Add MLKZG support (Nova forward port) (microsoft#172)

* Support for multilinear KZG commitments (microsoft#269)

* multilinear KZG PCS as a provider; builds

* fix two tests

* fix third test; cut duplicate code

* Tidy up source code comments

Signed-off-by: Greg Zaverucha <gregz@microsoft.com>

* impl PairingGroup for bn256

* remove unneeded imports

* simplify CommitmentKey

* fix build; migrate G1Affine

* fmt

* checkpoint

* migrate G2Affine and pairing

* fix clippy; use unimplemented!

* switch to affine form for compressed commitments

* add a test with mlkzg

* cargo fmt

* cleanup

* go back to compressed group

* address clippy

* rename

* cleanup

* add an alias

* deduplicate

* Revert "add an alias"

This reverts commit 97cade6.

* Use an alias for PreprocessedGroupElements

Signed-off-by: Greg Zaverucha <gregz@microsoft.com>

* cargo fmt

* update README.md

---------

Signed-off-by: Greg Zaverucha <gregz@microsoft.com>
Co-authored-by: Greg Zaverucha <gregz@microsoft.com>

* refactor: clean up the needed scaffolding in MLKZG

Summary:

- THe MLKZG implementation re-implements some group traits, so as to give it maximum generality and depende maximally on the Nova traits.
- However, the way in which it imports a pairing (using pairing::Engine) already implicitly constrains perfrectly usable group implementations to be available on the same types.  This commit therefore removes the boilerplate and uses those external traits.
- Finally, so as to mutualize part of the pairing implementation, this commit also leverages the MultiMillerLoop trait, a subtrait of `pairing::Engine`.
- In sum, this commit only moves types - no actual data was harmed in its making.

In detail:

- Removed the `PairingGroup` trait and its related implementations from the `traits.rs` and `bn256_grumpkin.rs` files.
- Simplified the imports from `halo2curves::bn256` in `bn256_grumpkin.rs` and removed unused types such as `pairing`, `G2Affine`, `G2Compressed`, `Gt`, and `G2`.
- Deleted substantial amount of code associated with `G2` from `bn256_grumpkin.rs`.

* make Minroot example generic over the supported curve cycles (microsoft#272)

* make Minroot example generic over the supported curve cycles

* upgrade version

* refactor: Refactor and enhance point infinity handling in `to_transcript_bytes`

- Enhanced the functionality of `to_transcript_bytes` method in `TranscriptReprTrait` for `Affine` in both `pasta.rs` and `traits.rs`.
- Combined the x and y coordinates with the `is_infinity_byte` into a single byte stream for ease of handling.
- Integrated additional checks for 'infinity' conditions to ensure accurate extractions of coordinate values.

* refactor: Relocate multi-scalar multiplication module

- Restructure the `provider` module by moving `msm` to the `util` subdirectory.

* chore: Rename UV(KZG{ProverKey, VerifierKey}|UniversalKZGParam) -> \1

* refactor: Apply univariate polynomial evaluation

- chore: move comment
- fix: standardize power sequences computation
- fix: parallelize several poly computations

refactor: Refactor `EvaluationArgument` struct in mlkzg.rs

- Renamed several fields in `EvaluationArgument` struct within `src/provider/mlkzg.rs` for increased clarity.
- Adjusted the `prove` and `verify` methods in `src/provider/mlkzg.rs` to reflect these name changes.
- Modified test code to align with the updates in the `EvaluationArgument` structure.

---------

Signed-off-by: Greg Zaverucha <gregz@microsoft.com>
Co-authored-by: Srinath Setty <srinath@microsoft.com>
Co-authored-by: Greg Zaverucha <gregz@microsoft.com>

src/lib.rs

@@ -1192,18 +1192,19 @@ mod tests {
     );
     test_ivc_nontrivial_with_compression_with::<Secp256k1Engine, Secq256k1Engine, EE<_>, EE<_>>();
 
-    test_ivc_nontrivial_with_spark_compression_with::<
-      Bn256EngineKZG,
-      GrumpkinEngine,
-      provider::hyperkzg::EvaluationEngine<_>,
-      EE<_>,
-    >();
     test_ivc_nontrivial_with_compression_with::<
       Bn256EngineZM,
       GrumpkinEngine,
       ZMPCS<Bn256, _>,
       EE<_>,
     >();
+
+    test_ivc_nontrivial_with_spark_compression_with::<
+      Bn256EngineKZG,
+      GrumpkinEngine,
+      provider::hyperkzg::EvaluationEngine<_>,
+      EE<_>,
+    >();
   }
 
   fn test_ivc_nontrivial_with_spark_compression_with<E1, E2, EE1, EE2>()

src/provider/bn256_grumpkin.rs

@@ -2,7 +2,7 @@
 use crate::{
   errors::NovaError,
   impl_traits,
-  provider::traits::{CompressedGroup, DlogGroup, PairingGroup},
+  provider::traits::{CompressedGroup, DlogGroup},
   traits::{Group, PrimeFieldExt, TranscriptReprTrait},
 };
 use digest::{ExtendableOutput, Update};
@@ -24,6 +24,8 @@ use rayon::prelude::*;
 use sha3::Shake256;
 use std::io::Read;
 
+use super::traits::PairingGroup;
+
 /// Re-exports that give access to the standard aliases used in the code base, for bn256
 pub mod bn256 {
   pub use halo2curves::bn256::{Fq as Base, Fr as Scalar, G1Affine as Affine, G1 as Point};

src/provider/kzg_commitment.rs

@@ -16,7 +16,7 @@ use crate::traits::{
 };
 
 use crate::provider::{
-  non_hiding_kzg::{UVKZGCommitment, UVUniversalKZGParam},
+  non_hiding_kzg::{UVKZGCommitment, UniversalKZGParam},
   pedersen::Commitment,
   traits::DlogGroup,
 };
@@ -35,7 +35,7 @@ where
   E::G2Affine: Serialize + for<'de> Deserialize<'de>,
   E::Fr: PrimeFieldBits, // TODO due to use of gen_srs_for_testing, make optional
 {
-  type CommitmentKey = UVUniversalKZGParam<E>;
+  type CommitmentKey = UniversalKZGParam<E>;
   type Commitment = Commitment<NE>;
 
   fn setup(label: &'static [u8], n: usize) -> Self::CommitmentKey {
@@ -44,7 +44,7 @@ where
     let len = label.len().min(32);
     bytes[..len].copy_from_slice(&label[..len]);
     let rng = &mut StdRng::from_seed(bytes);
-    UVUniversalKZGParam::gen_srs_for_testing(rng, n.next_power_of_two())
+    UniversalKZGParam::gen_srs_for_testing(rng, n.next_power_of_two())
   }
 
   fn commit(ck: &Self::CommitmentKey, v: &[<E::G1 as Group>::Scalar]) -> Self::Commitment {

src/provider/mod.rs

@@ -152,6 +152,7 @@ impl Engine for VestaEngine {
 #[cfg(test)]
 mod tests {
   use crate::provider::{bn256_grumpkin::bn256, secp_secq::secp256k1, traits::DlogGroup};
+
   use digest::{ExtendableOutput, Update};
   use group::Curve;
   use halo2curves::CurveExt;

src/provider/non_hiding_kzg.rs

@@ -19,7 +19,7 @@ use crate::{
   serialize = "E::G1Affine: Serialize, E::G2Affine: Serialize",
   deserialize = "E::G1Affine: Deserialize<'de>, E::G2Affine: Deserialize<'de>"
 ))]
-pub struct UVUniversalKZGParam<E: Engine> {
+pub struct UniversalKZGParam<E: Engine> {
   /// Group elements of the form `{ β^i G }`, where `i` ranges from 0 to
   /// `degree`.
   pub powers_of_g: Vec<E::G1Affine>,
@@ -28,14 +28,14 @@ pub struct UVUniversalKZGParam<E: Engine> {
   pub powers_of_h: Vec<E::G2Affine>,
 }
 
-impl<E: Engine> PartialEq for UVUniversalKZGParam<E> {
-  fn eq(&self, other: &UVUniversalKZGParam<E>) -> bool {
+impl<E: Engine> PartialEq for UniversalKZGParam<E> {
+  fn eq(&self, other: &UniversalKZGParam<E>) -> bool {
     self.powers_of_g == other.powers_of_g && self.powers_of_h == other.powers_of_h
   }
 }
 
 // for the purpose of the Len trait, we count commitment bases, i.e. G1 elements
-impl<E: Engine> Len for UVUniversalKZGParam<E> {
+impl<E: Engine> Len for UniversalKZGParam<E> {
   fn length(&self) -> usize {
     self.powers_of_g.len()
   }
@@ -47,7 +47,7 @@ impl<E: Engine> Len for UVUniversalKZGParam<E> {
   serialize = "E::G1Affine: Serialize",
   deserialize = "E::G1Affine: Deserialize<'de>"
 ))]
-pub struct UVKZGProverKey<E: Engine> {
+pub struct KZGProverKey<E: Engine> {
   /// generators
   pub powers_of_g: Vec<E::G1Affine>,
 }
@@ -59,7 +59,7 @@ pub struct UVKZGProverKey<E: Engine> {
   serialize = "E::G1Affine: Serialize, E::G2Affine: Serialize",
   deserialize = "E::G1Affine: Deserialize<'de>, E::G2Affine: Deserialize<'de>"
 ))]
-pub struct UVKZGVerifierKey<E: Engine> {
+pub struct KZGVerifierKey<E: Engine> {
   /// The generator of G1.
   pub g: E::G1Affine,
   /// The generator of G2.
@@ -68,7 +68,7 @@ pub struct UVKZGVerifierKey<E: Engine> {
   pub beta_h: E::G2Affine,
 }
 
-impl<E: Engine> UVUniversalKZGParam<E> {
+impl<E: Engine> UniversalKZGParam<E> {
   /// Returns the maximum supported degree
   pub fn max_degree(&self) -> usize {
     self.powers_of_g.len()
@@ -78,21 +78,21 @@ impl<E: Engine> UVUniversalKZGParam<E> {
   ///
   /// # Panics
   /// if `supported_size` is greater than `self.max_degree()`
-  pub fn extract_prover_key(&self, supported_size: usize) -> UVKZGProverKey<E> {
+  pub fn extract_prover_key(&self, supported_size: usize) -> KZGProverKey<E> {
     let powers_of_g = self.powers_of_g[..=supported_size].to_vec();
-    UVKZGProverKey { powers_of_g }
+    KZGProverKey { powers_of_g }
   }
 
   /// Returns the verifier parameters
   ///
   /// # Panics
   /// If self.prover_params is empty.
-  pub fn extract_verifier_key(&self, supported_size: usize) -> UVKZGVerifierKey<E> {
+  pub fn extract_verifier_key(&self, supported_size: usize) -> KZGVerifierKey<E> {
     assert!(
       self.powers_of_g.len() >= supported_size,
       "supported_size is greater than self.max_degree()"
     );
-    UVKZGVerifierKey {
+    KZGVerifierKey {
       g: self.powers_of_g[0],
       h: self.powers_of_h[0],
       beta_h: self.powers_of_h[1],
@@ -106,11 +106,11 @@ impl<E: Engine> UVUniversalKZGParam<E> {
   ///
   /// # Panics
   /// If `supported_size` is greater than `self.max_degree()`, or `self.max_degree()` is zero.
-  pub fn trim(&self, supported_size: usize) -> (UVKZGProverKey<E>, UVKZGVerifierKey<E>) {
+  pub fn trim(&self, supported_size: usize) -> (KZGProverKey<E>, KZGVerifierKey<E>) {
     let powers_of_g = self.powers_of_g[..=supported_size].to_vec();
 
-    let pk = UVKZGProverKey { powers_of_g };
-    let vk = UVKZGVerifierKey {
+    let pk = KZGProverKey { powers_of_g };
+    let vk = KZGVerifierKey {
       g: self.powers_of_g[0],
       h: self.powers_of_h[0],
       beta_h: self.powers_of_h[1],
@@ -119,7 +119,7 @@ impl<E: Engine> UVUniversalKZGParam<E> {
   }
 }
 
-impl<E: Engine> UVUniversalKZGParam<E>
+impl<E: Engine> UniversalKZGParam<E>
 where
   E::Fr: PrimeFieldBits,
 {
@@ -229,7 +229,7 @@ where
   /// Generate a commitment for a polynomial
   /// Note that the scheme is not hidding
   pub fn commit(
-    prover_param: impl Borrow<UVKZGProverKey<E>>,
+    prover_param: impl Borrow<KZGProverKey<E>>,
     poly: &UVKZGPoly<E::Fr>,
   ) -> Result<UVKZGCommitment<E>, NovaError> {
     let prover_param = prover_param.borrow();
@@ -247,7 +247,7 @@ where
   /// On input a polynomial `p` and a point `point`, outputs a proof for the
   /// same.
   pub fn open(
-    prover_param: impl Borrow<UVKZGProverKey<E>>,
+    prover_param: impl Borrow<KZGProverKey<E>>,
     polynomial: &UVKZGPoly<E::Fr>,
     point: &E::Fr,
   ) -> Result<(UVKZGProof<E>, UVKZGEvaluation<E>), NovaError> {
@@ -277,7 +277,7 @@ where
   /// committed inside `comm`.
   #[allow(dead_code)]
   pub fn verify(
-    verifier_param: impl Borrow<UVKZGVerifierKey<E>>,
+    verifier_param: impl Borrow<KZGVerifierKey<E>>,
     commitment: &UVKZGCommitment<E>,
     point: &E::Fr,
     proof: &UVKZGProof<E>,
@@ -324,7 +324,7 @@ mod tests {
       let mut rng = &mut thread_rng();
       let degree = rng.gen_range(2..20);
 
-      let pp = UVUniversalKZGParam::<E>::gen_srs_for_testing(&mut rng, degree);
+      let pp = UniversalKZGParam::<E>::gen_srs_for_testing(&mut rng, degree);
       let (ck, vk) = pp.trim(degree);
       let p = random(degree, rng);
       let comm = UVKZGPCS::<E>::commit(&ck, &p)?;

src/provider/non_hiding_zeromorph.rs

@@ -6,8 +6,8 @@ use crate::{
   errors::{NovaError, PCSError},
   provider::{
     non_hiding_kzg::{
-      UVKZGCommitment, UVKZGEvaluation, UVKZGPoly, UVKZGProof, UVKZGProverKey, UVKZGVerifierKey,
-      UVUniversalKZGParam, UVKZGPCS,
+      KZGProverKey, KZGVerifierKey, UVKZGCommitment, UVKZGEvaluation, UVKZGPoly, UVKZGProof,
+      UniversalKZGParam, UVKZGPCS,
     },
     traits::DlogGroup,
   },
@@ -39,8 +39,8 @@ use crate::provider::kzg_commitment::KZGCommitmentEngine;
   deserialize = "E::G1Affine: Deserialize<'de>"
 ))]
 pub struct ZMProverKey<E: Engine> {
-  commit_pp: UVKZGProverKey<E>,
-  open_pp: UVKZGProverKey<E>,
+  commit_pp: KZGProverKey<E>,
+  open_pp: KZGProverKey<E>,
 }
 
 /// `ZMVerifierKey` is used to check evaluation proofs for a given
@@ -51,7 +51,7 @@ pub struct ZMProverKey<E: Engine> {
   deserialize = "E::G1Affine: Deserialize<'de>, E::G2Affine: Deserialize<'de>"
 ))]
 pub struct ZMVerifierKey<E: Engine> {
-  vp: UVKZGVerifierKey<E>,
+  vp: KZGVerifierKey<E>,
   s_offset_h: E::G2Affine,
 }
 
@@ -66,14 +66,14 @@ pub struct ZMVerifierKey<E: Engine> {
 // TODO: important, we need a better way to handle that the commitment key should be 2^max_degree sized,
 // see the runtime error in commit() below
 pub fn trim<E: Engine>(
-  params: &UVUniversalKZGParam<E>,
+  params: &UniversalKZGParam<E>,
   max_degree: usize,
 ) -> (ZMProverKey<E>, ZMVerifierKey<E>) {
   let (commit_pp, vp) = params.trim(max_degree);
   let offset = params.powers_of_g.len() - max_degree;
   let open_pp = {
     let offset_powers_of_g1 = params.powers_of_g[offset..].to_vec();
-    UVKZGProverKey {
+    KZGProverKey {
       powers_of_g: offset_powers_of_g1,
     }
   };
@@ -470,12 +470,12 @@ where
 
   type EvaluationArgument = ZMProof<E>;
 
-  fn setup(ck: &UVUniversalKZGParam<E>) -> (Self::ProverKey, Self::VerifierKey) {
+  fn setup(ck: &UniversalKZGParam<E>) -> (Self::ProverKey, Self::VerifierKey) {
     trim(ck, ck.length() - 1)
   }
 
   fn prove(
-    _ck: &UVUniversalKZGParam<E>,
+    _ck: &UniversalKZGParam<E>,
     pk: &Self::ProverKey,
     transcript: &mut NE::TE,
     comm: &Commitment<NE>,
@@ -525,7 +525,7 @@ mod test {
   use crate::{
     provider::{
       keccak::Keccak256Transcript,
-      non_hiding_kzg::{UVKZGPoly, UVUniversalKZGParam},
+      non_hiding_kzg::{UVKZGPoly, UniversalKZGParam},
       non_hiding_zeromorph::{
         batched_lifted_degree_quotient, eval_and_quotient_scalars, trim, ZMEvaluation, ZMPCS,
       },
@@ -545,7 +545,7 @@ mod test {
     let max_vars = 16;
     let mut rng = thread_rng();
     let max_poly_size = 1 << (max_vars + 1);
-    let universal_setup = UVUniversalKZGParam::<E>::gen_srs_for_testing(&mut rng, max_poly_size);
+    let universal_setup = UniversalKZGParam::<E>::gen_srs_for_testing(&mut rng, max_poly_size);
 
     for num_vars in 3..max_vars {
       // Setup

src/provider/util/mod.rs

@@ -1,2 +1,2 @@
 /// Utilities for provider module
-pub(crate) mod fb_msm;
+pub(in crate::provider) mod fb_msm;

src/spartan/mod.rs

@@ -26,12 +26,9 @@ use rayon::{iter::IntoParallelRefIterator, prelude::*};
 // Creates a vector of the first `n` powers of `s`.
 fn powers<E: Engine>(s: &E::Scalar, n: usize) -> Vec<E::Scalar> {
   assert!(n >= 1);
-  let mut powers = Vec::with_capacity(n);
-  powers.push(E::Scalar::ONE);
-  for i in 1..n {
-    powers.push(powers[i - 1] * s);
-  }
-  powers
+  std::iter::successors(Some(E::Scalar::ONE), |&x| Some(x * s))
+    .take(n)
+    .collect()
 }
 
 /// A type that holds a witness to a polynomial evaluation instance