373 lines
13 KiB
Rust
373 lines
13 KiB
Rust
//! The ciphertext validity sigma proof system.
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//!
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//! The ciphertext validity proof is defined with respect to a Pedersen commitment and two
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//! decryption handles. The proof certifies that a given Pedersen commitment can be decrypted using
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//! ElGamal private keys that are associated with each of the two decryption handles. To generate
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//! the proof, a prover must provide the Pedersen opening associated with the commitment.
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//!
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//! The protocol guarantees computational soundness (by the hardness of discrete log) and perfect
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//! zero-knowledge in the random oracle model.
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#[cfg(not(target_os = "solana"))]
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use {
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crate::{
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encryption::{
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elgamal::{DecryptHandle, ElGamalPubkey},
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pedersen::{PedersenCommitment, PedersenOpening, G, H},
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},
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sigma_proofs::{canonical_scalar_from_optional_slice, ristretto_point_from_optional_slice},
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UNIT_LEN,
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},
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curve25519_dalek::traits::MultiscalarMul,
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rand::rngs::OsRng,
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zeroize::Zeroize,
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};
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use {
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crate::{
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sigma_proofs::errors::{SigmaProofVerificationError, ValidityProofVerificationError},
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transcript::TranscriptProtocol,
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},
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curve25519_dalek::{
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ristretto::{CompressedRistretto, RistrettoPoint},
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scalar::Scalar,
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traits::{IsIdentity, VartimeMultiscalarMul},
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},
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merlin::Transcript,
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};
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/// Byte length of a grouped ciphertext validity proof for 2 handles
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const GROUPED_CIPHERTEXT_2_HANDLES_VALIDITY_PROOF_LEN: usize = UNIT_LEN * 5;
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/// The grouped ciphertext validity proof for 2 handles.
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///
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/// Contains all the elliptic curve and scalar components that make up the sigma protocol.
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#[allow(non_snake_case)]
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#[derive(Clone)]
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pub struct GroupedCiphertext2HandlesValidityProof {
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Y_0: CompressedRistretto,
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Y_1: CompressedRistretto,
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Y_2: CompressedRistretto,
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z_r: Scalar,
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z_x: Scalar,
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}
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#[allow(non_snake_case)]
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#[cfg(not(target_os = "solana"))]
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impl GroupedCiphertext2HandlesValidityProof {
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/// Creates a grouped ciphertext validity proof for 2 handles.
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///
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/// The function does *not* hash the public keys, commitment, or decryption handles into the
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/// transcript. For security, the caller (the main protocol) should hash these public
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/// components prior to invoking this constructor.
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///
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/// This function is randomized. It uses `OsRng` internally to generate random scalars.
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///
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/// Note that the proof constructor does not take the actual Pedersen commitment or decryption
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/// handles as input; it only takes the associated Pedersen opening instead.
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///
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/// * `(destination_pubkey, auditor_pubkey)` - The ElGamal public keys associated with the decryption
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/// handles
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/// * `amount` - The committed message in the commitment
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/// * `opening` - The opening associated with the Pedersen commitment
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/// * `transcript` - The transcript that does the bookkeeping for the Fiat-Shamir heuristic
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pub fn new<T: Into<Scalar>>(
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(destination_pubkey, auditor_pubkey): (&ElGamalPubkey, &ElGamalPubkey), // TODO: rename auditor_pubkey
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amount: T,
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opening: &PedersenOpening,
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transcript: &mut Transcript,
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) -> Self {
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transcript.grouped_ciphertext_validity_proof_domain_separator();
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// extract the relevant scalar and Ristretto points from the inputs
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let P_dest = destination_pubkey.get_point();
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let P_auditor = auditor_pubkey.get_point();
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let x = amount.into();
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let r = opening.get_scalar();
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// generate random masking factors that also serves as nonces
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let mut y_r = Scalar::random(&mut OsRng);
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let mut y_x = Scalar::random(&mut OsRng);
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let Y_0 = RistrettoPoint::multiscalar_mul(vec![&y_r, &y_x], vec![&(*H), &(*G)]).compress();
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let Y_1 = (&y_r * P_dest).compress();
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let Y_2 = (&y_r * P_auditor).compress();
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// record masking factors in transcript and get challenges
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transcript.append_point(b"Y_0", &Y_0);
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transcript.append_point(b"Y_1", &Y_1);
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transcript.append_point(b"Y_2", &Y_2);
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let c = transcript.challenge_scalar(b"c");
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transcript.challenge_scalar(b"w");
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// compute masked message and opening
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let z_r = &(&c * r) + &y_r;
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let z_x = &(&c * &x) + &y_x;
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y_r.zeroize();
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y_x.zeroize();
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Self {
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Y_0,
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Y_1,
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Y_2,
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z_r,
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z_x,
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}
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}
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/// Verifies a grouped ciphertext validity proof for 2 handles.
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///
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/// * `commitment` - The Pedersen commitment
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/// * `(destination_pubkey, auditor_pubkey)` - The ElGamal pubkeys associated with the decryption
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/// handles
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/// * `(destination_handle, auditor_handle)` - The decryption handles
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/// * `transcript` - The transcript that does the bookkeeping for the Fiat-Shamir heuristic
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pub fn verify(
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self,
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commitment: &PedersenCommitment,
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(destination_pubkey, auditor_pubkey): (&ElGamalPubkey, &ElGamalPubkey),
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(destination_handle, auditor_handle): (&DecryptHandle, &DecryptHandle),
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transcript: &mut Transcript,
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) -> Result<(), ValidityProofVerificationError> {
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transcript.grouped_ciphertext_validity_proof_domain_separator();
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// include Y_0, Y_1, Y_2 to transcript and extract challenges
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transcript.validate_and_append_point(b"Y_0", &self.Y_0)?;
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transcript.validate_and_append_point(b"Y_1", &self.Y_1)?;
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// Y_2 can be an all zero point if the auditor public key is all zero
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transcript.append_point(b"Y_2", &self.Y_2);
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let c = transcript.challenge_scalar(b"c");
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let w = transcript.challenge_scalar(b"w");
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let ww = &w * &w;
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let w_negated = -&w;
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let ww_negated = -&ww;
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// check the required algebraic conditions
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let Y_0 = self
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.Y_0
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.decompress()
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.ok_or(SigmaProofVerificationError::Deserialization)?;
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let Y_1 = self
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.Y_1
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.decompress()
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.ok_or(SigmaProofVerificationError::Deserialization)?;
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let Y_2 = self
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.Y_2
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.decompress()
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.ok_or(SigmaProofVerificationError::Deserialization)?;
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let P_dest = destination_pubkey.get_point();
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let P_auditor = auditor_pubkey.get_point();
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let C = commitment.get_point();
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let D_dest = destination_handle.get_point();
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let D_auditor = auditor_handle.get_point();
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let check = RistrettoPoint::vartime_multiscalar_mul(
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vec![
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&self.z_r, // z_r
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&self.z_x, // z_x
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&(-&c), // -c
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&-(&Scalar::one()), // -identity
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&(&w * &self.z_r), // w * z_r
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&(&w_negated * &c), // -w * c
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&w_negated, // -w
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&(&ww * &self.z_r), // ww * z_r
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&(&ww_negated * &c), // -ww * c
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&ww_negated, // -ww
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],
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vec![
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&(*H), // H
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&(*G), // G
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C, // C
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&Y_0, // Y_0
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P_dest, // P_dest
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D_dest, // D_dest
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&Y_1, // Y_1
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P_auditor, // P_auditor
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D_auditor, // D_auditor
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&Y_2, // Y_2
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],
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);
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if check.is_identity() {
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Ok(())
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} else {
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Err(SigmaProofVerificationError::AlgebraicRelation.into())
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}
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}
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pub fn to_bytes(&self) -> [u8; GROUPED_CIPHERTEXT_2_HANDLES_VALIDITY_PROOF_LEN] {
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let mut buf = [0_u8; GROUPED_CIPHERTEXT_2_HANDLES_VALIDITY_PROOF_LEN];
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let mut chunks = buf.chunks_mut(UNIT_LEN);
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chunks.next().unwrap().copy_from_slice(self.Y_0.as_bytes());
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chunks.next().unwrap().copy_from_slice(self.Y_1.as_bytes());
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chunks.next().unwrap().copy_from_slice(self.Y_2.as_bytes());
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chunks.next().unwrap().copy_from_slice(self.z_r.as_bytes());
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chunks.next().unwrap().copy_from_slice(self.z_x.as_bytes());
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buf
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}
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pub fn from_bytes(bytes: &[u8]) -> Result<Self, ValidityProofVerificationError> {
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let mut chunks = bytes.chunks(UNIT_LEN);
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let Y_0 = ristretto_point_from_optional_slice(chunks.next())?;
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let Y_1 = ristretto_point_from_optional_slice(chunks.next())?;
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let Y_2 = ristretto_point_from_optional_slice(chunks.next())?;
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let z_r = canonical_scalar_from_optional_slice(chunks.next())?;
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let z_x = canonical_scalar_from_optional_slice(chunks.next())?;
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Ok(GroupedCiphertext2HandlesValidityProof {
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Y_0,
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Y_1,
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Y_2,
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z_r,
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z_x,
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})
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}
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}
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#[cfg(test)]
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mod test {
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use {
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super::*,
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crate::encryption::{elgamal::ElGamalKeypair, pedersen::Pedersen},
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};
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#[test]
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fn test_grouped_ciphertext_validity_proof_correctness() {
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let destination_keypair = ElGamalKeypair::new_rand();
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let destination_pubkey = destination_keypair.pubkey();
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let auditor_keypair = ElGamalKeypair::new_rand();
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let auditor_pubkey = auditor_keypair.pubkey();
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let amount: u64 = 55;
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let (commitment, opening) = Pedersen::new(amount);
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let destination_handle = destination_pubkey.decrypt_handle(&opening);
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let auditor_handle = auditor_pubkey.decrypt_handle(&opening);
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let mut prover_transcript = Transcript::new(b"Test");
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let mut verifier_transcript = Transcript::new(b"Test");
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let proof = GroupedCiphertext2HandlesValidityProof::new(
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(destination_pubkey, auditor_pubkey),
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amount,
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&opening,
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&mut prover_transcript,
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);
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assert!(proof
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.verify(
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&commitment,
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(destination_pubkey, auditor_pubkey),
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(&destination_handle, &auditor_handle),
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&mut verifier_transcript,
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)
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.is_ok());
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}
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#[test]
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fn test_grouped_ciphertext_validity_proof_edge_cases() {
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// if destination public key zeroed, then the proof should always reject
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let destination_pubkey = ElGamalPubkey::try_from([0u8; 32].as_slice()).unwrap();
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let auditor_keypair = ElGamalKeypair::new_rand();
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let auditor_pubkey = auditor_keypair.pubkey();
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let amount: u64 = 55;
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let (commitment, opening) = Pedersen::new(amount);
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let destination_handle = destination_pubkey.decrypt_handle(&opening);
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let auditor_handle = auditor_pubkey.decrypt_handle(&opening);
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let mut prover_transcript = Transcript::new(b"Test");
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let mut verifier_transcript = Transcript::new(b"Test");
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let proof = GroupedCiphertext2HandlesValidityProof::new(
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(&destination_pubkey, auditor_pubkey),
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amount,
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&opening,
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&mut prover_transcript,
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);
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assert!(proof
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.verify(
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&commitment,
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(&destination_pubkey, auditor_pubkey),
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(&destination_handle, &auditor_handle),
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&mut verifier_transcript,
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)
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.is_err());
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// all zeroed ciphertext should still be valid
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let destination_keypair = ElGamalKeypair::new_rand();
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let destination_pubkey = destination_keypair.pubkey();
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let auditor_keypair = ElGamalKeypair::new_rand();
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let auditor_pubkey = auditor_keypair.pubkey();
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let amount: u64 = 0;
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let commitment = PedersenCommitment::from_bytes(&[0u8; 32]).unwrap();
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let opening = PedersenOpening::from_bytes(&[0u8; 32]).unwrap();
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let destination_handle = destination_pubkey.decrypt_handle(&opening);
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let auditor_handle = auditor_pubkey.decrypt_handle(&opening);
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let mut prover_transcript = Transcript::new(b"Test");
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let mut verifier_transcript = Transcript::new(b"Test");
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let proof = GroupedCiphertext2HandlesValidityProof::new(
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(destination_pubkey, auditor_pubkey),
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amount,
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&opening,
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&mut prover_transcript,
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);
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assert!(proof
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.verify(
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&commitment,
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(destination_pubkey, auditor_pubkey),
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(&destination_handle, &auditor_handle),
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&mut verifier_transcript,
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)
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.is_ok());
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// decryption handles can be zero as long as the Pedersen commitment is valid
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let destination_keypair = ElGamalKeypair::new_rand();
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let destination_pubkey = destination_keypair.pubkey();
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let auditor_keypair = ElGamalKeypair::new_rand();
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let auditor_pubkey = auditor_keypair.pubkey();
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let amount: u64 = 55;
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let (commitment, opening) = Pedersen::new(amount);
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let destination_handle = destination_pubkey.decrypt_handle(&opening);
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let auditor_handle = auditor_pubkey.decrypt_handle(&opening);
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let mut prover_transcript = Transcript::new(b"Test");
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let mut verifier_transcript = Transcript::new(b"Test");
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let proof = GroupedCiphertext2HandlesValidityProof::new(
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(destination_pubkey, auditor_pubkey),
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amount,
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&opening,
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&mut prover_transcript,
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);
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assert!(proof
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.verify(
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&commitment,
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(destination_pubkey, auditor_pubkey),
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(&destination_handle, &auditor_handle),
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&mut verifier_transcript,
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)
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.is_ok());
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}
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}
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