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Use an XOF instead of a PRNG to derive ZK proof challenges. #45

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Nov 8, 2023
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Use an XOF instead of a PRNG to derive ZK proof challenges. #45

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1 change: 0 additions & 1 deletion synedrion/Cargo.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -18,7 +18,6 @@ sha3 = { version = "0.10", default-features = false }
digest = { version = "0.10", default-features = false, features = ["alloc"]}
hex = { version = "0.4", default-features = false, features = ["alloc"] }
base64 = { version = "0.21", default-features = false, features = ["alloc"] }
rand_chacha = { version = "0.3", default-features = false }

crypto-bigint = { version = "0.5.3", features = ["serde"] }
crypto-primes = "0.5"
Expand Down
20 changes: 13 additions & 7 deletions synedrion/src/cggmp21/sigma/aff_g.rs
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Expand Up @@ -9,7 +9,7 @@ use crate::paillier::{
Ciphertext, PaillierParams, PublicKeyPaillierPrecomputed, RPCommitment, RPParamsMod,
Randomizer, RandomizerMod,
};
use crate::tools::hashing::{Chain, Hash, Hashable};
use crate::tools::hashing::{Chain, Hashable, XofHash};
use crate::uint::{FromScalar, NonZero, Signed};

const HASH_TAG: &[u8] = b"P_aff_g";
Expand Down Expand Up @@ -45,10 +45,13 @@ impl<P: SchemeParams> AffGProof<P> {
aux_rp: &RPParamsMod<P::Paillier>, // $\hat{N}$, $s$, $t$
aux: &impl Hashable,
) -> Self {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());
let e_wide = e.into_wide();

let hat_cap_n = &aux_rp.public_key().modulus_nonzero();
Expand Down Expand Up @@ -128,12 +131,15 @@ impl<P: SchemeParams> AffGProof<P> {
aux_rp: &RPParamsMod<P::Paillier>, // $\hat{N}$, $s$, $t$
aux: &impl Hashable,
) -> bool {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();

let aux_pk = aux_rp.public_key();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

let aux_pk = aux_rp.public_key();

// C^{z_1} (1 + N_0)^{z_2} \omega^{N_0} = A D^e \mod N_0^2
// => C (*) z_1 (+) encrypt_0(z_2, \omega) = A (+) D (*) e
Expand Down
16 changes: 11 additions & 5 deletions synedrion/src/cggmp21/sigma/dec.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -9,7 +9,7 @@ use crate::paillier::{
Ciphertext, PaillierParams, PublicKeyPaillierPrecomputed, RPCommitment, RPParamsMod,
Randomizer, RandomizerMod,
};
use crate::tools::hashing::{Chain, Hash, Hashable};
use crate::tools::hashing::{Chain, Hashable, XofHash};
use crate::uint::{FromScalar, NonZero, Signed};

const HASH_TAG: &[u8] = b"P_dec";
Expand All @@ -34,10 +34,13 @@ impl<P: SchemeParams> DecProof<P> {
aux_rp: &RPParamsMod<P::Paillier>, // $\hat{N}$, $s$, $t$
aux: &impl Hashable,
) -> Self {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

let hat_cap_n = &aux_rp.public_key().modulus_nonzero(); // $\hat{N}$

Expand Down Expand Up @@ -75,10 +78,13 @@ impl<P: SchemeParams> DecProof<P> {
aux_rp: &RPParamsMod<P::Paillier>, // $\hat{N}$, $s$, $t$
aux: &impl Hashable,
) -> bool {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

// enc(z_1, \omega) == A (+) C (*) e
if Ciphertext::new_with_randomizer_signed(pk, &self.z1, &self.omega)
Expand Down
16 changes: 11 additions & 5 deletions synedrion/src/cggmp21/sigma/enc.rs
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Expand Up @@ -8,7 +8,7 @@ use crate::paillier::{
Ciphertext, PaillierParams, PublicKeyPaillierPrecomputed, RPCommitment, RPParamsMod,
Randomizer, RandomizerMod, SecretKeyPaillierPrecomputed,
};
use crate::tools::hashing::{Chain, Hash, Hashable};
use crate::tools::hashing::{Chain, Hashable, XofHash};
use crate::uint::{NonZero, Signed};

const HASH_TAG: &[u8] = b"P_enc";
Expand All @@ -32,10 +32,13 @@ impl<P: SchemeParams> EncProof<P> {
aux_rp: &RPParamsMod<P::Paillier>, // $\hat{N}$, $s$, $t$
aux: &impl Hashable,
) -> Self {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

let pk = sk.public_key();
let hat_cap_n = &aux_rp.public_key().modulus_nonzero(); // $\hat{N}$
Expand Down Expand Up @@ -72,10 +75,13 @@ impl<P: SchemeParams> EncProof<P> {
aux_rp: &RPParamsMod<P::Paillier>, // $s$, $t$
aux: &impl Hashable, // CHECK: used to derive `\hat{N}, s, t`
) -> bool {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

// z_1 \in \pm 2^{\ell + \eps}
if !self.z1.in_range_bits(P::L_BOUND + P::EPS_BOUND) {
Expand Down
16 changes: 11 additions & 5 deletions synedrion/src/cggmp21/sigma/fac.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -8,7 +8,7 @@ use crate::paillier::{
PaillierParams, PublicKeyPaillierPrecomputed, RPCommitment, RPParamsMod,
SecretKeyPaillierPrecomputed,
};
use crate::tools::hashing::{Chain, Hash, Hashable};
use crate::tools::hashing::{Chain, Hashable, XofHash};
use crate::uint::{HasWide, Integer, NonZero, Signed};

const HASH_TAG: &[u8] = b"P_fac";
Expand All @@ -35,10 +35,13 @@ impl<P: SchemeParams> FacProof<P> {
aux_rp: &RPParamsMod<P::Paillier>, // $\hat{N}$, $s$, $t$
aux: &impl Hashable,
) -> Self {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());
let e_wide = e.into_wide();

let pk = sk.public_key();
Expand Down Expand Up @@ -109,10 +112,13 @@ impl<P: SchemeParams> FacProof<P> {
aux_rp: &RPParamsMod<P::Paillier>, // $s$, $t$
aux: &impl Hashable,
) -> bool {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

let aux_pk = aux_rp.public_key();

Expand Down
16 changes: 11 additions & 5 deletions synedrion/src/cggmp21/sigma/log_star.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -9,7 +9,7 @@ use crate::paillier::{
Ciphertext, PaillierParams, PublicKeyPaillierPrecomputed, RPCommitment, RPParamsMod,
Randomizer, RandomizerMod,
};
use crate::tools::hashing::{Chain, Hash, Hashable};
use crate::tools::hashing::{Chain, Hashable, XofHash};
use crate::uint::{FromScalar, NonZero, Signed};

const HASH_TAG: &[u8] = b"P_log*";
Expand All @@ -36,10 +36,13 @@ impl<P: SchemeParams> LogStarProof<P> {
aux_rp: &RPParamsMod<P::Paillier>, // $\hat{N}$, $s$, $t$
aux: &impl Hashable,
) -> Self {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

let hat_cap_n = &aux_rp.public_key().modulus_nonzero(); // $\hat{N}$

Expand Down Expand Up @@ -78,10 +81,13 @@ impl<P: SchemeParams> LogStarProof<P> {
aux_rp: &RPParamsMod<P::Paillier>, // $s$, $t$
aux: &impl Hashable,
) -> bool {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

// enc_0(z1, z2) == A (+) C (*) e
let c = Ciphertext::new_with_randomizer_signed(pk, &self.z1, &self.z2);
Expand Down
11 changes: 7 additions & 4 deletions synedrion/src/cggmp21/sigma/mod_.rs
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Expand Up @@ -7,8 +7,8 @@ use serde::{Deserialize, Serialize};

use super::super::SchemeParams;
use crate::paillier::{PaillierParams, PublicKeyPaillierPrecomputed, SecretKeyPaillierPrecomputed};
use crate::tools::hashing::{Chain, Hash, Hashable};
use crate::uint::{JacobiSymbol, JacobiSymbolTrait, RandomMod, Retrieve, UintModLike};
use crate::tools::hashing::{Chain, Hashable, XofHash};
use crate::uint::{JacobiSymbol, JacobiSymbolTrait, RandomMod, Retrieve, UintLike, UintModLike};

const HASH_TAG: &[u8] = b"P_mod";

Expand All @@ -35,10 +35,13 @@ struct ModChallenge<P: SchemeParams>(Vec<<P::Paillier as PaillierParams>::Uint>)

impl<P: SchemeParams> ModChallenge<P> {
fn new(aux: &impl Hashable, pk: &PublicKeyPaillierPrecomputed<P::Paillier>) -> Self {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

let modulus = pk.modulus_nonzero();
let ys = (0..P::SECURITY_PARAMETER)
.map(|_| <P::Paillier as PaillierParams>::Uint::random_mod(&mut aux_rng, &modulus))
.map(|_| <P::Paillier as PaillierParams>::Uint::from_xof(&mut reader, &modulus))
.collect();
Self(ys)
}
Expand Down
16 changes: 11 additions & 5 deletions synedrion/src/cggmp21/sigma/mul.rs
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Expand Up @@ -7,7 +7,7 @@ use super::super::SchemeParams;
use crate::paillier::{
Ciphertext, PaillierParams, PublicKeyPaillierPrecomputed, Randomizer, RandomizerMod,
};
use crate::tools::hashing::{Chain, Hash, Hashable};
use crate::tools::hashing::{Chain, Hashable, XofHash};
use crate::uint::{Bounded, NonZero, Retrieve, Signed};

const HASH_TAG: &[u8] = b"P_mul";
Expand All @@ -32,10 +32,13 @@ impl<P: SchemeParams> MulProof<P> {
cap_y: &Ciphertext<P::Paillier>, // $Y$
aux: &impl Hashable,
) -> Self {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

let alpha_mod = pk.random_invertible_group_elem(rng);
let r_mod = RandomizerMod::random(rng, pk);
Expand Down Expand Up @@ -75,10 +78,13 @@ impl<P: SchemeParams> MulProof<P> {
cap_c: &Ciphertext<P::Paillier>, // $C = (Y (*) x) * \rho^N$
aux: &impl Hashable,
) -> bool {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

// Y^z u^N = A * C^e \mod N^2
if cap_y
Expand Down
16 changes: 11 additions & 5 deletions synedrion/src/cggmp21/sigma/mul_star.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -11,7 +11,7 @@ use crate::paillier::{
Ciphertext, PaillierParams, PublicKeyPaillierPrecomputed, RPCommitment, RPParamsMod,
Randomizer, RandomizerMod,
};
use crate::tools::hashing::{Chain, Hash, Hashable};
use crate::tools::hashing::{Chain, Hashable, XofHash};
use crate::uint::{FromScalar, NonZero, Signed};

const HASH_TAG: &[u8] = b"P_mul*";
Expand Down Expand Up @@ -46,10 +46,13 @@ impl<P: SchemeParams> MulStarProof<P> {
(and judging by the condition the verifier checks, it should be == 0)
*/

let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

let hat_cap_n = &aux_rp.public_key().modulus_nonzero(); // $\hat{N}$

Expand Down Expand Up @@ -90,10 +93,13 @@ impl<P: SchemeParams> MulStarProof<P> {
aux_rp: &RPParamsMod<P::Paillier>, // $\hat{N}$, $s$, $t$
aux: &impl Hashable,
) -> bool {
let mut aux_rng = Hash::new_with_dst(HASH_TAG).chain(aux).finalize_to_rng();
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.finalize_to_reader();

// Non-interactive challenge
let e = Signed::random_bounded(&mut aux_rng, &NonZero::new(P::CURVE_ORDER).unwrap());
let e =
Signed::from_xof_reader_bounded(&mut reader, &NonZero::new(P::CURVE_ORDER).unwrap());

let aux_pk = aux_rp.public_key();

Expand Down
12 changes: 6 additions & 6 deletions synedrion/src/cggmp21/sigma/prm.rs
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Expand Up @@ -5,16 +5,16 @@

use alloc::{vec, vec::Vec};

use rand_core::{CryptoRngCore, RngCore};

use digest::XofReader;
use rand_core::CryptoRngCore;
use serde::{Deserialize, Serialize};

use super::super::SchemeParams;
use crate::paillier::{
PaillierParams, PublicKeyPaillierPrecomputed, RPParamsMod, RPSecret,
SecretKeyPaillierPrecomputed,
};
use crate::tools::hashing::{Chain, Hash, Hashable};
use crate::tools::hashing::{Chain, Hashable, XofHash};
use crate::uint::{
subtle::{Choice, ConditionallySelectable},
Bounded, Retrieve, UintModLike,
Expand Down Expand Up @@ -73,12 +73,12 @@ struct PrmChallenge(Vec<bool>);
impl PrmChallenge {
fn new<P: SchemeParams>(aux: &impl Hashable, commitment: &PrmCommitment<P>) -> Self {
// TODO: generate m/8 random bytes instead and fill the vector bit by bit.
let mut aux_rng = Hash::new_with_dst(HASH_TAG)
let mut reader = XofHash::new_with_dst(HASH_TAG)
.chain(aux)
.chain(commitment)
.finalize_to_rng();
.finalize_to_reader();
let mut bytes = vec![0u8; P::SECURITY_PARAMETER];
aux_rng.fill_bytes(&mut bytes);
reader.read(&mut bytes);
Self(bytes.iter().map(|b| b & 1 == 1).collect())
}
}
Expand Down
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