428 lines
15 KiB
Rust
428 lines
15 KiB
Rust
//! The ciphertext-commitment equality sigma proof system.
|
|
//!
|
|
//! A ciphertext-commitment equality proof is defined with respect to a twisted ElGamal ciphertext
|
|
//! and a Pedersen commitment. The proof certifies that a given ciphertext and a commitment pair
|
|
//! encrypts/encodes the same message. To generate the proof, a prover must provide the decryption
|
|
//! key for the first ciphertext and the Pedersen opening for the commitment.
|
|
//!
|
|
//! The protocol guarantees computationally soundness (by the hardness of discrete log) and perfect
|
|
//! zero-knowledge in the random oracle model.
|
|
|
|
#[cfg(not(target_os = "solana"))]
|
|
use {
|
|
crate::{
|
|
encryption::{
|
|
elgamal::{ElGamalCiphertext, ElGamalKeypair, ElGamalPubkey},
|
|
pedersen::{PedersenCommitment, PedersenOpening, G, H},
|
|
},
|
|
sigma_proofs::{canonical_scalar_from_optional_slice, ristretto_point_from_optional_slice},
|
|
UNIT_LEN,
|
|
},
|
|
curve25519_dalek::traits::MultiscalarMul,
|
|
rand::rngs::OsRng,
|
|
zeroize::Zeroize,
|
|
};
|
|
use {
|
|
crate::{
|
|
sigma_proofs::errors::{EqualityProofVerificationError, SigmaProofVerificationError},
|
|
transcript::TranscriptProtocol,
|
|
},
|
|
curve25519_dalek::{
|
|
ristretto::{CompressedRistretto, RistrettoPoint},
|
|
scalar::Scalar,
|
|
traits::{IsIdentity, VartimeMultiscalarMul},
|
|
},
|
|
merlin::Transcript,
|
|
};
|
|
|
|
/// Byte length of a ciphertext-commitment equality proof.
|
|
const CIPHERTEXT_COMMITMENT_EQUALITY_PROOF_LEN: usize = UNIT_LEN * 6;
|
|
|
|
/// Equality proof.
|
|
///
|
|
/// Contains all the elliptic curve and scalar components that make up the sigma protocol.
|
|
#[allow(non_snake_case)]
|
|
#[derive(Clone)]
|
|
pub struct CiphertextCommitmentEqualityProof {
|
|
Y_0: CompressedRistretto,
|
|
Y_1: CompressedRistretto,
|
|
Y_2: CompressedRistretto,
|
|
z_s: Scalar,
|
|
z_x: Scalar,
|
|
z_r: Scalar,
|
|
}
|
|
|
|
#[allow(non_snake_case)]
|
|
#[cfg(not(target_os = "solana"))]
|
|
impl CiphertextCommitmentEqualityProof {
|
|
/// Creates a ciphertext-commitment equality proof.
|
|
///
|
|
/// The function does *not* hash the public key, ciphertext, or commitment into the transcript.
|
|
/// For security, the caller (the main protocol) should hash these public components prior to
|
|
/// invoking this constructor.
|
|
///
|
|
/// This function is randomized. It uses `OsRng` internally to generate random scalars.
|
|
///
|
|
/// Note that the proof constructor does not take the actual Pedersen commitment as input; it
|
|
/// takes the associated Pedersen opening instead.
|
|
///
|
|
/// * `source_keypair` - The ElGamal keypair associated with the first to be proved
|
|
/// * `source_ciphertext` - The main ElGamal ciphertext to be proved
|
|
/// * `amount` - The message associated with the ElGamal ciphertext and Pedersen commitment
|
|
/// * `opening` - The opening associated with the main Pedersen commitment to be proved
|
|
/// * `transcript` - The transcript that does the bookkeeping for the Fiat-Shamir heuristic
|
|
pub fn new(
|
|
source_keypair: &ElGamalKeypair,
|
|
source_ciphertext: &ElGamalCiphertext,
|
|
opening: &PedersenOpening,
|
|
amount: u64,
|
|
transcript: &mut Transcript,
|
|
) -> Self {
|
|
transcript.equality_proof_domain_separator();
|
|
|
|
// extract the relevant scalar and Ristretto points from the inputs
|
|
let P_source = source_keypair.pubkey().get_point();
|
|
let D_source = source_ciphertext.handle.get_point();
|
|
|
|
let s = source_keypair.secret().get_scalar();
|
|
let x = Scalar::from(amount);
|
|
let r = opening.get_scalar();
|
|
|
|
// generate random masking factors that also serves as nonces
|
|
let mut y_s = Scalar::random(&mut OsRng);
|
|
let mut y_x = Scalar::random(&mut OsRng);
|
|
let mut y_r = Scalar::random(&mut OsRng);
|
|
|
|
let Y_0 = (&y_s * P_source).compress();
|
|
let Y_1 =
|
|
RistrettoPoint::multiscalar_mul(vec![&y_x, &y_s], vec![&(*G), D_source]).compress();
|
|
let Y_2 = RistrettoPoint::multiscalar_mul(vec![&y_x, &y_r], vec![&(*G), &(*H)]).compress();
|
|
|
|
// record masking factors in the transcript
|
|
transcript.append_point(b"Y_0", &Y_0);
|
|
transcript.append_point(b"Y_1", &Y_1);
|
|
transcript.append_point(b"Y_2", &Y_2);
|
|
|
|
let c = transcript.challenge_scalar(b"c");
|
|
transcript.challenge_scalar(b"w");
|
|
|
|
// compute the masked values
|
|
let z_s = &(&c * s) + &y_s;
|
|
let z_x = &(&c * &x) + &y_x;
|
|
let z_r = &(&c * r) + &y_r;
|
|
|
|
// zeroize random scalars
|
|
y_s.zeroize();
|
|
y_x.zeroize();
|
|
y_r.zeroize();
|
|
|
|
CiphertextCommitmentEqualityProof {
|
|
Y_0,
|
|
Y_1,
|
|
Y_2,
|
|
z_s,
|
|
z_x,
|
|
z_r,
|
|
}
|
|
}
|
|
|
|
/// Verifies a ciphertext-commitment equality proof.
|
|
///
|
|
/// * `source_pubkey` - The ElGamal pubkey associated with the ciphertext to be proved
|
|
/// * `source_ciphertext` - The main ElGamal ciphertext to be proved
|
|
/// * `destination_commitment` - The main Pedersen commitment to be proved
|
|
/// * `transcript` - The transcript that does the bookkeeping for the Fiat-Shamir heuristic
|
|
pub fn verify(
|
|
self,
|
|
source_pubkey: &ElGamalPubkey,
|
|
source_ciphertext: &ElGamalCiphertext,
|
|
destination_commitment: &PedersenCommitment,
|
|
transcript: &mut Transcript,
|
|
) -> Result<(), EqualityProofVerificationError> {
|
|
transcript.equality_proof_domain_separator();
|
|
|
|
// extract the relevant scalar and Ristretto points from the inputs
|
|
let P_source = source_pubkey.get_point();
|
|
let C_source = source_ciphertext.commitment.get_point();
|
|
let D_source = source_ciphertext.handle.get_point();
|
|
let C_destination = destination_commitment.get_point();
|
|
|
|
// include Y_0, Y_1, Y_2 to transcript and extract challenges
|
|
transcript.validate_and_append_point(b"Y_0", &self.Y_0)?;
|
|
transcript.validate_and_append_point(b"Y_1", &self.Y_1)?;
|
|
transcript.validate_and_append_point(b"Y_2", &self.Y_2)?;
|
|
|
|
let c = transcript.challenge_scalar(b"c");
|
|
let w = transcript.challenge_scalar(b"w"); // w used for batch verification
|
|
let ww = &w * &w;
|
|
|
|
let w_negated = -&w;
|
|
let ww_negated = -&ww;
|
|
|
|
// check that the required algebraic condition holds
|
|
let Y_0 = self
|
|
.Y_0
|
|
.decompress()
|
|
.ok_or(SigmaProofVerificationError::Deserialization)?;
|
|
let Y_1 = self
|
|
.Y_1
|
|
.decompress()
|
|
.ok_or(SigmaProofVerificationError::Deserialization)?;
|
|
let Y_2 = self
|
|
.Y_2
|
|
.decompress()
|
|
.ok_or(SigmaProofVerificationError::Deserialization)?;
|
|
|
|
let check = RistrettoPoint::vartime_multiscalar_mul(
|
|
vec![
|
|
&self.z_s, // z_s
|
|
&(-&c), // -c
|
|
&(-&Scalar::one()), // -identity
|
|
&(&w * &self.z_x), // w * z_x
|
|
&(&w * &self.z_s), // w * z_s
|
|
&(&w_negated * &c), // -w * c
|
|
&w_negated, // -w
|
|
&(&ww * &self.z_x), // ww * z_x
|
|
&(&ww * &self.z_r), // ww * z_r
|
|
&(&ww_negated * &c), // -ww * c
|
|
&ww_negated, // -ww
|
|
],
|
|
vec![
|
|
P_source, // P_source
|
|
&(*H), // H
|
|
&Y_0, // Y_0
|
|
&(*G), // G
|
|
D_source, // D_source
|
|
C_source, // C_source
|
|
&Y_1, // Y_1
|
|
&(*G), // G
|
|
&(*H), // H
|
|
C_destination, // C_destination
|
|
&Y_2, // Y_2
|
|
],
|
|
);
|
|
|
|
if check.is_identity() {
|
|
Ok(())
|
|
} else {
|
|
Err(SigmaProofVerificationError::AlgebraicRelation.into())
|
|
}
|
|
}
|
|
|
|
pub fn to_bytes(&self) -> [u8; CIPHERTEXT_COMMITMENT_EQUALITY_PROOF_LEN] {
|
|
let mut buf = [0_u8; CIPHERTEXT_COMMITMENT_EQUALITY_PROOF_LEN];
|
|
let mut chunks = buf.chunks_mut(UNIT_LEN);
|
|
chunks.next().unwrap().copy_from_slice(self.Y_0.as_bytes());
|
|
chunks.next().unwrap().copy_from_slice(self.Y_1.as_bytes());
|
|
chunks.next().unwrap().copy_from_slice(self.Y_2.as_bytes());
|
|
chunks.next().unwrap().copy_from_slice(self.z_s.as_bytes());
|
|
chunks.next().unwrap().copy_from_slice(self.z_x.as_bytes());
|
|
chunks.next().unwrap().copy_from_slice(self.z_r.as_bytes());
|
|
buf
|
|
}
|
|
|
|
pub fn from_bytes(bytes: &[u8]) -> Result<Self, EqualityProofVerificationError> {
|
|
let mut chunks = bytes.chunks(UNIT_LEN);
|
|
let Y_0 = ristretto_point_from_optional_slice(chunks.next())?;
|
|
let Y_1 = ristretto_point_from_optional_slice(chunks.next())?;
|
|
let Y_2 = ristretto_point_from_optional_slice(chunks.next())?;
|
|
let z_s = canonical_scalar_from_optional_slice(chunks.next())?;
|
|
let z_x = canonical_scalar_from_optional_slice(chunks.next())?;
|
|
let z_r = canonical_scalar_from_optional_slice(chunks.next())?;
|
|
|
|
Ok(CiphertextCommitmentEqualityProof {
|
|
Y_0,
|
|
Y_1,
|
|
Y_2,
|
|
z_s,
|
|
z_x,
|
|
z_r,
|
|
})
|
|
}
|
|
}
|
|
|
|
#[cfg(test)]
|
|
mod test {
|
|
use {
|
|
super::*,
|
|
crate::encryption::{elgamal::ElGamalSecretKey, pedersen::Pedersen},
|
|
};
|
|
|
|
#[test]
|
|
fn test_ciphertext_commitment_equality_proof_correctness() {
|
|
// success case
|
|
let source_keypair = ElGamalKeypair::new_rand();
|
|
let message: u64 = 55;
|
|
|
|
let source_ciphertext = source_keypair.pubkey().encrypt(message);
|
|
let (destination_commitment, destination_opening) = Pedersen::new(message);
|
|
|
|
let mut prover_transcript = Transcript::new(b"Test");
|
|
let mut verifier_transcript = Transcript::new(b"Test");
|
|
|
|
let proof = CiphertextCommitmentEqualityProof::new(
|
|
&source_keypair,
|
|
&source_ciphertext,
|
|
&destination_opening,
|
|
message,
|
|
&mut prover_transcript,
|
|
);
|
|
|
|
assert!(proof
|
|
.verify(
|
|
source_keypair.pubkey(),
|
|
&source_ciphertext,
|
|
&destination_commitment,
|
|
&mut verifier_transcript
|
|
)
|
|
.is_ok());
|
|
|
|
// fail case: encrypted and committed messages are different
|
|
let source_keypair = ElGamalKeypair::new_rand();
|
|
let encrypted_message: u64 = 55;
|
|
let committed_message: u64 = 77;
|
|
|
|
let source_ciphertext = source_keypair.pubkey().encrypt(encrypted_message);
|
|
let (destination_commitment, destination_opening) = Pedersen::new(committed_message);
|
|
|
|
let mut prover_transcript = Transcript::new(b"Test");
|
|
let mut verifier_transcript = Transcript::new(b"Test");
|
|
|
|
let proof = CiphertextCommitmentEqualityProof::new(
|
|
&source_keypair,
|
|
&source_ciphertext,
|
|
&destination_opening,
|
|
message,
|
|
&mut prover_transcript,
|
|
);
|
|
|
|
assert!(proof
|
|
.verify(
|
|
source_keypair.pubkey(),
|
|
&source_ciphertext,
|
|
&destination_commitment,
|
|
&mut verifier_transcript
|
|
)
|
|
.is_err());
|
|
}
|
|
|
|
#[test]
|
|
fn test_ciphertext_commitment_equality_proof_edge_cases() {
|
|
// if ElGamal public key zero (public key is invalid), then the proof should always reject
|
|
let public = ElGamalPubkey::try_from([0u8; 32].as_slice()).unwrap();
|
|
let secret = ElGamalSecretKey::new_rand();
|
|
|
|
let elgamal_keypair = ElGamalKeypair::new_for_tests(public, secret);
|
|
|
|
let message: u64 = 55;
|
|
let ciphertext = elgamal_keypair.pubkey().encrypt(message);
|
|
let (commitment, opening) = Pedersen::new(message);
|
|
|
|
let mut prover_transcript = Transcript::new(b"Test");
|
|
let mut verifier_transcript = Transcript::new(b"Test");
|
|
|
|
let proof = CiphertextCommitmentEqualityProof::new(
|
|
&elgamal_keypair,
|
|
&ciphertext,
|
|
&opening,
|
|
message,
|
|
&mut prover_transcript,
|
|
);
|
|
|
|
assert!(proof
|
|
.verify(
|
|
elgamal_keypair.pubkey(),
|
|
&ciphertext,
|
|
&commitment,
|
|
&mut verifier_transcript
|
|
)
|
|
.is_err());
|
|
|
|
// if ciphertext is all-zero (valid commitment of 0) and commitment is also all-zero, then
|
|
// the proof should still accept
|
|
let elgamal_keypair = ElGamalKeypair::new_rand();
|
|
|
|
let message: u64 = 0;
|
|
let ciphertext = ElGamalCiphertext::from_bytes(&[0u8; 64]).unwrap();
|
|
let commitment = PedersenCommitment::from_bytes(&[0u8; 32]).unwrap();
|
|
let opening = PedersenOpening::from_bytes(&[0u8; 32]).unwrap();
|
|
|
|
let mut prover_transcript = Transcript::new(b"Test");
|
|
let mut verifier_transcript = Transcript::new(b"Test");
|
|
|
|
let proof = CiphertextCommitmentEqualityProof::new(
|
|
&elgamal_keypair,
|
|
&ciphertext,
|
|
&opening,
|
|
message,
|
|
&mut prover_transcript,
|
|
);
|
|
|
|
assert!(proof
|
|
.verify(
|
|
elgamal_keypair.pubkey(),
|
|
&ciphertext,
|
|
&commitment,
|
|
&mut verifier_transcript
|
|
)
|
|
.is_ok());
|
|
|
|
// if commitment is all-zero and the ciphertext is a correct encryption of 0, then the
|
|
// proof should still accept
|
|
let elgamal_keypair = ElGamalKeypair::new_rand();
|
|
|
|
let message: u64 = 0;
|
|
let ciphertext = elgamal_keypair.pubkey().encrypt(message);
|
|
let commitment = PedersenCommitment::from_bytes(&[0u8; 32]).unwrap();
|
|
let opening = PedersenOpening::from_bytes(&[0u8; 32]).unwrap();
|
|
|
|
let mut prover_transcript = Transcript::new(b"Test");
|
|
let mut verifier_transcript = Transcript::new(b"Test");
|
|
|
|
let proof = CiphertextCommitmentEqualityProof::new(
|
|
&elgamal_keypair,
|
|
&ciphertext,
|
|
&opening,
|
|
message,
|
|
&mut prover_transcript,
|
|
);
|
|
|
|
assert!(proof
|
|
.verify(
|
|
elgamal_keypair.pubkey(),
|
|
&ciphertext,
|
|
&commitment,
|
|
&mut verifier_transcript
|
|
)
|
|
.is_ok());
|
|
|
|
// if ciphertext is all zero and commitment correctly encodes 0, then the proof should
|
|
// still accept
|
|
let elgamal_keypair = ElGamalKeypair::new_rand();
|
|
|
|
let message: u64 = 0;
|
|
let ciphertext = ElGamalCiphertext::from_bytes(&[0u8; 64]).unwrap();
|
|
let (commitment, opening) = Pedersen::new(message);
|
|
|
|
let mut prover_transcript = Transcript::new(b"Test");
|
|
let mut verifier_transcript = Transcript::new(b"Test");
|
|
|
|
let proof = CiphertextCommitmentEqualityProof::new(
|
|
&elgamal_keypair,
|
|
&ciphertext,
|
|
&opening,
|
|
message,
|
|
&mut prover_transcript,
|
|
);
|
|
|
|
assert!(proof
|
|
.verify(
|
|
elgamal_keypair.pubkey(),
|
|
&ciphertext,
|
|
&commitment,
|
|
&mut verifier_transcript
|
|
)
|
|
.is_ok());
|
|
}
|
|
}
|