@ -16,24 +16,18 @@ use crate::{
} ;
} ;
use arithmetic ::evaluate_opt ;
use arithmetic ::evaluate_opt ;
use ark_ec ::{
use ark_ec ::{
msm ::{ FixedBaseMSM , VariableBaseMSM } ,
AffineCurve , PairingEngine , ProjectiveCurve ,
pairing ::Pairing ,
scalar_mul ::{ fixed_base ::FixedBase , variable_base ::VariableBaseMSM } ,
AffineRepr , CurveGroup ,
} ;
} ;
use ark_ff ::PrimeField ;
use ark_ff ::PrimeField ;
use ark_poly ::{ DenseMultilinearExtension , MultilinearExtension } ;
use ark_poly ::{ DenseMultilinearExtension , MultilinearExtension } ;
use ark_serialize ::{ CanonicalDeserialize , CanonicalSerialize , Read , SerializationError , Write } ;
use ark_serialize ::{ CanonicalDeserialize , CanonicalSerialize } ;
use ark_std ::{
use ark_std ::{
borrow ::Borrow ,
end_timer , format ,
marker ::PhantomData ,
rand ::{ CryptoRng , RngCore } ,
start_timer ,
string ::ToString ,
sync ::Arc ,
vec ,
vec ::Vec ,
One , Zero ,
borrow ::Borrow , end_timer , format , marker ::PhantomData , rand ::Rng , start_timer ,
string ::ToString , sync ::Arc , vec , vec ::Vec , One , Zero ,
} ;
} ;
use std ::ops ::Mul ;
// use batching::{batch_verify_internal, multi_open_internal};
// use batching::{batch_verify_internal, multi_open_internal};
use srs ::{ MultilinearProverParam , MultilinearUniversalParams , MultilinearVerifierParam } ;
use srs ::{ MultilinearProverParam , MultilinearUniversalParams , MultilinearVerifierParam } ;
use transcript ::IOPTranscript ;
use transcript ::IOPTranscript ;
@ -41,27 +35,27 @@ use transcript::IOPTranscript;
use self ::batching ::{ batch_verify_internal , multi_open_internal } ;
use self ::batching ::{ batch_verify_internal , multi_open_internal } ;
/// KZG Polynomial Commitment Scheme on multilinear polynomials.
/// KZG Polynomial Commitment Scheme on multilinear polynomials.
pub struct MultilinearKzgPCS < E : PairingEngine > {
pub struct MultilinearKzgPCS < E : Pairing > {
#[ doc(hidden) ]
#[ doc(hidden) ]
phantom : PhantomData < E > ,
phantom : PhantomData < E > ,
}
}
#[ derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug, PartialEq, Eq) ]
#[ derive(CanonicalSerialize, CanonicalDeserialize, Clone, Debug, PartialEq, Eq) ]
/// proof of opening
/// proof of opening
pub struct MultilinearKzgProof < E : PairingEngine > {
pub struct MultilinearKzgProof < E : Pairing > {
/// Evaluation of quotients
/// Evaluation of quotients
pub proofs : Vec < E ::G1Affine > ,
pub proofs : Vec < E ::G1Affine > ,
}
}
impl < E : PairingEngine > PolynomialCommitmentScheme < E > for MultilinearKzgPCS < E > {
impl < E : Pairing > PolynomialCommitmentScheme < E > for MultilinearKzgPCS < E > {
// Parameters
// Parameters
type ProverParam = MultilinearProverParam < E > ;
type ProverParam = MultilinearProverParam < E > ;
type VerifierParam = MultilinearVerifierParam < E > ;
type VerifierParam = MultilinearVerifierParam < E > ;
type SRS = MultilinearUniversalParams < E > ;
type SRS = MultilinearUniversalParams < E > ;
// Polynomial and its associated types
// Polynomial and its associated types
type Polynomial = Arc < DenseMultilinearExtension < E ::Fr > > ;
type Point = Vec < E ::Fr > ;
type Evaluation = E ::Fr ;
type Polynomial = Arc < DenseMultilinearExtension < E ::ScalarField > > ;
type Point = Vec < E ::ScalarField > ;
type Evaluation = E ::ScalarField ;
// Commitments and proofs
// Commitments and proofs
type Commitment = Commitment < E > ;
type Commitment = Commitment < E > ;
type Proof = MultilinearKzgProof < E > ;
type Proof = MultilinearKzgProof < E > ;
@ -74,10 +68,7 @@ impl PolynomialCommitmentScheme for MultilinearKzgPCS {
///
///
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
/// WARNING: THIS FUNCTION IS FOR TESTING PURPOSE ONLY.
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
/// THE OUTPUT SRS SHOULD NOT BE USED IN PRODUCTION.
fn gen_srs_for_testing < R : RngCore + CryptoRng > (
rng : & mut R ,
log_size : usize ,
) -> Result < Self ::SRS , PCSError > {
fn gen_srs_for_testing < R : Rng > ( rng : & mut R , log_size : usize ) -> Result < Self ::SRS , PCSError > {
MultilinearUniversalParams ::< E > ::gen_srs_for_testing ( rng , log_size )
MultilinearUniversalParams ::< E > ::gen_srs_for_testing ( rng , log_size )
}
}
@ -121,20 +112,14 @@ impl PolynomialCommitmentScheme for MultilinearKzgPCS {
) ) ) ;
) ) ) ;
}
}
let ignored = prover_param . num_vars - poly . num_vars ;
let ignored = prover_param . num_vars - poly . num_vars ;
let scalars : Vec < _ > = poly
. to_evaluations ( )
. into_iter ( )
. map ( | x | x . into_repr ( ) )
. collect ( ) ;
let scalars : Vec < _ > = poly . to_evaluations ( ) ;
let msm_timer = start_timer ! ( | | format ! (
let msm_timer = start_timer ! ( | | format ! (
"msm of size {}" ,
"msm of size {}" ,
prover_param . powers_of_g [ ignored ] . evals . len ( )
prover_param . powers_of_g [ ignored ] . evals . len ( )
) ) ;
) ) ;
let commitment = VariableBaseMSM ::multi_scalar_mul (
& prover_param . powers_of_g [ ignored ] . evals ,
scalars . as_slice ( ) ,
)
. into_affine ( ) ;
let commitment =
E ::G1 ::msm_unchecked ( & prover_param . powers_of_g [ ignored ] . evals , scalars . as_slice ( ) )
. into_affine ( ) ;
end_timer ! ( msm_timer ) ;
end_timer ! ( msm_timer ) ;
end_timer ! ( commit_timer ) ;
end_timer ! ( commit_timer ) ;
@ -165,7 +150,7 @@ impl PolynomialCommitmentScheme for MultilinearKzgPCS {
polynomials : & [ Self ::Polynomial ] ,
polynomials : & [ Self ::Polynomial ] ,
points : & [ Self ::Point ] ,
points : & [ Self ::Point ] ,
evals : & [ Self ::Evaluation ] ,
evals : & [ Self ::Evaluation ] ,
transcript : & mut IOPTranscript < E ::Fr > ,
transcript : & mut IOPTranscript < E ::ScalarField > ,
) -> Result < BatchProof < E , Self > , PCSError > {
) -> Result < BatchProof < E , Self > , PCSError > {
multi_open_internal (
multi_open_internal (
prover_param . borrow ( ) ,
prover_param . borrow ( ) ,
@ -186,7 +171,7 @@ impl PolynomialCommitmentScheme for MultilinearKzgPCS {
verifier_param : & Self ::VerifierParam ,
verifier_param : & Self ::VerifierParam ,
commitment : & Self ::Commitment ,
commitment : & Self ::Commitment ,
point : & Self ::Point ,
point : & Self ::Point ,
value : & E ::Fr ,
value : & E ::ScalarField ,
proof : & Self ::Proof ,
proof : & Self ::Proof ,
) -> Result < bool , PCSError > {
) -> Result < bool , PCSError > {
verify_internal ( verifier_param , commitment , point , value , proof )
verify_internal ( verifier_param , commitment , point , value , proof )
@ -199,7 +184,7 @@ impl PolynomialCommitmentScheme for MultilinearKzgPCS {
commitments : & [ Self ::Commitment ] ,
commitments : & [ Self ::Commitment ] ,
points : & [ Self ::Point ] ,
points : & [ Self ::Point ] ,
batch_proof : & Self ::BatchProof ,
batch_proof : & Self ::BatchProof ,
transcript : & mut IOPTranscript < E ::Fr > ,
transcript : & mut IOPTranscript < E ::ScalarField > ,
) -> Result < bool , PCSError > {
) -> Result < bool , PCSError > {
batch_verify_internal ( verifier_param , commitments , points , batch_proof , transcript )
batch_verify_internal ( verifier_param , commitments , points , batch_proof , transcript )
}
}
@ -213,11 +198,11 @@ impl PolynomialCommitmentScheme for MultilinearKzgPCS {
/// G1:
/// G1:
/// - it proceeds with `num_var` number of rounds,
/// - it proceeds with `num_var` number of rounds,
/// - at round i, we compute an MSM for `2^{num_var - i}` number of G1 elements.
/// - at round i, we compute an MSM for `2^{num_var - i}` number of G1 elements.
fn open_internal < E : PairingEngine > (
fn open_internal < E : Pairing > (
prover_param : & MultilinearProverParam < E > ,
prover_param : & MultilinearProverParam < E > ,
polynomial : & DenseMultilinearExtension < E ::Fr > ,
point : & [ E ::Fr ] ,
) -> Result < ( MultilinearKzgProof < E > , E ::Fr ) , PCSError > {
polynomial : & DenseMultilinearExtension < E ::ScalarField > ,
point : & [ E ::ScalarField ] ,
) -> Result < ( MultilinearKzgProof < E > , E ::ScalarField ) , PCSError > {
let open_timer = start_timer ! ( | | format ! ( "open mle with {} variable" , polynomial . num_vars ) ) ;
let open_timer = start_timer ! ( | | format ! ( "open mle with {} variable" , polynomial . num_vars ) ) ;
if polynomial . num_vars ( ) > prover_param . num_vars {
if polynomial . num_vars ( ) > prover_param . num_vars {
@ -251,8 +236,8 @@ fn open_internal(
let k = nv - 1 - i ;
let k = nv - 1 - i ;
let cur_dim = 1 < < k ;
let cur_dim = 1 < < k ;
let mut q = vec ! [ E ::Fr zero ( ) ; cur_dim ] ;
let mut r = vec ! [ E ::Fr zero ( ) ; cur_dim ] ;
let mut q = vec ! [ E ::ScalarField zero ( ) ; cur_dim ] ;
let mut r = vec ! [ E ::ScalarField zero ( ) ; cur_dim ] ;
let ith_round_eval = start_timer ! ( | | format ! ( "{}-th round eval" , i ) ) ;
let ith_round_eval = start_timer ! ( | | format ! ( "{}-th round eval" , i ) ) ;
for b in 0 . . ( 1 < < k ) {
for b in 0 . . ( 1 < < k ) {
@ -264,12 +249,11 @@ fn open_internal(
}
}
f = r ;
f = r ;
end_timer ! ( ith_round_eval ) ;
end_timer ! ( ith_round_eval ) ;
let scalars : Vec < _ > = q . iter ( ) . map ( | x | x . into_repr ( ) ) . collect ( ) ;
// this is a MSM over G1 and is likely to be the bottleneck
// this is a MSM over G1 and is likely to be the bottleneck
let msm_timer = start_timer ! ( | | format ! ( "msm of size {} at round {}" , gi . evals . len ( ) , i ) ) ;
let msm_timer = start_timer ! ( | | format ! ( "msm of size {} at round {}" , gi . evals . len ( ) , i ) ) ;
proofs . push ( VariableBaseMSM ::multi_scalar_mul ( & gi . evals , & scalars ) . into_affine ( ) ) ;
proofs . push ( E ::G1 ::msm_unchecked ( & gi . evals , & q ) . into_affine ( ) ) ;
end_timer ! ( msm_timer ) ;
end_timer ! ( msm_timer ) ;
end_timer ! ( ith_round ) ;
end_timer ! ( ith_round ) ;
@ -285,11 +269,11 @@ fn open_internal(
/// This function takes
/// This function takes
/// - num_var number of pairing product.
/// - num_var number of pairing product.
/// - num_var number of MSM
/// - num_var number of MSM
fn verify_internal < E : PairingEngine > (
fn verify_internal < E : Pairing > (
verifier_param : & MultilinearVerifierParam < E > ,
verifier_param : & MultilinearVerifierParam < E > ,
commitment : & Commitment < E > ,
commitment : & Commitment < E > ,
point : & [ E ::Fr ] ,
value : & E ::Fr ,
point : & [ E ::ScalarField ] ,
value : & E ::ScalarField ,
proof : & MultilinearKzgProof < E > ,
proof : & MultilinearKzgProof < E > ,
) -> Result < bool , PCSError > {
) -> Result < bool , PCSError > {
let verify_timer = start_timer ! ( | | "verify" ) ;
let verify_timer = start_timer ! ( | | "verify" ) ;
@ -304,22 +288,18 @@ fn verify_internal(
let prepare_inputs_timer = start_timer ! ( | | "prepare pairing inputs" ) ;
let prepare_inputs_timer = start_timer ! ( | | "prepare pairing inputs" ) ;
let scalar_size = E ::Fr ::size_in_bits ( ) ;
let window_size = FixedBaseMSM ::get_mul_window_size ( num_var ) ;
let scalar_size = E ::ScalarField ::MODULUS_BIT_SIZE as usize ;
let window_size = FixedBase ::get_mul_window_size ( num_var ) ;
let h_table = FixedBaseMSM ::get_window_table (
scalar_size ,
window_size ,
verifier_param . h . into_projective ( ) ,
) ;
let h_mul : Vec < E ::G2Projective > =
FixedBaseMSM ::multi_scalar_mul ( scalar_size , window_size , & h_table , point ) ;
let h_table =
FixedBase ::get_window_table ( scalar_size , window_size , verifier_param . h . into_group ( ) ) ;
let h_mul : Vec < E ::G2 > = FixedBase ::msm ( scalar_size , window_size , & h_table , point ) ;
let ignored = verifier_param . num_vars - num_var ;
let ignored = verifier_param . num_vars - num_var ;
let h_vec : Vec < _ > = ( 0 . . num_var )
let h_vec : Vec < _ > = ( 0 . . num_var )
. map ( | i | verifier_param . h_mask [ ignored + i ] . into_projective ( ) - h_mul [ i ] )
. map ( | i | verifier_param . h_mask [ ignored + i ] . into_group ( ) - h_mul [ i ] )
. collect ( ) ;
. collect ( ) ;
let h_vec : Vec < E ::G2Affine > = E ::G2Projective ::batch_normalization_into_affine ( & h_vec ) ;
let h_vec : Vec < E ::G2Affine > = E ::G2 ::normalize_batch ( & h_vec ) ;
end_timer ! ( prepare_inputs_timer ) ;
end_timer ! ( prepare_inputs_timer ) ;
let pairing_product_timer = start_timer ! ( | | "pairing product" ) ;
let pairing_product_timer = start_timer ! ( | | "pairing product" ) ;
@ -333,12 +313,15 @@ fn verify_internal(
pairings . push ( (
pairings . push ( (
E ::G1Prepared ::from (
E ::G1Prepared ::from (
( verifier_param . g . mul ( * value ) - commitment . 0. into_projective ( ) ) . into_affine ( ) ,
( verifier_param . g . mul ( * value ) - commitment . 0. into_group ( ) ) . into_affine ( ) ,
) ,
) ,
E ::G2Prepared ::from ( verifier_param . h ) ,
E ::G2Prepared ::from ( verifier_param . h ) ,
) ) ;
) ) ;
let res = E ::product_of_pairings ( pairings . iter ( ) ) = = E ::Fqk ::one ( ) ;
let ps = pairings . iter ( ) . map ( | ( p , _ ) | p . clone ( ) ) ;
let hs = pairings . iter ( ) . map ( | ( _ , h ) | h . clone ( ) ) ;
let res = E ::multi_pairing ( ps , hs ) = = ark_ec ::pairing ::PairingOutput ( E ::TargetField ::one ( ) ) ;
end_timer ! ( pairing_product_timer ) ;
end_timer ! ( pairing_product_timer ) ;
end_timer ! ( verify_timer ) ;
end_timer ! ( verify_timer ) ;
@ -349,14 +332,14 @@ fn verify_internal(
mod tests {
mod tests {
use super ::* ;
use super ::* ;
use ark_bls12_381 ::Bls12_381 ;
use ark_bls12_381 ::Bls12_381 ;
use ark_ec ::PairingEngine ;
use ark_ec ::pairing ::Pairing ;
use ark_poly ::{ DenseMultilinearExtension , MultilinearExtension } ;
use ark_poly ::{ DenseMultilinearExtension , MultilinearExtension } ;
use ark_std ::{ rand ::RngCore , test_rng , vec ::Vec , UniformRand } ;
use ark_std ::{ test_rng , vec ::Vec , UniformRand } ;
type E = Bls12_381 ;
type E = Bls12_381 ;
type Fr = < E as PairingEngine > ::Fr ;
type Fr = < E as Pairing > ::ScalarField ;
fn test_single_helper < R : RngCore + CryptoRng > (
fn test_single_helper < R : Rng > (
params : & MultilinearUniversalParams < E > ,
params : & MultilinearUniversalParams < E > ,
poly : & Arc < DenseMultilinearExtension < Fr > > ,
poly : & Arc < DenseMultilinearExtension < Fr > > ,
rng : & mut R ,
rng : & mut R ,
Ivan Mikushin
1 year ago
GitHub