_t2w = 4 + 32*22; // T_2(xi omega)
+    uint16 constant pEval_inv = 4 + 32*23; // inv(batch) sent by the prover to avoid any inverse calculation to save gas,
+                                           // we check the correctness of the inv(batch) by computing batch
+                                           // and checking inv(batch) * batch == 1
+
+    // Memory data
+    // Challenges
+    uint16 constant pAlpha   = 0;   // alpha challenge
+    uint16 constant pBeta    = 32;  // beta challenge
+    uint16 constant pGamma   = 64;  // gamma challenge
+    uint16 constant pY       = 96;  // y challenge
+    uint16 constant pXiSeed  = 128; // xi seed, from this value we compute xi = xiSeed^24
+    uint16 constant pXiSeed2 = 160; // (xi seed)^2
+    uint16 constant pXi      = 192; // xi challenge
+
+    // Roots
+    // S_0 = roots_8(xi) = { h_0, h_0w_8, h_0w_8^2, h_0w_8^3, h_0w_8^4, h_0w_8^5, h_0w_8^6, h_0w_8^7 }
+    uint16 constant pH0w8_0 = 224;
+    uint16 constant pH0w8_1 = 256;
+    uint16 constant pH0w8_2 = 288;
+    uint16 constant pH0w8_3 = 320;
+    uint16 constant pH0w8_4 = 352;
+    uint16 constant pH0w8_5 = 384;
+    uint16 constant pH0w8_6 = 416;
+    uint16 constant pH0w8_7 = 448;
+
+    // S_1 = roots_4(xi) = { h_1, h_1w_4, h_1w_4^2, h_1w_4^3 }
+    uint16 constant pH1w4_0 = 480;
+    uint16 constant pH1w4_1 = 512;
+    uint16 constant pH1w4_2 = 544;
+    uint16 constant pH1w4_3 = 576;
+
+    // S_2 = roots_3(xi) U roots_3(xi omega)
+    // roots_3(xi) = { h_2, h_2w_3, h_2w_3^2 }
+    uint16 constant pH2w3_0 = 608;
+    uint16 constant pH2w3_1 = 640;
+    uint16 constant pH2w3_2 = 672;
+    // roots_3(xi omega) = { h_3, h_3w_3, h_3w_3^2 }
+    uint16 constant pH3w3_0 = 704;
+    uint16 constant pH3w3_1 = 736;
+    uint16 constant pH3w3_2 = 768;
+
+    uint16 constant pPi     = 800; // PI(xi)
+    uint16 constant pR0     = 832; // r0(y)
+    uint16 constant pR1     = 864; // r1(y)
+    uint16 constant pR2     = 896; // r2(y)
+
+    uint16 constant pF      = 928;  // [F]_1, 64 bytes
+    uint16 constant pE      = 992;  // [E]_1, 64 bytes
+    uint16 constant pJ      = 1056; // [J]_1, 64 bytes
+
+    uint16 constant pZh     = 1184; // Z_H(xi)
+    // From this point we write all the variables that must be computed using the Montgomery batch inversion
+    uint16 constant pZhInv  = 1216; // 1/Z_H(xi)
+    uint16 constant pDenH1  = 1248; // 1/( (y-h_1w_4) (y-h_1w_4^2) (y-h_1w_4^3) (y-h_1w_4^4) )
+    uint16 constant pDenH2  = 1280; // 1/( (y-h_2w_3) (y-h_2w_3^2) (y-h_2w_3^3) (y-h_3w_3) (y-h_3w_3^2) (y-h_3w_3^3) )
+    uint16 constant pLiS0Inv = 1312; // Reserve 8 * 32 bytes to compute r_0(X)
+    uint16 constant pLiS1Inv = 1568; // Reserve 4 * 32 bytes to compute r_1(X)
+    uint16 constant pLiS2Inv = 1696; // Reserve 6 * 32 bytes to compute r_2(X)
+    // Lagrange evaluations
+    
+    uint16 constant pEval_l1 = 1888;
+    
+    
+    uint16 constant lastMem = 1920;
+     
+
+    function verifyProof(bytes32[24] calldata proof, uint256[1] calldata pubSignals) public view returns (bool) {
+        assembly {
+            // Computes the inverse of an array of values
+            // See https://vitalik.ca/general/2018/07/21/starks_part_3.html in section where explain fields operations
+            // To save the inverse to be computed on chain the prover sends the inverse as an evaluation in commits.eval_inv
+            function inverseArray(pMem) {
+
+                let pAux := mload(0x40)     // Point to the next free position
+                let acc := mload(add(pMem,pZhInv))       // Read the first element
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pDenH1)), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pDenH2)), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pLiS0Inv)), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 32))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 64))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 96))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 128))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 160))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 192))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 224))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pLiS1Inv)), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 32))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 64))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 96))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pLiS2Inv)), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 32))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 64))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 96))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 128))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 160))), q)
+                mstore(pAux, acc)
+
+                pAux := add(pAux, 32)
+                acc := mulmod(acc, mload(add(pMem, pEval_l1)), q)
+                mstore(pAux, acc)
+
+
+                let inv := calldataload(pEval_inv)
+
+                // Before using the inverse sent by the prover the verifier checks inv(batch) * batch === 1
+                if iszero(eq(1, mulmod(acc, inv, q))) {
+                    mstore(0, 0)
+                    return(0,0x20)
+                }
+
+                acc := inv
+
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pEval_l1)), q)
+                mstore(add(pMem, pEval_l1), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 160))), q)
+                mstore(add(pMem, add(pLiS2Inv, 160)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 128))), q)
+                mstore(add(pMem, add(pLiS2Inv, 128)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 96))), q)
+                mstore(add(pMem, add(pLiS2Inv, 96)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 64))), q)
+                mstore(add(pMem, add(pLiS2Inv, 64)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 32))), q)
+                mstore(add(pMem, add(pLiS2Inv, 32)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pLiS2Inv)), q)
+                mstore(add(pMem, pLiS2Inv), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 96))), q)
+                mstore(add(pMem, add(pLiS1Inv, 96)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 64))), q)
+                mstore(add(pMem, add(pLiS1Inv, 64)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 32))), q)
+                mstore(add(pMem, add(pLiS1Inv, 32)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pLiS1Inv)), q)
+                mstore(add(pMem, pLiS1Inv), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 224))), q)
+                mstore(add(pMem, add(pLiS0Inv, 224)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 192))), q)
+                mstore(add(pMem, add(pLiS0Inv, 192)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 160))), q)
+                mstore(add(pMem, add(pLiS0Inv, 160)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 128))), q)
+                mstore(add(pMem, add(pLiS0Inv, 128)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 96))), q)
+                mstore(add(pMem, add(pLiS0Inv, 96)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 64))), q)
+                mstore(add(pMem, add(pLiS0Inv, 64)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 32))), q)
+                mstore(add(pMem, add(pLiS0Inv, 32)), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pLiS0Inv)), q)
+                mstore(add(pMem, pLiS0Inv), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pDenH2)), q)
+                mstore(add(pMem, pDenH2), inv)
+                pAux := sub(pAux, 32)
+                inv := mulmod(acc, mload(pAux), q)
+                acc := mulmod(acc, mload(add(pMem, pDenH1)), q)
+                mstore(add(pMem, pDenH1), inv)
+
+                mstore(add(pMem, pZhInv), acc)
+            }
+
+            function checkField(v) {
+                if iszero(lt(v, q)) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+            }
+
+            function checkPointBelongsToBN128Curve(p) {
+                let x := calldataload(p)
+                let y := calldataload(add(p, 32))
+
+                // Check that the point is on the curve
+                // y^2 = x^3 + 3
+                let x3_3 := addmod(mulmod(x, mulmod(x, x, qf), qf), 3, qf)
+                let y2 := mulmod(y, y, qf)
+
+                if iszero(eq(x3_3, y2)) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+            }  
+            
+            // Validate all the evaluations sent by the prover ∈ F
+            function checkInput() {
+                // Check proof commitments fullfill bn128 curve equation Y^2 = X^3 + 3
+                checkPointBelongsToBN128Curve(pC1)
+                checkPointBelongsToBN128Curve(pC2)
+                checkPointBelongsToBN128Curve(pW1)
+                checkPointBelongsToBN128Curve(pW2)
+
+                checkField(calldataload(pEval_ql))
+                checkField(calldataload(pEval_qr))
+                checkField(calldataload(pEval_qm))
+                checkField(calldataload(pEval_qo))
+                checkField(calldataload(pEval_qc))
+                checkField(calldataload(pEval_s1))
+                checkField(calldataload(pEval_s2))
+                checkField(calldataload(pEval_s3))
+                checkField(calldataload(pEval_a))
+                checkField(calldataload(pEval_b))
+                checkField(calldataload(pEval_c))
+                checkField(calldataload(pEval_z))
+                checkField(calldataload(pEval_zw))
+                checkField(calldataload(pEval_t1w))
+                checkField(calldataload(pEval_t2w))
+                checkField(calldataload(pEval_inv))
+
+                // Points are checked in the point operations precompiled smart contracts
+            }
+
+            function computeChallenges(pMem, pPublic) {
+                // Compute challenge.beta & challenge.gamma
+                mstore(add(pMem, 1920 ), C0x)
+                mstore(add(pMem, 1952 ), C0y)
+
+                mstore(add(pMem, 1984), calldataload(pPublic))
+                
+                
+
+                mstore(add(pMem, 2016 ),  calldataload(pC1))
+                mstore(add(pMem, 2048 ),  calldataload(add(pC1, 32)))
+
+                mstore(add(pMem, pBeta),  mod(keccak256(add(pMem, lastMem), 160), q))
+                mstore(add(pMem, pGamma), mod(keccak256(add(pMem, pBeta), 32), q))
+
+                // Get xiSeed & xiSeed2
+                mstore(add(pMem, lastMem), mload(add(pMem, pGamma)))
+                mstore(add(pMem, 1952), calldataload(pC2))
+                mstore(add(pMem, 1984), calldataload(add(pC2, 32)))
+                let xiSeed := mod(keccak256(add(pMem, lastMem), 96), q)
+
+                mstore(add(pMem, pXiSeed), xiSeed)
+                mstore(add(pMem, pXiSeed2), mulmod(xiSeed, xiSeed, q))
+
+                // Compute roots.S0.h0w8
+                mstore(add(pMem, pH0w8_0), mulmod(mload(add(pMem, pXiSeed2)), mload(add(pMem, pXiSeed)), q))
+                mstore(add(pMem, pH0w8_1), mulmod(mload(add(pMem, pH0w8_0)), w8_1, q))
+                mstore(add(pMem, pH0w8_2), mulmod(mload(add(pMem, pH0w8_0)), w8_2, q))
+                mstore(add(pMem, pH0w8_3), mulmod(mload(add(pMem, pH0w8_0)), w8_3, q))
+                mstore(add(pMem, pH0w8_4), mulmod(mload(add(pMem, pH0w8_0)), w8_4, q))
+                mstore(add(pMem, pH0w8_5), mulmod(mload(add(pMem, pH0w8_0)), w8_5, q))
+                mstore(add(pMem, pH0w8_6), mulmod(mload(add(pMem, pH0w8_0)), w8_6, q))
+                mstore(add(pMem, pH0w8_7), mulmod(mload(add(pMem, pH0w8_0)), w8_7, q))
+
+                // Compute roots.S1.h1w4
+                mstore(add(pMem, pH1w4_0), mulmod(mload(add(pMem, pH0w8_0)), mload(add(pMem, pH0w8_0)), q))
+                mstore(add(pMem, pH1w4_1), mulmod(mload(add(pMem, pH1w4_0)), w4, q))
+                mstore(add(pMem, pH1w4_2), mulmod(mload(add(pMem, pH1w4_0)), w4_2, q))
+                mstore(add(pMem, pH1w4_3), mulmod(mload(add(pMem, pH1w4_0)), w4_3, q))
+
+                // Compute roots.S2.h2w3
+                mstore(add(pMem, pH2w3_0), mulmod(mload(add(pMem, pH1w4_0)), mload(add(pMem, pXiSeed2)), q))
+                mstore(add(pMem, pH2w3_1), mulmod(mload(add(pMem, pH2w3_0)), w3, q))
+                mstore(add(pMem, pH2w3_2), mulmod(mload(add(pMem, pH2w3_0)), w3_2, q))
+
+                // Compute roots.S2.h2w3
+                mstore(add(pMem, pH3w3_0), mulmod(mload(add(pMem, pH2w3_0)), wr, q))
+                mstore(add(pMem, pH3w3_1), mulmod(mload(add(pMem, pH3w3_0)), w3, q))
+                mstore(add(pMem, pH3w3_2), mulmod(mload(add(pMem, pH3w3_0)), w3_2, q))
+
+                let xin := mulmod(mulmod(mload(add(pMem, pH2w3_0)), mload(add(pMem, pH2w3_0)), q), mload(add(pMem, pH2w3_0)), q)
+                mstore(add(pMem, pXi), xin)
+
+                // Compute xi^n
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                xin:= mulmod(xin, xin, q)
+                
+                
+                xin:= mod(add(sub(xin, 1), q), q)
+                mstore(add(pMem, pZh), xin)
+                mstore(add(pMem, pZhInv), xin)  // We will invert later together with lagrange pols
+
+                // Compute challenge.alpha
+                mstore(add(pMem, lastMem), xiSeed)
+
+                calldatacopy(add(pMem, 1952), pEval_ql, 480)
+                mstore(add(pMem, pAlpha), mod(keccak256(add(pMem, lastMem), 512), q))
+
+                // Compute challenge.y
+                mstore(add(pMem, lastMem), mload(add(pMem, pAlpha)))
+                mstore(add(pMem, 1952 ),  calldataload(pW1))
+                mstore(add(pMem, 1984 ),  calldataload(add(pW1, 32)))
+                mstore(add(pMem, pY), mod(keccak256(add(pMem, lastMem), 96), q))
+            }
+
+            function computeLiS0(pMem) {
+                let root0 := mload(add(pMem, pH0w8_0))
+                let y := mload(add(pMem, pY))
+                let den1 := 1
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                
+                den1 := mulmod(8, den1, q)
+
+                let den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 0), 8), 32))))
+                let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(0, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 1), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(1, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 2), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(2, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 3), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(3, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 4), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(4, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 128)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 5), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(5, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 160)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 6), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(6, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 192)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH0w8_0, mul(mod(mul(7, 7), 8), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(7, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS0Inv, 224)), mulmod(den1, mulmod(den2, den3, q), q))
+            
+            }
+
+            function computeLiS1(pMem) {
+                let root0 := mload(add(pMem, pH1w4_0))
+                let y := mload(add(pMem, pY))
+                let den1 := 1
+                den1 := mulmod(den1, root0, q)
+                den1 := mulmod(den1, root0, q)
+                
+                den1 := mulmod(4, den1, q)
+
+                let den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 0), 4), 32))))
+                let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(0, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS1Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 1), 4), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(1, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS1Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 2), 4), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(2, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS1Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH1w4_0, mul(mod(mul(3, 3), 4), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(3, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS1Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q))            
+            }
+
+            function computeLiS2(pMem) {
+
+                let y := mload(add(pMem, pY))
+
+                let den1 := mulmod(mulmod(3,mload(add(pMem, pH2w3_0)),q), addmod(mload(add(pMem, pXi)) ,mod(sub(q, mulmod(mload(add(pMem, pXi)), w1 ,q)), q), q), q)
+
+                let den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 0), 3), 32))))
+                let den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(0, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 0)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 1), 3), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(1, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 32)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH2w3_0, mul(mod(mul(2, 2), 3), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(2, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 64)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den1 := mulmod(mulmod(3,mload(add(pMem, pH3w3_0)),q), addmod(mulmod(mload(add(pMem, pXi)), w1 ,q),mod(sub(q, mload(add(pMem, pXi))), q), q), q)
+
+                den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 0), 3), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(0, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 96)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 1), 3), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(1, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 128)), mulmod(den1, mulmod(den2, den3, q), q))
+
+                den2 := mload(add(pMem, add(pH3w3_0, mul(mod(mul(2, 2), 3), 32))))
+                den3 := addmod(y, mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(2, 32))))), q), q)
+
+                mstore(add(pMem, add(pLiS2Inv, 160)), mulmod(den1, mulmod(den2, den3, q), q))
+            }
+
+            // Prepare all the denominators that must be inverted, placed them in consecutive memory addresses
+            function computeInversions(pMem) {
+                // 1/ZH(xi) used in steps 8 and 9 of the verifier to multiply by 1/Z_H(xi)
+                // Value computed during computeChallenges function and stores in pMem+pZhInv
+
+                // 1/((y - h1) (y - h1w4) (y - h1w4_2) (y - h1w4_3))
+                // used in steps 10 and 11 of the verifier
+                let y := mload(add(pMem, pY))
+                let w := addmod(y, mod(sub(q, mload(add(pMem, pH1w4_0))), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH1w4_1))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH1w4_2))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH1w4_3))), q), q), q)
+                mstore(add(pMem, pDenH1), w)
+
+                // 1/((y - h2) (y - h2w3) (y - h2w3_2) (y - h3) (y - h3w3) (y - h3w3_2))
+                w := addmod(y, mod(sub(q, mload(add(pMem, pH2w3_0))), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH2w3_1))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH2w3_2))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH3w3_0))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH3w3_1))), q), q), q)
+                w := mulmod(w, addmod(y, mod(sub(q, mload(add(pMem, pH3w3_2))), q), q), q)
+                mstore(add(pMem, pDenH2), w)
+
+                // Denominator needed in the verifier when computing L_i^{S0}(X)
+                computeLiS0(pMem)
+                
+                // Denominator needed in the verifier when computing L_i^{S1}(X)
+                computeLiS1(pMem)
+
+                // Denominator needed in the verifier when computing L_i^{S2}(X)
+                computeLiS2(pMem)
+
+                // L_i where i from 1 to num public inputs, needed in step 6 and 7 of the verifier to compute L_1(xi) and PI(xi)
+                w := 1
+                let xi := mload(add(pMem, pXi))
+                
+                mstore(add(pMem, pEval_l1), mulmod(n, mod(add(sub(xi, w), q), q), q))
+                
+
+                // Execute Montgomery batched inversions of the previous prepared values
+                inverseArray(pMem)            }
+
+            // Compute Lagrange polynomial evaluation L_i(xi)
+            function computeLagrange(pMem) {
+                let zh := mload(add(pMem, pZh))
+                let w := 1
+                
+                    mstore(add(pMem, pEval_l1 ), mulmod(mload(add(pMem, pEval_l1 )), zh, q))
+                    
+            }
+
+            // Compute public input polynomial evaluation PI(xi)
+            function computePi(pMem, pPub) {
+                let pi := 0
+                pi := mod(add(sub(pi, mulmod(mload(add(pMem, pEval_l1)), calldataload(pPub), q)), q), q)
+                
+                mstore(add(pMem, pPi), pi)
+            }
+
+            // Compute r0(y) by interpolating the polynomial r0(X) using 8 points (x,y)
+            // where x = {h9, h0w8, h0w8^2, h0w8^3, h0w8^4, h0w8^5, h0w8^6, h0w8^7}
+            // and   y = {C0(h0), C0(h0w8), C0(h0w8^2), C0(h0w8^3), C0(h0w8^4), C0(h0w8^5), C0(h0w8^6), C0(h0w8^7)}
+            // and computing C0(xi)
+            function computeR0(pMem) {
+                let num := 1
+                let y := mload(add(pMem, pY))
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+
+                num := addmod(num, mod(sub(q, mload(add(pMem, pXi))), q), q)
+
+                let res
+                let h0w80
+                let c0Value
+                let h0w8i
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_0))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 0))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_1))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 32))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_2))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 64))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_3))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 96))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_4))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 128))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_5))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 160))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_6))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 192))), q), q), q)
+
+                    
+                // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc +
+                //                      + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3
+                h0w80 := mload(add(pMem, pH0w8_7))
+                c0Value := addmod(calldataload(pEval_ql), mulmod(calldataload(pEval_qr), h0w80, q), q)
+                h0w8i := mulmod(h0w80, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qo), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qm), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_qc), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s1), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s2), h0w8i, q), q)
+                h0w8i := mulmod(h0w8i, h0w80, q)
+                c0Value := addmod(c0Value, mulmod(calldataload(pEval_s3), h0w8i, q), q)
+
+                res := addmod(res, mulmod(c0Value, mulmod(num, mload(add(pMem, add(pLiS0Inv, 224))), q), q), q)
+
+
+                mstore(add(pMem, pR0), res)
+            }
+
+            // Compute r1(y) by interpolating the polynomial r1(X) using 4 points (x,y)
+            // where x = {h1, h1w4, h1w4^2, h1w4^3}
+            // and   y = {C1(h1), C1(h1w4), C1(h1w4^2), C1(h1w4^3)}
+            // and computing T0(xi)
+            function computeR1(pMem) {
+                let num := 1
+                let y := mload(add(pMem, pY))
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+                num := mulmod(num, y, q)
+
+                num := addmod(num, mod(sub(q, mload(add(pMem, pXi))), q), q)
+
+                let t0
+                let evalA := calldataload(pEval_a)
+                let evalB := calldataload(pEval_b)
+                let evalC := calldataload(pEval_c)
+
+                t0 := mulmod(calldataload(pEval_ql), evalA, q)
+                t0 := addmod(t0, mulmod(calldataload(pEval_qr), evalB, q) ,q)
+                t0 := addmod(t0, mulmod(calldataload(pEval_qm), mulmod(evalA, evalB, q), q) ,q)
+                t0 := addmod(t0, mulmod(calldataload(pEval_qo), evalC, q) ,q)
+                t0 := addmod(t0, calldataload(pEval_qc) ,q)
+                t0 := addmod(t0, mload(add(pMem, pPi)), q)
+                t0 := mulmod(t0, mload(add(pMem, pZhInv)), q)
+
+                let res
+                let c1Value
+                let h1w4
+                let square
+                c1Value := evalA
+                h1w4 := mload(add(pMem, pH1w4_0))
+
+                c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q)
+                square := mulmod(h1w4, h1w4, q)
+                c1Value := addmod(c1Value, mulmod(square, evalC, q), q)
+                c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q)
+
+                res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(0, 32)))), q), q), q)
+
+                c1Value := evalA
+                h1w4 := mload(add(pMem, pH1w4_1))
+
+                c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q)
+                square := mulmod(h1w4, h1w4, q)
+                c1Value := addmod(c1Value, mulmod(square, evalC, q), q)
+                c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q)
+
+                res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(1, 32)))), q), q), q)
+
+                c1Value := evalA
+                h1w4 := mload(add(pMem, pH1w4_2))
+
+                c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q)
+                square := mulmod(h1w4, h1w4, q)
+                c1Value := addmod(c1Value, mulmod(square, evalC, q), q)
+                c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q)
+
+                res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(2, 32)))), q), q), q)
+
+                c1Value := evalA
+                h1w4 := mload(add(pMem, pH1w4_3))
+
+                c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q)
+                square := mulmod(h1w4, h1w4, q)
+                c1Value := addmod(c1Value, mulmod(square, evalC, q), q)
+                c1Value := addmod(c1Value, mulmod(mulmod(square, h1w4, q), t0, q), q)
+
+                res := addmod(res, mulmod(c1Value, mulmod(num, mload(add(pMem, add(pLiS1Inv, mul(3, 32)))), q), q), q)
+
+
+                mstore(add(pMem, pR1), res)
+            }
+
+            // Compute r2(y) by interpolating the polynomial r2(X) using 6 points (x,y)
+            // where x = {[h2, h2w3, h2w3^2], [h3, h3w3, h3w3^2]}
+            // and   y = {[C2(h2), C2(h2w3), C2(h2w3^2)], [C2(h3), C2(h3w3), C2(h3w3^2)]}
+            // and computing T1(xi) and T2(xi)
+            function computeR2(pMem) {
+                let y := mload(add(pMem, pY))
+                let num := 1
+                num := mulmod(y, num, q)
+                num := mulmod(y, num, q)
+                num := mulmod(y, num, q)
+                num := mulmod(y, num, q)
+                num := mulmod(y, num, q)
+                num := mulmod(y, num, q)
+
+                let num2 := 1
+                num2 := mulmod(y, num2, q)
+                num2 := mulmod(y, num2, q)
+                num2 := mulmod(y, num2, q)
+                num2 := mulmod(num2, addmod(mulmod(mload(add(pMem, pXi)), w1 ,q), mload(add(pMem, pXi)), q), q)
+
+                num := addmod(num, mod(sub(q, num2), q), q)
+
+                num2 := mulmod(mulmod(mload(add(pMem, pXi)), w1 ,q), mload(add(pMem, pXi)), q)
+
+                num := addmod(num, num2, q)
+
+                let t1
+                let t2
+                let betaXi := mulmod(mload(add(pMem, pBeta)), mload(add(pMem, pXi)), q)
+                let gamma := mload(add(pMem, pGamma))
+
+                t2 := addmod(calldataload( pEval_a), addmod(betaXi, gamma, q) ,q)
+                t2 := mulmod(t2,
+                            addmod(calldataload( pEval_b),
+                            addmod(mulmod(betaXi, k1, q), gamma, q) ,q), q)
+                t2 := mulmod(t2,
+                            addmod(calldataload( pEval_c),
+                            addmod(mulmod(betaXi, k2, q), gamma, q) ,q), q)
+                t2 := mulmod(t2, calldataload(pEval_z), q)
+
+                //Let's use t1 as a temporal variable to save one local
+                t1 := addmod(calldataload(pEval_a), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s1), q), gamma, q) ,q)
+                t1 := mulmod(t1,
+                      addmod(calldataload(pEval_b), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s2), q), gamma, q) ,q), q)
+                t1 := mulmod(t1,
+                      addmod(calldataload(pEval_c), addmod(mulmod(mload(add(pMem, pBeta)), calldataload(pEval_s3), q), gamma, q) ,q), q)
+                t1 := mulmod(t1, calldataload(pEval_zw), q)
+
+                t2:= addmod(t2, mod(sub(q, t1), q), q)
+                t2 := mulmod(t2, mload(add(pMem, pZhInv)), q)
+
+                // Compute T1(xi)
+                t1 := sub(calldataload(pEval_z), 1)
+                t1 := mulmod(t1, mload(add(pMem, pEval_l1)) ,q)
+                t1 := mulmod(t1, mload(add(pMem, pZhInv)) ,q)
+
+                // Let's use local variable gamma to save the result
+                gamma:=0
+                
+                let hw
+                let c2Value 
+
+                hw := mload(add(pMem, pH2w3_0))
+                c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(0, 32)))), q), q), q)
+
+                hw := mload(add(pMem, pH2w3_1))
+                c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(1, 32)))), q), q), q)
+
+                hw := mload(add(pMem, pH2w3_2))
+                c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(2, 32)))), q), q), q)
+
+                hw := mload(add(pMem, pH3w3_0))
+                c2Value := addmod(calldataload(pEval_zw), mulmod(hw, calldataload(pEval_t1w), q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(3, 32)))), q), q), q)
+
+                hw := mload(add(pMem, pH3w3_1))
+                c2Value := addmod(calldataload(pEval_zw), mulmod(hw, calldataload(pEval_t1w), q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(4, 32)))), q), q), q)
+
+                hw := mload(add(pMem, pH3w3_2))
+                c2Value := addmod(calldataload(pEval_zw), mulmod(hw, calldataload(pEval_t1w), q), q)
+                c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), q)
+                gamma := addmod(gamma, mulmod(c2Value, mulmod(num, mload(add(pMem, add(pLiS2Inv, mul(5, 32)))), q), q), q)
+
+                mstore(add(pMem, pR2), gamma)
+            }
+
+            // G1 function to accumulate a G1 value to an address
+            function g1_acc(pR, pP) {
+                let mIn := mload(0x40)
+                mstore(mIn, mload(pR))
+                mstore(add(mIn, 32), mload(add(pR, 32)))
+                mstore(add(mIn, 64), mload(pP))
+                mstore(add(mIn, 96), mload(add(pP, 32)))
+
+                let success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64)
+
+                if iszero(success) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+            }
+
+            // G1 function to multiply a G1 value to value in an address
+            function g1_mulAcc(pR, pP, s) {
+                let success
+                let mIn := mload(0x40)
+                mstore(mIn, calldataload(pP))
+                mstore(add(mIn, 32), calldataload(add(pP, 32)))
+                mstore(add(mIn, 64), s)
+
+                success := staticcall(sub(gas(), 2000), 7, mIn, 96, mIn, 64)
+
+                if iszero(success) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+
+                mstore(add(mIn, 64), mload(pR))
+                mstore(add(mIn, 96), mload(add(pR, 32)))
+
+                success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64)
+
+                if iszero(success) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+            }
+
+            // G1 function to multiply a G1 value(x,y) to value in an address
+            function g1_mulAccC(pR, x, y, s) {
+                let success
+                let mIn := mload(0x40)
+                mstore(mIn, x)
+                mstore(add(mIn, 32), y)
+                mstore(add(mIn, 64), s)
+
+                success := staticcall(sub(gas(), 2000), 7, mIn, 96, mIn, 64)
+
+                if iszero(success) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+
+                mstore(add(mIn, 64), mload(pR))
+                mstore(add(mIn, 96), mload(add(pR, 32)))
+
+                success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64)
+
+                if iszero(success) {
+                    mstore(0, 0)
+                    return(0, 0x20)
+                }
+            }
+
+            function computeFEJ(pMem) {
+                // Prepare shared numerator between F, E and J to reuse it
+                let y := mload(add(pMem, pY))
+                let numerator := addmod(y, mod(sub(q, mload(add(pMem, pH0w8_0))), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_1))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_2))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_3))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_4))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_5))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_6))), q), q), q)
+                numerator := mulmod(numerator, addmod(y, mod(sub(q, mload(add(pMem, pH0w8_7))), q), q), q)
+
+                // Prepare shared quotient between F and E to reuse it
+                let quotient1 := mulmod(mload(add(pMem, pAlpha)), mulmod(numerator, mload(add(pMem, pDenH1)), q), q)
+                let quotient2 := mulmod(mulmod(mload(add(pMem, pAlpha)), mload(add(pMem, pAlpha)), q), mulmod(numerator, mload(add(pMem, pDenH2)), q), q)
+
+                // Compute full batched polynomial commitment [F]_1
+                mstore(add(pMem, pF), C0x)
+                mstore(add(pMem, add(pF, 32)), C0y)
+                g1_mulAcc(add(pMem, pF), pC1, quotient1)
+                g1_mulAcc(add(pMem, pF), pC2, quotient2)
+
+                // Compute group-encoded batch evaluation [E]_1
+                g1_mulAccC(add(pMem, pE), G1x, G1y, addmod(mload(add(pMem, pR0)), addmod(mulmod(quotient1, mload(add(pMem, pR1)),q), mulmod(quotient2, mload(add(pMem, pR2)),q), q), q))
+
+                // Compute the full difference [J]_1
+                g1_mulAcc(add(pMem, pJ), pW1, numerator)
+            }
+
+            // Validate all evaluations with a pairing checking that e([F]_1 - [E]_1 - [J]_1 + y[W2]_1, [1]_2) == e([W']_1, [x]_2)
+            function checkPairing(pMem) -> isOk {
+                let mIn := mload(0x40)
+
+                // First pairing value
+                // Compute -E
+                mstore(add(add(pMem, pE), 32), mod(sub(qf, mload(add(add(pMem, pE), 32))), qf))
+                // Compute -J
+                mstore(add(add(pMem, pJ), 32), mod(sub(qf, mload(add(add(pMem, pJ), 32))), qf))
+                // F = F - E - J + y·W2
+                g1_acc(add(pMem, pF), add(pMem, pE))
+                g1_acc(add(pMem, pF), add(pMem, pJ))
+                g1_mulAcc(add(pMem, pF), pW2, mload(add(pMem, pY)))
+
+                mstore(mIn, mload(add(pMem, pF)))
+                mstore(add(mIn, 32), mload(add(add(pMem, pF), 32)))
+
+                // Second pairing value
+                mstore(add(mIn, 64), G2x2)
+                mstore(add(mIn, 96), G2x1)
+                mstore(add(mIn, 128), G2y2)
+                mstore(add(mIn, 160), G2y1)
+
+                // Third pairing value
+                // Compute -W2
+                mstore(add(mIn, 192), calldataload(pW2))
+                let s := calldataload(add(pW2, 32))
+                s := mod(sub(qf, s), qf)
+                mstore(add(mIn, 224), s)
+
+                // Fourth pairing value
+                mstore(add(mIn, 256), X2x2)
+                mstore(add(mIn, 288), X2x1)
+                mstore(add(mIn, 320), X2y2)
+                mstore(add(mIn, 352), X2y1)
+
+                let success := staticcall(sub(gas(), 2000), 8, mIn, 384, mIn, 0x20)
+
+                isOk := and(success, mload(mIn))
+            }
+
+            let pMem := mload(0x40)
+            mstore(0x40, add(pMem, lastMem))
+
+            // Validate that all evaluations ∈ F
+            checkInput()
+
+            // Compute the challenges: beta, gamma, xi, alpha and y ∈ F, h1w4/h2w3/h3w3 roots, xiN and zh(xi)
+            computeChallenges(pMem, pubSignals)
+
+            // To divide prime fields the Extended Euclidean Algorithm for computing modular inverses is needed.
+            // The Montgomery batch inversion algorithm allow us to compute n inverses reducing to a single one inversion.
+            // More info: https://vitalik.ca/general/2018/07/21/starks_part_3.html
+            // To avoid this single inverse computation on-chain, it has been computed in proving time and send it to the verifier.
+            // Therefore, the verifier:
+            //      1) Prepare all the denominators to inverse
+            //      2) Check the inverse sent by the prover it is what it should be
+            //      3) Compute the others inverses using the Montgomery Batched Algorithm using the inverse sent to avoid the inversion operation it does.
+            computeInversions(pMem)
+
+            // Compute Lagrange polynomial evaluations Li(xi)
+            computeLagrange(pMem)
+
+            // Compute public input polynomial evaluation PI(xi) = \sum_i^l -public_input_i·L_i(xi)
+            computePi(pMem, pubSignals)
+
+            // Computes r1(y) and r2(y)
+            computeR0(pMem)
+            computeR1(pMem)
+            computeR2(pMem)
+
+            // Compute full batched polynomial commitment [F]_1, group-encoded batch evaluation [E]_1 and the full difference [J]_1
+            computeFEJ(pMem)
+
+            // Validate all evaluations
+            let isValid := checkPairing(pMem)
+
+            mstore(0, isValid)
+            return(0, 0x20)
+        }
+    }
+}
\ No newline at end of file
diff --git a/docs/v2/lib/PolygonRollupBaseEtrog.md b/docs/v2/lib/PolygonRollupBaseEtrog.md
index c8d40e1e8..a2184b926 100644
--- a/docs/v2/lib/PolygonRollupBaseEtrog.md
+++ b/docs/v2/lib/PolygonRollupBaseEtrog.md
@@ -236,6 +236,15 @@ Generate Initialize transaction for hte bridge on L2
 |`_gasTokenNetwork` | uint32 | Indicates the native network of the token address
 |`_gasTokenMetadata` | bytes | Abi encoded gas token metadata
 
+### _verifyOrigin
+```solidity
+  function _verifyOrigin(
+  ) internal returns (bytes gasTokenMetadata)
+```
+
+
+
+
 ## Events
 ### SequenceBatches
 ```solidity
diff --git a/tools/deployVerifier/.gitignore b/tools/deployVerifier/.gitignore
new file mode 100644
index 000000000..f5c01b984
--- /dev/null
+++ b/tools/deployVerifier/.gitignore
@@ -0,0 +1 @@
+deploy_verifier_parameters.json
\ No newline at end of file
diff --git a/tools/deployVerifier/README.md b/tools/deployVerifier/README.md
new file mode 100644
index 000000000..08deda9b9
--- /dev/null
+++ b/tools/deployVerifier/README.md
@@ -0,0 +1,36 @@
+# Deploy verifier
+Script to deploy `verifier` smart contract
+
+## Install
+```
+npm i
+```
+
+## Setup
+- Config file
+  - `realVerifier`: select between a real or a mock verifer
+  - `forkID`: Select fork to verifier to be deployed (if a real verfifier is selected)
+  - `deployerPvtKey`: private key deployer
+    - First option will load `deployerPvtKey`. Otherwise, `process.env.MNEMONIC` will be loaded from the `.env` file
+  - `maxFeePerGas`: set custom gas
+  - `maxPriorityFeePerGas`: set custom gas
+  - `multiplierGas`: set custom gas
+- A network should be selected when running the script
+  - examples: `-- sepolia` or `--mainnet`
+  - This uses variables set in `hardhat.config.ts`
+  - Which uses some nvironment variables that should be set in `.env`
+> All paths are from roor repository
+
+## Usage
+> All commands are done from root repository.
+
+- Copy configuration file:
+```
+cp ./tools/deployVerifier/deploy_verifier_parameters.example ./tools/deployVerifier/deploy_verifier_parameters.json
+```
+
+- Set your parameters
+- Run tool:
+```
+npx hardhat run ./tools/addRollupType/deployVerififer.ts --network sepolia
+```
diff --git a/tools/deployVerifier/deployVerifier.ts b/tools/deployVerifier/deployVerifier.ts
index 9a58d68a0..89a1eecbb 100644
--- a/tools/deployVerifier/deployVerifier.ts
+++ b/tools/deployVerifier/deployVerifier.ts
@@ -56,27 +56,33 @@ async function main() {
         [deployer] = await ethers.getSigners();
     }
 
-    console.log("deploying with: ", deployer.address);
+    console.log("--> Deploying with: ", deployer.address);
 
     /*
-     *Deployment pol
+     * Deployment Verifier
      */
+    const verifierName = `FflonkVerifier_${deployParameters.forkID}`;
     let verifierContract;
     if (deployParameters.realVerifier === true) {
-        const VerifierRollup = await ethers.getContractFactory("FflonkVerifier", deployer);
+        const VerifierRollup = await ethers.getContractFactory(verifierName, deployer);
+        console.log(`--> Deploying verifier: ${verifierName}`);
         verifierContract = await VerifierRollup.deploy();
         await verifierContract.waitForDeployment();
     } else {
         const VerifierRollupHelperFactory = await ethers.getContractFactory("VerifierRollupHelperMock", deployer);
+        console.log("Deploying verifier VerifierRollupHelperMock");
         verifierContract = await VerifierRollupHelperFactory.deploy();
         await verifierContract.waitForDeployment();
     }
-    console.log("#######################\n");
+    // print contract address deployed
+    console.log("\n#######################");
     console.log("Verifier deployed to:", verifierContract.target);
     console.log("#######################\n");
-    console.log("verifierContract deployed to:", verifierContract.target);
-    console.log("you can verify the new verifierContract address with:");
-    console.log(`npx hardhat verify ${verifierContract.target} --network ${process.env.HARDHAT_NETWORK}\n`);
+    // print verification command line
+    console.log("#######################");
+    console.log("you can verify the new verifierContract address with the following command:");
+    console.log(`npx hardhat verify ${verifierContract.target} --network ${process.env.HARDHAT_NETWORK}`);
+    console.log("#######################");
 }
 
 main().catch((e) => {
diff --git a/tools/deployVerifier/deploy_verifier_parameters.example b/tools/deployVerifier/deploy_verifier_parameters.example
index 82d313e24..7234d1595 100644
--- a/tools/deployVerifier/deploy_verifier_parameters.example
+++ b/tools/deployVerifier/deploy_verifier_parameters.example
@@ -1,5 +1,6 @@
 {
     "realVerifier": true,
+    "forkID": 10,
     "deployerPvtKey": "",
     "maxFeePerGas":"",
     "maxPriorityFeePerGas":"",