traits for a vector commitment engine and a polynomial evaluation engine (#136)

make spartan generic over the evaluation engine

update version

disable Wasm CI check

.github/workflows/rust.yml

@@ -17,12 +17,8 @@ jobs:
       run: rustup component add rustfmt
     - name: Install clippy
       run: rustup component add clippy
-    - name: Install Wasm target
-      run: rustup target add wasm32-unknown-unknown
     - name: Build
       run: cargo build --verbose
-    - name: Wasm build
-      run: cargo build --target wasm32-unknown-unknown
     - name: Build examples
       run: cargo build --examples --verbose
     - name: Run tests

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "nova-snark"
-version = "0.12.0"
+version = "0.13.0"
 authors = ["Srinath Setty <srinath@microsoft.com>"]
 edition = "2021"
 description = "Recursive zkSNARKs without trusted setup"
@@ -13,7 +13,7 @@ keywords = ["zkSNARKs", "cryptography", "proofs"]
 [dependencies]
 bellperson = { version = "0.24", default-features = false }
 ff = { version = "0.12.0", features = ["derive"] }
-merlin = "2.0.0"
+merlin = "3.0.0"
 digest = "0.8.1"
 sha3 = "0.8.2"
 rayon = "1.3.0"

benches/compressed-snark.rs

@@ -15,8 +15,10 @@ use std::time::Duration;
 
 type G1 = pasta_curves::pallas::Point;
 type G2 = pasta_curves::vesta::Point;
-type S1 = nova_snark::spartan_with_ipa_pc::RelaxedR1CSSNARK<G1>;
+type EE1 = nova_snark::provider::ipa_pc::EvaluationEngine<G1>;
-type S2 = nova_snark::spartan_with_ipa_pc::RelaxedR1CSSNARK<G2>;
+type EE2 = nova_snark::provider::ipa_pc::EvaluationEngine<G2>;
+type S1 = nova_snark::spartan::RelaxedR1CSSNARK<G1, EE1>;
+type S2 = nova_snark::spartan::RelaxedR1CSSNARK<G2, EE2>;
 type C1 = NonTrivialTestCircuit<<G1 as Group>::Scalar>;
 type C2 = TrivialTestCircuit<<G2 as Group>::Scalar>;
 

examples/minroot.rs

@@ -257,8 +257,11 @@ fn main() {
     // produce a compressed SNARK
     println!("Generating a CompressedSNARK using Spartan with IPA-PC...");
     let start = Instant::now();
-    type S1 = nova_snark::spartan_with_ipa_pc::RelaxedR1CSSNARK<G1>;
+    type EE1 = nova_snark::provider::ipa_pc::EvaluationEngine<G1>;
-    type S2 = nova_snark::spartan_with_ipa_pc::RelaxedR1CSSNARK<G2>;
+    type EE2 = nova_snark::provider::ipa_pc::EvaluationEngine<G2>;
+    type S1 = nova_snark::spartan::RelaxedR1CSSNARK<G1, EE1>;
+    type S2 = nova_snark::spartan::RelaxedR1CSSNARK<G2, EE2>;
+
     let res = CompressedSNARK::<_, _, _, _, S1, S2>::prove(&pp, &recursive_snark);
     println!(
       "CompressedSNARK::prove: {:?}, took {:?}",

examples/signature.rs

@@ -182,7 +182,6 @@ pub fn synthesize_bits<F: PrimeField, CS: ConstraintSystem<F>>(
   bits: Option<Vec<bool>>,
 ) -> Result<Vec<AllocatedBit>, SynthesisError> {
   (0..F::NUM_BITS)
-    .into_iter()
     .map(|i| {
       AllocatedBit::alloc(
         cs.namespace(|| format!("bit {i}")),

src/circuit.rs

@@ -6,8 +6,7 @@
 //! H(params = H(shape, gens), i, z0, zi, U). Each circuit folds the last invocation of
 //! the other into the running instance
 
-use super::{
+use crate::{
-  commitments::Commitment,
   constants::{NUM_FE_WITHOUT_IO_FOR_CRHF, NUM_HASH_BITS},
   gadgets::{
     ecc::AllocatedPoint,
@@ -17,7 +16,10 @@ use super::{
     },
   },
   r1cs::{R1CSInstance, RelaxedR1CSInstance},
-  traits::{circuit::StepCircuit, Group, ROCircuitTrait, ROConstantsCircuit},
+  traits::{
+    circuit::StepCircuit, commitment::CommitmentTrait, Group, ROCircuitTrait, ROConstantsCircuit,
+  },
+  Commitment,
 };
 use bellperson::{
   gadgets::{
@@ -59,10 +61,7 @@ pub struct NovaAugmentedCircuitInputs<G: Group> {
   T: Option<Commitment<G>>,
 }
 
-impl<G> NovaAugmentedCircuitInputs<G>
+impl<G: Group> NovaAugmentedCircuitInputs<G> {
-where
-  G: Group,
-{
   /// Create new inputs/witness for the verification circuit
   #[allow(clippy::too_many_arguments)]
   pub fn new(
@@ -88,22 +87,14 @@ where
 
 /// The augmented circuit F' in Nova that includes a step circuit F
 /// and the circuit for the verifier in Nova's non-interactive folding scheme
-pub struct NovaAugmentedCircuit<G, SC>
+pub struct NovaAugmentedCircuit<G: Group, SC: StepCircuit<G::Base>> {
-where
-  G: Group,
-  SC: StepCircuit<G::Base>,
-{
   params: NovaAugmentedCircuitParams,
   ro_consts: ROConstantsCircuit<G>,
   inputs: Option<NovaAugmentedCircuitInputs<G>>,
   step_circuit: SC, // The function that is applied for each step
 }
 
-impl<G, SC> NovaAugmentedCircuit<G, SC>
+impl<G: Group, SC: StepCircuit<G::Base>> NovaAugmentedCircuit<G, SC> {
-where
-  G: Group,
-  SC: StepCircuit<G::Base>,
-{
   /// Create a new verification circuit for the input relaxed r1cs instances
   pub fn new(
     params: NovaAugmentedCircuitParams,
@@ -186,10 +177,7 @@ where
     let T = AllocatedPoint::alloc(
       cs.namespace(|| "allocate T"),
       self.inputs.get().map_or(None, |inputs| {
-        inputs
+        inputs.T.get().map_or(None, |T| Some(T.to_coordinates()))
-          .T
-          .get()
-          .map_or(None, |T| Some(T.comm.to_coordinates()))
       }),
     )?;
 
@@ -274,10 +262,8 @@ where
   }
 }
 
-impl<G, SC> Circuit<<G as Group>::Base> for NovaAugmentedCircuit<G, SC>
+impl<G: Group, SC: StepCircuit<G::Base>> Circuit<<G as Group>::Base>
-where
+  for NovaAugmentedCircuit<G, SC>
-  G: Group,
-  SC: StepCircuit<G::Base>,
 {
   fn synthesize<CS: ConstraintSystem<<G as Group>::Base>>(
     self,
@@ -388,10 +374,11 @@ mod tests {
   use crate::bellperson::{shape_cs::ShapeCS, solver::SatisfyingAssignment};
   type G1 = pasta_curves::pallas::Point;
   type G2 = pasta_curves::vesta::Point;
+
   use crate::constants::{BN_LIMB_WIDTH, BN_N_LIMBS};
   use crate::{
     bellperson::r1cs::{NovaShape, NovaWitness},
-    poseidon::PoseidonConstantsCircuit,
+    provider::poseidon::PoseidonConstantsCircuit,
     traits::{circuit::TrivialTestCircuit, ROConstantsTrait},
   };
 

src/gadgets/r1cs.rs

@@ -13,7 +13,7 @@ use crate::{
     },
   },
   r1cs::{R1CSInstance, RelaxedR1CSInstance},
-  traits::{Group, ROCircuitTrait, ROConstantsCircuit},
+  traits::{commitment::CommitmentTrait, Group, ROCircuitTrait, ROConstantsCircuit},
 };
 use bellperson::{
   gadgets::{boolean::Boolean, num::AllocatedNum, Assignment},
@@ -23,19 +23,13 @@ use ff::Field;
 
 /// An Allocated R1CS Instance
 #[derive(Clone)]
-pub struct AllocatedR1CSInstance<G>
+pub struct AllocatedR1CSInstance<G: Group> {
-where
-  G: Group,
-{
   pub(crate) W: AllocatedPoint<G>,
   pub(crate) X0: AllocatedNum<G::Base>,
   pub(crate) X1: AllocatedNum<G::Base>,
 }
 
-impl<G> AllocatedR1CSInstance<G>
+impl<G: Group> AllocatedR1CSInstance<G> {
-where
-  G: Group,
-{
   /// Takes the r1cs instance and creates a new allocated r1cs instance
   pub fn alloc<CS: ConstraintSystem<<G as Group>::Base>>(
     mut cs: CS,
@@ -44,8 +38,7 @@ where
     // Check that the incoming instance has exactly 2 io
     let W = AllocatedPoint::alloc(
       cs.namespace(|| "allocate W"),
-      u.get()
+      u.get().map_or(None, |u| Some(u.comm_W.to_coordinates())),
-        .map_or(None, |u| Some(u.comm_W.comm.to_coordinates())),
     )?;
 
     let X0 = alloc_scalar_as_base::<G, _>(
@@ -71,10 +64,7 @@ where
 }
 
 /// An Allocated Relaxed R1CS Instance
-pub struct AllocatedRelaxedR1CSInstance<G>
+pub struct AllocatedRelaxedR1CSInstance<G: Group> {
-where
-  G: Group,
-{
   pub(crate) W: AllocatedPoint<G>,
   pub(crate) E: AllocatedPoint<G>,
   pub(crate) u: AllocatedNum<G::Base>,
@@ -82,10 +72,7 @@ where
   pub(crate) X1: BigNat<G::Base>,
 }
 
-impl<G> AllocatedRelaxedR1CSInstance<G>
+impl<G: Group> AllocatedRelaxedR1CSInstance<G> {
-where
-  G: Group,
-{
   /// Allocates the given RelaxedR1CSInstance as a witness of the circuit
   pub fn alloc<CS: ConstraintSystem<<G as Group>::Base>>(
     mut cs: CS,
@@ -97,14 +84,14 @@ where
       cs.namespace(|| "allocate W"),
       inst
         .get()
-        .map_or(None, |inst| Some(inst.comm_W.comm.to_coordinates())),
+        .map_or(None, |inst| Some(inst.comm_W.to_coordinates())),
     )?;
 
     let E = AllocatedPoint::alloc(
       cs.namespace(|| "allocate E"),
       inst
         .get()
-        .map_or(None, |inst| Some(inst.comm_E.comm.to_coordinates())),
+        .map_or(None, |inst| Some(inst.comm_E.to_coordinates())),
     )?;
 
     // u << |G::Base| despite the fact that u is a scalar.

src/lib.rs

@@ -6,17 +6,15 @@
 // private modules
 mod bellperson;
 mod circuit;
-mod commitments;
 mod constants;
 mod nifs;
-mod poseidon;
 mod r1cs;
 
 // public modules
 pub mod errors;
 pub mod gadgets;
-pub mod pasta;
+pub mod provider;
-pub mod spartan_with_ipa_pc;
+pub mod spartan;
 pub mod traits;
 
 use crate::bellperson::{
@@ -37,8 +35,10 @@ use r1cs::{
 };
 use serde::{Deserialize, Serialize};
 use traits::{
-  circuit::StepCircuit, snark::RelaxedR1CSSNARKTrait, AbsorbInROTrait, Group, ROConstants,
+  circuit::StepCircuit,
-  ROConstantsCircuit, ROConstantsTrait, ROTrait,
+  commitment::{CommitmentEngineTrait, CompressedCommitmentTrait},
+  snark::RelaxedR1CSSNARKTrait,
+  AbsorbInROTrait, Group, ROConstants, ROConstantsCircuit, ROConstantsTrait, ROTrait,
 };
 
 /// A type that holds public parameters of Nova
@@ -717,13 +717,20 @@ where
   }
 }
 
+type CommitmentGens<G> = <<G as traits::Group>::CE as CommitmentEngineTrait<G>>::CommitmentGens;
+type Commitment<G> = <<G as Group>::CE as CommitmentEngineTrait<G>>::Commitment;
+type CompressedCommitment<G> = <<G as Group>::CE as CommitmentEngineTrait<G>>::CompressedCommitment;
+type CE<G> = <G as Group>::CE;
+
 #[cfg(test)]
 mod tests {
   use super::*;
   type G1 = pasta_curves::pallas::Point;
   type G2 = pasta_curves::vesta::Point;
-  type S1 = spartan_with_ipa_pc::RelaxedR1CSSNARK<G1>;
+  type EE1 = provider::ipa_pc::EvaluationEngine<G1>;
-  type S2 = spartan_with_ipa_pc::RelaxedR1CSSNARK<G2>;
+  type EE2 = provider::ipa_pc::EvaluationEngine<G2>;
+  type S1 = spartan::RelaxedR1CSSNARK<G1, EE1>;
+  type S2 = spartan::RelaxedR1CSSNARK<G2, EE2>;
   use ::bellperson::{gadgets::num::AllocatedNum, ConstraintSystem, SynthesisError};
   use core::marker::PhantomData;
   use ff::PrimeField;

src/nifs.rs

@@ -2,12 +2,15 @@
 #![allow(non_snake_case)]
 #![allow(clippy::type_complexity)]
 
-use super::{
+use crate::{
-  commitments::CompressedCommitment,
   constants::{NUM_CHALLENGE_BITS, NUM_FE_FOR_RO},
   errors::NovaError,
   r1cs::{R1CSGens, R1CSInstance, R1CSShape, R1CSWitness, RelaxedR1CSInstance, RelaxedR1CSWitness},
-  traits::{AbsorbInROTrait, Group, ROTrait},
+  traits::{
+    commitment::{CommitmentTrait, CompressedCommitmentTrait},
+    AbsorbInROTrait, Group, ROTrait,
+  },
+  CompressedCommitment,
 };
 use core::marker::PhantomData;
 use serde::{Deserialize, Serialize};
@@ -15,8 +18,9 @@ use serde::{Deserialize, Serialize};
 /// A SNARK that holds the proof of a step of an incremental computation
 #[allow(clippy::upper_case_acronyms)]
 #[derive(Clone, Debug, Serialize, Deserialize)]
+#[serde(bound = "")]
 pub struct NIFS<G: Group> {
-  pub(crate) comm_T: CompressedCommitment<G::CompressedGroupElement>,
+  pub(crate) comm_T: CompressedCommitment<G>,
   _p: PhantomData<G>,
 }
 

src/provider/ipa_pc.rs

@@ -1,7 +1,15 @@
+//! This module implements `EvaluationEngine` using an IPA-based polynomial commitment scheme
 #![allow(clippy::too_many_arguments)]
-use crate::commitments::{CommitGens, CommitTrait, Commitment, CompressedCommitment};
+use crate::{
-use crate::errors::NovaError;
+  errors::NovaError,
-use crate::traits::{AppendToTranscriptTrait, ChallengeTrait, Group};
+  spartan::polynomial::EqPolynomial,
+  traits::{
+    commitment::{CommitmentEngineTrait, CommitmentGensTrait, CommitmentTrait},
+    evaluation::EvaluationEngineTrait,
+    AppendToTranscriptTrait, ChallengeTrait, Group,
+  },
+  Commitment, CommitmentGens, CompressedCommitment, CE,
+};
 use core::{cmp::max, iter};
 use ff::Field;
 use merlin::Transcript;
@@ -9,7 +17,131 @@ use rayon::prelude::*;
 use serde::{Deserialize, Serialize};
 use std::marker::PhantomData;
 
-pub fn inner_product<T>(a: &[T], b: &[T]) -> T
+/// Provides an implementation of generators for proving evaluations
+#[derive(Clone, Debug, Serialize, Deserialize)]
+#[serde(bound = "")]
+pub struct EvaluationGens<G: Group> {
+  gens_v: CommitmentGens<G>,
+  gens_s: CommitmentGens<G>,
+}
+
+/// Provides an implementation of a polynomial evaluation argument
+#[derive(Clone, Debug, Serialize, Deserialize)]
+#[serde(bound = "")]
+pub struct EvaluationArgument<G: Group> {
+  nifs: Vec<NIFSForInnerProduct<G>>,
+  ipa: InnerProductArgument<G>,
+}
+
+/// Provides an implementation of a polynomial evaluation engine using IPA
+#[derive(Clone, Debug, Serialize, Deserialize)]
+pub struct EvaluationEngine<G: Group> {
+  _p: PhantomData<G>,
+}
+
+impl<G: Group> EvaluationEngineTrait<G> for EvaluationEngine<G> {
+  type CE = G::CE;
+  type EvaluationGens = EvaluationGens<G>;
+  type EvaluationArgument = EvaluationArgument<G>;
+
+  fn setup(gens: &<Self::CE as CommitmentEngineTrait<G>>::CommitmentGens) -> Self::EvaluationGens {
+    EvaluationGens {
+      gens_v: gens.clone(),
+      gens_s: CommitmentGens::<G>::new(b"ipa", 1),
+    }
+  }
+
+  fn prove_batch(
+    gens: &Self::EvaluationGens,
+    transcript: &mut Transcript,
+    comms: &[Commitment<G>],
+    polys: &[Vec<G::Scalar>],
+    points: &[Vec<G::Scalar>],
+    evals: &[G::Scalar],
+  ) -> Result<Self::EvaluationArgument, NovaError> {
+    // sanity checks (these should never fail)
+    assert!(polys.len() >= 2);
+    assert_eq!(comms.len(), polys.len());
+    assert_eq!(comms.len(), points.len());
+    assert_eq!(comms.len(), evals.len());
+
+    let mut r_U = InnerProductInstance::new(
+      &comms[0],
+      &EqPolynomial::new(points[0].clone()).evals(),
+      &evals[0],
+    );
+    let mut r_W = InnerProductWitness::new(&polys[0]);
+    let mut nifs = Vec::new();
+
+    for i in 1..polys.len() {
+      let (n, u, w) = NIFSForInnerProduct::prove(
+        &r_U,
+        &r_W,
+        &InnerProductInstance::new(
+          &comms[i],
+          &EqPolynomial::new(points[i].clone()).evals(),
+          &evals[i],
+        ),
+        &InnerProductWitness::new(&polys[i]),
+        transcript,
+      );
+      nifs.push(n);
+      r_U = u;
+      r_W = w;
+    }
+
+    let ipa = InnerProductArgument::prove(&gens.gens_v, &gens.gens_s, &r_U, &r_W, transcript)?;
+
+    Ok(EvaluationArgument { nifs, ipa })
+  }
+
+  /// A method to verify purported evaluations of a batch of polynomials
+  fn verify_batch(
+    gens: &Self::EvaluationGens,
+    transcript: &mut Transcript,
+    comms: &[<Self::CE as CommitmentEngineTrait<G>>::Commitment],
+    points: &[Vec<G::Scalar>],
+    evals: &[G::Scalar],
+    arg: &Self::EvaluationArgument,
+  ) -> Result<(), NovaError> {
+    // sanity checks (these should never fail)
+    assert!(comms.len() >= 2);
+    assert_eq!(comms.len(), points.len());
+    assert_eq!(comms.len(), evals.len());
+
+    let mut r_U = InnerProductInstance::new(
+      &comms[0],
+      &EqPolynomial::new(points[0].clone()).evals(),
+      &evals[0],
+    );
+    let mut num_vars = points[0].len();
+    for i in 1..comms.len() {
+      let u = arg.nifs[i - 1].verify(
+        &r_U,
+        &InnerProductInstance::new(
+          &comms[i],
+          &EqPolynomial::new(points[i].clone()).evals(),
+          &evals[i],
+        ),
+        transcript,
+      );
+      r_U = u;
+      num_vars = max(num_vars, points[i].len());
+    }
+
+    arg.ipa.verify(
+      &gens.gens_v,
+      &gens.gens_s,
+      (2_usize).pow(num_vars as u32),
+      &r_U,
+      transcript,
+    )?;
+
+    Ok(())
+  }
+}
+
+fn inner_product<T>(a: &[T], b: &[T]) -> T
 where
   T: Field + Send + Sync,
 {
@@ -29,7 +161,7 @@ pub struct InnerProductInstance<G: Group> {
 }
 
 impl<G: Group> InnerProductInstance<G> {
-  pub fn new(comm_a_vec: &Commitment<G>, b_vec: &[G::Scalar], c: &G::Scalar) -> Self {
+  fn new(comm_a_vec: &Commitment<G>, b_vec: &[G::Scalar], c: &G::Scalar) -> Self {
     InnerProductInstance {
       comm_a_vec: *comm_a_vec,
       b_vec: b_vec.to_vec(),
@@ -37,7 +169,7 @@ impl<G: Group> InnerProductInstance<G> {
     }
   }
 
-  pub fn pad(&self, n: usize) -> InnerProductInstance<G> {
+  fn pad(&self, n: usize) -> InnerProductInstance<G> {
     let mut b_vec = self.b_vec.clone();
     b_vec.resize(n, G::Scalar::zero());
     InnerProductInstance {
@@ -48,18 +180,18 @@ impl<G: Group> InnerProductInstance<G> {
   }
 }
 
-pub struct InnerProductWitness<G: Group> {
+struct InnerProductWitness<G: Group> {
   a_vec: Vec<G::Scalar>,
 }
 
 impl<G: Group> InnerProductWitness<G> {
-  pub fn new(a_vec: &[G::Scalar]) -> Self {
+  fn new(a_vec: &[G::Scalar]) -> Self {
     InnerProductWitness {
       a_vec: a_vec.to_vec(),
     }
   }
 
-  pub fn pad(&self, n: usize) -> InnerProductWitness<G> {
+  fn pad(&self, n: usize) -> InnerProductWitness<G> {
     let mut a_vec = self.a_vec.clone();
     a_vec.resize(n, G::Scalar::zero());
     InnerProductWitness { a_vec }
@@ -67,17 +199,17 @@ impl<G: Group> InnerProductWitness<G> {
 }
 
 /// A non-interactive folding scheme (NIFS) for inner product relations
-#[derive(Serialize, Deserialize)]
+#[derive(Clone, Debug, Serialize, Deserialize)]
 pub struct NIFSForInnerProduct<G: Group> {
   cross_term: G::Scalar,
 }
 
 impl<G: Group> NIFSForInnerProduct<G> {
-  pub fn protocol_name() -> &'static [u8] {
+  fn protocol_name() -> &'static [u8] {
     b"NIFSForInnerProduct"
   }
 
-  pub fn prove(
+  fn prove(
     U1: &InnerProductInstance<G>,
     W1: &InnerProductWitness<G>,
     U2: &InnerProductInstance<G>,
@@ -136,7 +268,7 @@ impl<G: Group> NIFSForInnerProduct<G> {
     (NIFSForInnerProduct { cross_term }, U, W)
   }
 
-  pub fn verify(
+  fn verify(
     &self,
     U1: &InnerProductInstance<G>,
     U2: &InnerProductInstance<G>,
@@ -183,10 +315,11 @@ impl<G: Group> NIFSForInnerProduct<G> {
 }
 
 /// An inner product argument
-#[derive(Debug, Serialize, Deserialize)]
+#[derive(Clone, Debug, Serialize, Deserialize)]
-pub struct InnerProductArgument<G: Group> {
+#[serde(bound = "")]
-  L_vec: Vec<CompressedCommitment<G::CompressedGroupElement>>,
+struct InnerProductArgument<G: Group> {
-  R_vec: Vec<CompressedCommitment<G::CompressedGroupElement>>,
+  L_vec: Vec<CompressedCommitment<G>>,
+  R_vec: Vec<CompressedCommitment<G>>,
   a_hat: G::Scalar,
   _p: PhantomData<G>,
 }
@@ -196,9 +329,9 @@ impl<G: Group> InnerProductArgument<G> {
     b"inner product argument"
   }
 
-  pub fn prove(
+  fn prove(
-    gens: &CommitGens<G>,
+    gens: &CommitmentGens<G>,
-    gens_c: &CommitGens<G>,
+    gens_c: &CommitmentGens<G>,
     U: &InnerProductInstance<G>,
     W: &InnerProductWitness<G>,
     transcript: &mut Transcript,
@@ -220,15 +353,15 @@ impl<G: Group> InnerProductArgument<G> {
     // a closure that executes a step of the recursive inner product argument
     let prove_inner = |a_vec: &[G::Scalar],
                        b_vec: &[G::Scalar],
-                       gens: &CommitGens<G>,
+                       gens: &CommitmentGens<G>,
                        transcript: &mut Transcript|
      -> Result<
       (
-        CompressedCommitment<G::CompressedGroupElement>,
+        CompressedCommitment<G>,
-        CompressedCommitment<G::CompressedGroupElement>,
+        CompressedCommitment<G>,
         Vec<G::Scalar>,
         Vec<G::Scalar>,
-        CommitGens<G>,
+        CommitmentGens<G>,
       ),
       NovaError,
     > {
@@ -238,20 +371,24 @@ impl<G: Group> InnerProductArgument<G> {
       let c_L = inner_product(&a_vec[0..n / 2], &b_vec[n / 2..n]);
       let c_R = inner_product(&a_vec[n / 2..n], &b_vec[0..n / 2]);
 
-      let L = a_vec[0..n / 2]
+      let L = CE::<G>::commit(
-        .iter()
+        &gens_R.combine(&gens_c),
-        .chain(iter::once(&c_L))
+        &a_vec[0..n / 2]
-        .copied()
+          .iter()
-        .collect::<Vec<G::Scalar>>()
+          .chain(iter::once(&c_L))
-        .commit(&gens_R.combine(&gens_c))
+          .copied()
-        .compress();
+          .collect::<Vec<G::Scalar>>(),
-      let R = a_vec[n / 2..n]
+      )
-        .iter()
+      .compress();
-        .chain(iter::once(&c_R))
+      let R = CE::<G>::commit(
-        .copied()
+        &gens_L.combine(&gens_c),
-        .collect::<Vec<G::Scalar>>()
+        &a_vec[n / 2..n]
-        .commit(&gens_L.combine(&gens_c))
+          .iter()
-        .compress();
+          .chain(iter::once(&c_R))
+          .copied()
+          .collect::<Vec<G::Scalar>>(),
+      )
+      .compress();
 
       L.append_to_transcript(b"L", transcript);
       R.append_to_transcript(b"R", transcript);
@@ -278,8 +415,8 @@ impl<G: Group> InnerProductArgument<G> {
     };
 
     // two vectors to hold the logarithmic number of group elements
-    let mut L_vec: Vec<CompressedCommitment<G::CompressedGroupElement>> = Vec::new();
+    let mut L_vec: Vec<CompressedCommitment<G>> = Vec::new();
-    let mut R_vec: Vec<CompressedCommitment<G::CompressedGroupElement>> = Vec::new();
+    let mut R_vec: Vec<CompressedCommitment<G>> = Vec::new();
 
     // we create mutable copies of vectors and generators
     let mut a_vec = W.a_vec.to_vec();
@@ -304,10 +441,10 @@ impl<G: Group> InnerProductArgument<G> {
     })
   }
 
-  pub fn verify(
+  fn verify(
     &self,
-    gens: &CommitGens<G>,
+    gens: &CommitmentGens<G>,
-    gens_c: &CommitGens<G>,
+    gens_c: &CommitmentGens<G>,
     n: usize,
     U: &InnerProductInstance<G>,
     transcript: &mut Transcript,
@@ -329,7 +466,7 @@ impl<G: Group> InnerProductArgument<G> {
     let r = G::Scalar::challenge(b"r", transcript);
     let gens_c = gens_c.scale(&r);
 
-    let P = U.comm_a_vec + [U.c].commit(&gens_c);
+    let P = U.comm_a_vec + CE::<G>::commit(&gens_c, &[U.c]);
 
     let batch_invert = |v: &[G::Scalar]| -> Result<Vec<G::Scalar>, NovaError> {
       let mut products = vec![G::Scalar::zero(); v.len()];
@@ -396,29 +533,37 @@ impl<G: Group> InnerProductArgument<G> {
     };
 
     let gens_hat = {
-      let c = s.commit(gens).compress();
+      let c = CE::<G>::commit(gens, &s).compress();
-      CommitGens::reinterpret_commitments_as_gens(&[c])?
+      CommitmentGens::<G>::reinterpret_commitments_as_gens(&[c])?
     };
 
     let b_hat = inner_product(&U.b_vec, &s);
 
     let P_hat = {
       let gens_folded = {
-        let gens_L = CommitGens::reinterpret_commitments_as_gens(&self.L_vec)?;
+        let gens_L = CommitmentGens::<G>::reinterpret_commitments_as_gens(&self.L_vec)?;
-        let gens_R = CommitGens::reinterpret_commitments_as_gens(&self.R_vec)?;
+        let gens_R = CommitmentGens::<G>::reinterpret_commitments_as_gens(&self.R_vec)?;
-        let gens_P = CommitGens::reinterpret_commitments_as_gens(&[P.compress()])?;
+        let gens_P = CommitmentGens::<G>::reinterpret_commitments_as_gens(&[P.compress()])?;
         gens_L.combine(&gens_R).combine(&gens_P)
       };
-      r_square
+
-        .iter()
+      CE::<G>::commit(
-        .chain(r_inverse_square.iter())
+        &gens_folded,
-        .chain(iter::once(&G::Scalar::one()))
+        &r_square
-        .copied()
+          .iter()
-        .collect::<Vec<G::Scalar>>()
+          .chain(r_inverse_square.iter())
-        .commit(&gens_folded)
+          .chain(iter::once(&G::Scalar::one()))
+          .copied()
+          .collect::<Vec<G::Scalar>>(),
+      )
     };
 
-    if P_hat == [self.a_hat, self.a_hat * b_hat].commit(&gens_hat.combine(&gens_c)) {
+    if P_hat
+      == CE::<G>::commit(
+        &gens_hat.combine(&gens_c),
+        &[self.a_hat, self.a_hat * b_hat],
+      )
+    {
       Ok(())
     } else {
       Err(NovaError::InvalidIPA)

src/provider/mod.rs

@@ -0,0 +1,10 @@
+//! This module implements Nova's traits using the following configuration:
+//! `CommitmentEngine` with Pedersen's commitments
+//! `Group` with pasta curves
+//! `RO` traits with Poseidon
+//! `EvaluationEngine` with an IPA-based polynomial evaluation argument
+
+pub mod ipa_pc;
+pub mod pasta;
+pub mod pedersen;
+pub mod poseidon;

src/provider/pasta.rs

@@ -1,6 +1,9 @@
 //! This module implements the Nova traits for pallas::Point, pallas::Scalar, vesta::Point, vesta::Scalar.
 use crate::{
-  poseidon::{PoseidonRO, PoseidonROCircuit},
+  provider::{
+    pedersen::CommitmentEngine,
+    poseidon::{PoseidonRO, PoseidonROCircuit},
+  },
   traits::{ChallengeTrait, CompressedGroup, Group},
 };
 use digest::{ExtendableOutput, Input};
@@ -61,6 +64,7 @@ macro_rules! impl_traits {
       type PreprocessedGroupElement = $name::Affine;
       type RO = PoseidonRO<Self::Base, Self::Scalar>;
       type ROCircuit = PoseidonROCircuit<Self::Base>;
+      type CE = CommitmentEngine<Self>;
 
       #[cfg(any(target_arch = "x86_64", target_arch = "aarch64"))]
       fn vartime_multiscalar_mul(

src/provider/pedersen.rs

@@ -1,6 +1,12 @@
-use super::{
+//! This module provides an implementation of a commitment engine
+use crate::{
   errors::NovaError,
-  traits::{AbsorbInROTrait, AppendToTranscriptTrait, CompressedGroup, Group, ROTrait},
+  traits::{
+    commitment::{
+      CommitmentEngineTrait, CommitmentGensTrait, CommitmentTrait, CompressedCommitmentTrait,
+    },
+    AbsorbInROTrait, AppendToTranscriptTrait, CompressedGroup, Group, ROTrait,
+  },
 };
 use core::{
   fmt::Debug,
@@ -12,27 +18,33 @@ use merlin::Transcript;
 use rayon::prelude::*;
 use serde::{Deserialize, Serialize};
 
-#[derive(Clone, Debug, Serialize, Deserialize)]
+/// A type that holds commitment generators
-pub struct CommitGens<G: Group> {
+#[derive(Clone, Debug, PartialEq, Eq, Serialize, Deserialize)]
+pub struct CommitmentGens<G: Group> {
   gens: Vec<G::PreprocessedGroupElement>,
   _p: PhantomData<G>,
 }
 
+/// A type that holds a commitment
 #[derive(Clone, Copy, Debug, PartialEq, Eq, Serialize, Deserialize)]
 #[serde(bound = "")]
 pub struct Commitment<G: Group> {
   pub(crate) comm: G,
 }
 
-#[derive(Clone, Debug, PartialEq, Eq, Serialize, Deserialize)]
+/// A type that holds a compressed commitment
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Serialize, Deserialize)]
 #[serde(bound = "")]
 pub struct CompressedCommitment<C: CompressedGroup> {
   comm: C,
 }
 
-impl<G: Group> CommitGens<G> {
+impl<G: Group> CommitmentGensTrait<G> for CommitmentGens<G> {
-  pub fn new(label: &'static [u8], n: usize) -> Self {
+  type Commitment = Commitment<G>;
-    CommitGens {
+  type CompressedCommitment = CompressedCommitment<G::CompressedGroupElement>;
+
+  fn new(label: &'static [u8], n: usize) -> Self {
+    CommitmentGens {
       gens: G::from_label(label, n.next_power_of_two()),
       _p: Default::default(),
     }
@@ -42,76 +54,83 @@ impl<G: Group> CommitGens<G> {
     self.gens.len()
   }
 
-  pub fn split_at(&self, n: usize) -> (CommitGens<G>, CommitGens<G>) {
+  fn commit(&self, v: &[G::Scalar]) -> Self::Commitment {
+    assert!(self.gens.len() >= v.len());
+    Commitment {
+      comm: G::vartime_multiscalar_mul(v, &self.gens[..v.len()]),
+    }
+  }
+
+  fn split_at(&self, n: usize) -> (CommitmentGens<G>, CommitmentGens<G>) {
     (
-      CommitGens {
+      CommitmentGens {
         gens: self.gens[0..n].to_vec(),
         _p: Default::default(),
       },
-      CommitGens {
+      CommitmentGens {
         gens: self.gens[n..].to_vec(),
         _p: Default::default(),
       },
     )
   }
 
-  pub fn combine(&self, other: &CommitGens<G>) -> CommitGens<G> {
+  fn combine(&self, other: &CommitmentGens<G>) -> CommitmentGens<G> {
     let gens = {
       let mut c = self.gens.clone();
       c.extend(other.gens.clone());
       c
     };
-    CommitGens {
+    CommitmentGens {
       gens,
       _p: Default::default(),
     }
   }
 
   // combines the left and right halves of `self` using `w1` and `w2` as the weights
-  pub fn fold(&self, w1: &G::Scalar, w2: &G::Scalar) -> CommitGens<G> {
+  fn fold(&self, w1: &G::Scalar, w2: &G::Scalar) -> CommitmentGens<G> {
     let w = vec![*w1, *w2];
     let (L, R) = self.split_at(self.len() / 2);
 
     let gens = (0..self.len() / 2)
       .into_par_iter()
       .map(|i| {
-        let gens = CommitGens::<G> {
+        let gens = CommitmentGens::<G> {
           gens: [L.gens[i].clone(), R.gens[i].clone()].to_vec(),
           _p: Default::default(),
         };
-        w.commit(&gens).comm.preprocessed()
+        gens.commit(&w).comm.preprocessed()
       })
       .collect();
 
-    CommitGens {
+    CommitmentGens {
       gens,
       _p: Default::default(),
     }
   }
 
   /// Scales each element in `self` by `r`
-  pub fn scale(&self, r: &G::Scalar) -> Self {
+  fn scale(&self, r: &G::Scalar) -> Self {
     let gens_scaled = self
       .gens
       .clone()
       .into_par_iter()
       .map(|g| {
-        let gens = CommitGens::<G> {
+        let gens = CommitmentGens::<G> {
           gens: vec![g],
           _p: Default::default(),
         };
-        [*r].commit(&gens).comm.preprocessed()
+        gens.commit(&[*r]).comm.preprocessed()
       })
       .collect();
 
-    CommitGens {
+    CommitmentGens {
       gens: gens_scaled,
       _p: Default::default(),
     }
   }
 
   /// reinterprets a vector of commitments as a set of generators
-  pub fn reinterpret_commitments_as_gens(
+  fn reinterpret_commitments_as_gens(
     c: &[CompressedCommitment<G::CompressedGroupElement>],
   ) -> Result<Self, NovaError> {
     let d = (0..c.len())
@@ -122,19 +141,25 @@ impl<G: Group> CommitGens<G> {
       .into_par_iter()
       .map(|i| d[i].comm.preprocessed())
       .collect();
-    Ok(CommitGens {
+    Ok(CommitmentGens {
       gens,
       _p: Default::default(),
     })
   }
 }
 
-impl<G: Group> Commitment<G> {
+impl<G: Group> CommitmentTrait<G> for Commitment<G> {
-  pub fn compress(&self) -> CompressedCommitment<G::CompressedGroupElement> {
+  type CompressedCommitment = CompressedCommitment<G::CompressedGroupElement>;
+
+  fn compress(&self) -> CompressedCommitment<G::CompressedGroupElement> {
     CompressedCommitment {
       comm: self.comm.compress(),
     }
   }
+
+  fn to_coordinates(&self) -> (G::Base, G::Base, bool) {
+    self.comm.to_coordinates()
+  }
 }
 
 impl<G: Group> Default for Commitment<G> {
@@ -143,8 +168,10 @@ impl<G: Group> Default for Commitment<G> {
   }
 }
 
-impl<C: CompressedGroup> CompressedCommitment<C> {
+impl<C: CompressedGroup> CompressedCommitmentTrait<C> for CompressedCommitment<C> {
-  pub fn decompress(&self) -> Result<Commitment<C::GroupElement>, NovaError> {
+  type Commitment = Commitment<C::GroupElement>;
+
+  fn decompress(&self) -> Result<Self::Commitment, NovaError> {
     let comm = self.comm.decompress();
     if comm.is_none() {
       return Err(NovaError::DecompressionError);
@@ -155,19 +182,6 @@ impl<C: CompressedGroup> CompressedCommitment<C> {
   }
 }
 
-pub trait CommitTrait<G: Group> {
-  fn commit(&self, gens: &CommitGens<G>) -> Commitment<G>;
-}
-
-impl<G: Group> CommitTrait<G> for [G::Scalar] {
-  fn commit(&self, gens: &CommitGens<G>) -> Commitment<G> {
-    assert!(gens.gens.len() >= self.len());
-    Commitment {
-      comm: G::vartime_multiscalar_mul(self, &gens.gens[..self.len()]),
-    }
-  }
-}
-
 impl<G: Group> AppendToTranscriptTrait for Commitment<G> {
   fn append_to_transcript(&self, label: &'static [u8], transcript: &mut Transcript) {
     transcript.append_message(label, self.comm.compress().as_bytes());
@@ -193,8 +207,8 @@ impl<C: CompressedGroup> AppendToTranscriptTrait for CompressedCommitment<C> {
   }
 }
 
-impl<'b, G: Group> MulAssign<&'b G::Scalar> for Commitment<G> {
+impl<G: Group> MulAssign<G::Scalar> for Commitment<G> {
-  fn mul_assign(&mut self, scalar: &'b G::Scalar) {
+  fn mul_assign(&mut self, scalar: G::Scalar) {
     let result = (self as &Commitment<G>).comm * scalar;
     *self = Commitment { comm: result };
   }
@@ -272,3 +286,19 @@ macro_rules! define_add_assign_variants {
 
 define_add_assign_variants!(G = Group, LHS = Commitment<G>, RHS = Commitment<G>);
 define_add_variants!(G = Group, LHS = Commitment<G>, RHS = Commitment<G>, Output = Commitment<G>);
+
+/// Provides a commitment engine
+#[derive(Clone, Debug, PartialEq, Eq, Serialize, Deserialize)]
+pub struct CommitmentEngine<G: Group> {
+  _p: PhantomData<G>,
+}
+
+impl<G: Group> CommitmentEngineTrait<G> for CommitmentEngine<G> {
+  type CommitmentGens = CommitmentGens<G>;
+  type Commitment = Commitment<G>;
+  type CompressedCommitment = CompressedCommitment<G::CompressedGroupElement>;
+
+  fn commit(gens: &Self::CommitmentGens, v: &[G::Scalar]) -> Self::Commitment {
+    gens.commit(v)
+  }
+}

src/provider/poseidon.rs

@@ -1,5 +1,5 @@
 //! Poseidon Constants and Poseidon-based RO used in Nova
-use super::traits::{ROCircuitTrait, ROConstantsTrait, ROTrait};
+use crate::traits::{ROCircuitTrait, ROConstantsTrait, ROTrait};
 use bellperson::{
   gadgets::{
     boolean::{AllocatedBit, Boolean},

src/r1cs.rs

@@ -1,12 +1,17 @@
 //! This module defines R1CS related types and a folding scheme for Relaxed R1CS
 #![allow(clippy::type_complexity)]
-use super::gadgets::nonnative::{bignat::nat_to_limbs, util::f_to_nat};
+use crate::{
-use super::{
-  commitments::{CommitGens, CommitTrait, Commitment},
   constants::{BN_LIMB_WIDTH, BN_N_LIMBS, NUM_HASH_BITS},
   errors::NovaError,
-  gadgets::utils::scalar_as_base,
+  gadgets::{
-  traits::{AbsorbInROTrait, AppendToTranscriptTrait, Group, ROTrait},
+    nonnative::{bignat::nat_to_limbs, util::f_to_nat},
+    utils::scalar_as_base,
+  },
+  traits::{
+    commitment::{CommitmentEngineTrait, CommitmentGensTrait},
+    AbsorbInROTrait, AppendToTranscriptTrait, Group, ROTrait,
+  },
+  Commitment, CommitmentGens, CE,
 };
 use core::cmp::max;
 use ff::Field;
@@ -21,7 +26,7 @@ use sha3::{Digest, Sha3_256};
 #[derive(Clone, Serialize, Deserialize)]
 #[serde(bound = "")]
 pub struct R1CSGens<G: Group> {
-  pub(crate) gens: CommitGens<G>,
+  pub(crate) gens: CommitmentGens<G>,
 }
 
 /// A type that holds the shape of the R1CS matrices
@@ -71,7 +76,7 @@ impl<G: Group> R1CSGens<G> {
   /// Samples public parameters for the specified number of constraints and variables in an R1CS
   pub fn new(num_cons: usize, num_vars: usize) -> R1CSGens<G> {
     R1CSGens {
-      gens: CommitGens::new(b"gens", max(num_vars, num_cons)),
+      gens: CommitmentGens::<G>::new(b"gens", max(num_vars, num_cons)),
     }
   }
 }
@@ -202,7 +207,10 @@ impl<G: Group> R1CSShape<G> {
 
     // verify if comm_E and comm_W are commitments to E and W
     let res_comm: bool = {
-      let (comm_W, comm_E) = rayon::join(|| W.W.commit(&gens.gens), || W.E.commit(&gens.gens));
+      let (comm_W, comm_E) = rayon::join(
+        || CE::<G>::commit(&gens.gens, &W.W),
+        || CE::<G>::commit(&gens.gens, &W.E),
+      );
       U.comm_W == comm_W && U.comm_E == comm_E
     };
 
@@ -239,7 +247,7 @@ impl<G: Group> R1CSShape<G> {
     };
 
     // verify if comm_W is a commitment to W
-    let res_comm: bool = U.comm_W == W.W.commit(&gens.gens);
+    let res_comm: bool = U.comm_W == gens.gens.commit(&W.W);
 
     if res_eq && res_comm {
       Ok(())
@@ -293,7 +301,7 @@ impl<G: Group> R1CSShape<G> {
       .map(|(((a, b), c), d)| *a + *b - *c - *d)
       .collect::<Vec<G::Scalar>>();
 
-    let comm_T = T.commit(&gens.gens);
+    let comm_T = gens.gens.commit(&T);
 
     Ok((T, comm_T))
   }
@@ -458,7 +466,7 @@ impl<G: Group> R1CSWitness<G> {
 
   /// Commits to the witness using the supplied generators
   pub fn commit(&self, gens: &R1CSGens<G>) -> Commitment<G> {
-    self.W.commit(&gens.gens)
+    gens.gens.commit(&self.W)
   }
 }
 
@@ -515,7 +523,10 @@ impl<G: Group> RelaxedR1CSWitness<G> {
 
   /// Commits to the witness using the supplied generators
   pub fn commit(&self, gens: &R1CSGens<G>) -> (Commitment<G>, Commitment<G>) {
-    (self.W.commit(&gens.gens), self.E.commit(&gens.gens))
+    (
+      CE::<G>::commit(&gens.gens, &self.W),
+      CE::<G>::commit(&gens.gens, &self.E),
+    )
   }
 
   /// Folds an incoming R1CSWitness into the current one
@@ -566,7 +577,7 @@ impl<G: Group> RelaxedR1CSWitness<G> {
 impl<G: Group> RelaxedR1CSInstance<G> {
   /// Produces a default RelaxedR1CSInstance given R1CSGens and R1CSShape
   pub fn default(_gens: &R1CSGens<G>, S: &R1CSShape<G>) -> RelaxedR1CSInstance<G> {
-    let (comm_W, comm_E) = (Commitment::default(), Commitment::default());
+    let (comm_W, comm_E) = (Commitment::<G>::default(), Commitment::<G>::default());
     RelaxedR1CSInstance {
       comm_W,
       comm_E,
@@ -605,7 +616,7 @@ impl<G: Group> RelaxedR1CSInstance<G> {
       .zip(X2)
       .map(|(a, b)| *a + *r * *b)
       .collect::<Vec<G::Scalar>>();
-    let comm_W = comm_W_1 + comm_W_2 * r;
+    let comm_W = *comm_W_1 + *comm_W_2 * *r;
     let comm_E = *comm_E_1 + *comm_T * *r;
     let u = *u1 + *r;
 

src/spartan/mod.rs

@@ -1,21 +1,18 @@
-//! This module implements RelaxedR1CSSNARKTrait using a Spartan variant
+//! This module implements RelaxedR1CSSNARKTrait using Spartan that is generic
-//! instantiated with an IPA-based polynomial commitment scheme
+//! over the polynomial commitment and evaluation argument (i.e., a PCS)
-mod ipa;
+pub mod polynomial;
-mod polynomial;
 mod sumcheck;
 
-use super::{
+use crate::{
-  commitments::CommitGens,
   errors::NovaError,
   r1cs::{R1CSGens, R1CSShape, RelaxedR1CSInstance, RelaxedR1CSWitness},
   traits::{
+    evaluation::EvaluationEngineTrait,
     snark::{ProverKeyTrait, RelaxedR1CSSNARKTrait, VerifierKeyTrait},
     AppendToTranscriptTrait, ChallengeTrait, Group,
   },
 };
-use core::cmp::max;
 use ff::Field;
-use ipa::{InnerProductArgument, InnerProductInstance, InnerProductWitness, NIFSForInnerProduct};
 use itertools::concat;
 use merlin::Transcript;
 use polynomial::{EqPolynomial, MultilinearPolynomial, SparsePolynomial};
@@ -26,17 +23,15 @@ use sumcheck::SumcheckProof;
 /// A type that represents the prover's key
 #[derive(Serialize, Deserialize)]
 #[serde(bound = "")]
-pub struct ProverKey<G: Group> {
+pub struct ProverKey<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> {
-  gens_r1cs: R1CSGens<G>,
+  gens: EE::EvaluationGens,
-  gens_ipa: CommitGens<G>,
   S: R1CSShape<G>,
 }
 
-impl<G: Group> ProverKeyTrait<G> for ProverKey<G> {
+impl<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> ProverKeyTrait<G> for ProverKey<G, EE> {
   fn new(gens: &R1CSGens<G>, S: &R1CSShape<G>) -> Self {
     ProverKey {
-      gens_r1cs: gens.clone(),
+      gens: EE::setup(&gens.gens),
-      gens_ipa: CommitGens::new(b"ipa", 1),
       S: S.clone(),
     }
   }
@@ -45,17 +40,17 @@ impl<G: Group> ProverKeyTrait<G> for ProverKey<G> {
 /// A type that represents the verifier's key
 #[derive(Serialize, Deserialize)]
 #[serde(bound = "")]
-pub struct VerifierKey<G: Group> {
+pub struct VerifierKey<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> {
-  gens_r1cs: R1CSGens<G>,
+  gens: EE::EvaluationGens,
-  gens_ipa: CommitGens<G>,
   S: R1CSShape<G>,
 }
 
-impl<G: Group> VerifierKeyTrait<G> for VerifierKey<G> {
+impl<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> VerifierKeyTrait<G>
+  for VerifierKey<G, EE>
+{
   fn new(gens: &R1CSGens<G>, S: &R1CSShape<G>) -> Self {
     VerifierKey {
-      gens_r1cs: gens.clone(),
+      gens: EE::setup(&gens.gens),
-      gens_ipa: CommitGens::new(b"ipa", 1),
       S: S.clone(),
     }
   }
@@ -66,19 +61,20 @@ impl<G: Group> VerifierKeyTrait<G> for VerifierKey<G> {
 /// the commitment to a vector viewed as a polynomial commitment
 #[derive(Serialize, Deserialize)]
 #[serde(bound = "")]
-pub struct RelaxedR1CSSNARK<G: Group> {
+pub struct RelaxedR1CSSNARK<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> {
   sc_proof_outer: SumcheckProof<G>,
   claims_outer: (G::Scalar, G::Scalar, G::Scalar),
   sc_proof_inner: SumcheckProof<G>,
   eval_E: G::Scalar,
   eval_W: G::Scalar,
-  nifs_ip: NIFSForInnerProduct<G>,
+  eval_arg: EE::EvaluationArgument,
-  ipa: InnerProductArgument<G>,
 }
 
-impl<G: Group> RelaxedR1CSSNARKTrait<G> for RelaxedR1CSSNARK<G> {
+impl<G: Group, EE: EvaluationEngineTrait<G, CE = G::CE>> RelaxedR1CSSNARKTrait<G>
-  type ProverKey = ProverKey<G>;
+  for RelaxedR1CSSNARK<G, EE>
-  type VerifierKey = VerifierKey<G>;
+{
+  type ProverKey = ProverKey<G, EE>;
+  type VerifierKey = VerifierKey<G, EE>;
 
   /// produces a succinct proof of satisfiability of a RelaxedR1CS instance
   fn prove(
@@ -88,8 +84,6 @@ impl<G: Group> RelaxedR1CSSNARKTrait<G> for RelaxedR1CSSNARK<G> {
   ) -> Result<Self, NovaError> {
     let mut transcript = Transcript::new(b"RelaxedR1CSSNARK");
 
-    debug_assert!(pk.S.is_sat_relaxed(&pk.gens_r1cs, U, W).is_ok());
-
     // sanity check that R1CSShape has certain size characteristics
     assert_eq!(pk.S.num_cons.next_power_of_two(), pk.S.num_cons);
     assert_eq!(pk.S.num_vars.next_power_of_two(), pk.S.num_vars);
@@ -230,24 +224,13 @@ impl<G: Group> RelaxedR1CSSNARKTrait<G> for RelaxedR1CSSNARK<G> {
     let eval_W = MultilinearPolynomial::new(W.W.clone()).evaluate(&r_y[1..]);
     eval_W.append_to_transcript(b"eval_W", &mut transcript);
 
-    let (nifs_ip, r_U, r_W) = NIFSForInnerProduct::prove(
+    let eval_arg = EE::prove_batch(
-      &InnerProductInstance::new(&U.comm_E, &EqPolynomial::new(r_x).evals(), &eval_E),
+      &pk.gens,
-      &InnerProductWitness::new(&W.E),
-      &InnerProductInstance::new(
-        &U.comm_W,
-        &EqPolynomial::new(r_y[1..].to_vec()).evals(),
-        &eval_W,
-      ),
-      &InnerProductWitness::new(&W.W),
-      &mut transcript,
-    );
-
-    let ipa = InnerProductArgument::prove(
-      &pk.gens_r1cs.gens,
-      &pk.gens_ipa,
-      &r_U,
-      &r_W,
       &mut transcript,
+      &[U.comm_E, U.comm_W],
+      &[W.E.clone(), W.W.clone()],
+      &[r_x, r_y[1..].to_vec()],
+      &[eval_E, eval_W],
     )?;
 
     Ok(RelaxedR1CSSNARK {
@@ -256,8 +239,7 @@ impl<G: Group> RelaxedR1CSSNARKTrait<G> for RelaxedR1CSSNARK<G> {
       sc_proof_inner,
       eval_W,
       eval_E,
-      nifs_ip,
+      eval_arg,
-      ipa,
     })
   }
 
@@ -366,22 +348,13 @@ impl<G: Group> RelaxedR1CSSNARKTrait<G> for RelaxedR1CSSNARK<G> {
     // verify eval_W and eval_E
     self.eval_W.append_to_transcript(b"eval_W", &mut transcript); //eval_E is already in the transcript
 
-    let r_U = self.nifs_ip.verify(
+    EE::verify_batch(
-      &InnerProductInstance::new(&U.comm_E, &EqPolynomial::new(r_x).evals(), &self.eval_E),
+      &vk.gens,
-      &InnerProductInstance::new(
-        &U.comm_W,
-        &EqPolynomial::new(r_y[1..].to_vec()).evals(),
-        &self.eval_W,
-      ),
-      &mut transcript,
-    );
-
-    self.ipa.verify(
-      &vk.gens_r1cs.gens,
-      &vk.gens_ipa,
-      max(vk.S.num_vars, vk.S.num_cons),
-      &r_U,
       &mut transcript,
+      &[U.comm_E, U.comm_W],
+      &[r_x, r_y[1..].to_vec()],
+      &[self.eval_E, self.eval_W],
+      &self.eval_arg,
     )?;
 
     Ok(())

src/spartan/polynomial.rs

@@ -1,16 +1,19 @@
+//! This module defines basic types related to polynomials
 use core::ops::Index;
 use ff::PrimeField;
 use rayon::prelude::*;
 
-pub struct EqPolynomial<Scalar: PrimeField> {
+pub(crate) struct EqPolynomial<Scalar: PrimeField> {
   r: Vec<Scalar>,
 }
 
 impl<Scalar: PrimeField> EqPolynomial<Scalar> {
+  /// Creates a new polynomial from its succinct specification
   pub fn new(r: Vec<Scalar>) -> Self {
     EqPolynomial { r }
   }
 
+  /// Evaluates the polynomial at the specified point
   pub fn evaluate(&self, rx: &[Scalar]) -> Scalar {
     assert_eq!(self.r.len(), rx.len());
     (0..rx.len())
@@ -43,7 +46,7 @@ impl<Scalar: PrimeField> EqPolynomial<Scalar> {
 }
 
 #[derive(Debug)]
-pub struct MultilinearPolynomial<Scalar: PrimeField> {
+pub(crate) struct MultilinearPolynomial<Scalar: PrimeField> {
   num_vars: usize, // the number of variables in the multilinear polynomial
   Z: Vec<Scalar>,  // evaluations of the polynomial in all the 2^num_vars Boolean inputs
 }
@@ -105,7 +108,7 @@ impl<Scalar: PrimeField> Index<usize> for MultilinearPolynomial<Scalar> {
   }
 }
 
-pub struct SparsePolynomial<Scalar: PrimeField> {
+pub(crate) struct SparsePolynomial<Scalar: PrimeField> {
   num_vars: usize,
   Z: Vec<(usize, Scalar)>,
 }

src/spartan/sumcheck.rs

@@ -11,7 +11,7 @@ use serde::{Deserialize, Serialize};
 
 #[derive(Debug, Serialize, Deserialize)]
 #[serde(bound = "")]
-pub struct SumcheckProof<G: Group> {
+pub(crate) struct SumcheckProof<G: Group> {
   compressed_polys: Vec<CompressedUniPoly<G>>,
 }
 

src/traits/commitment.rs

@@ -0,0 +1,149 @@
+//! This module defines a collection of traits that define the behavior of a commitment engine
+//! We require the commitment engine to provide a commitment to vectors with a single group element
+use crate::{
+  errors::NovaError,
+  traits::{AbsorbInROTrait, AppendToTranscriptTrait, CompressedGroup, Group},
+};
+use core::{
+  fmt::Debug,
+  ops::{Add, AddAssign, Mul, MulAssign},
+};
+use serde::{Deserialize, Serialize};
+
+/// This trait defines the behavior of commitment key
+#[allow(clippy::len_without_is_empty)]
+pub trait CommitmentGensTrait<G: Group>:
+  Clone + Debug + Send + Sync + Serialize + for<'de> Deserialize<'de>
+{
+  /// Holds the type of the commitment that can be produced
+  type Commitment;
+
+  /// Holds the type of the compressed commitment
+  type CompressedCommitment;
+
+  /// Samples a new commitment key of a specified size
+  fn new(label: &'static [u8], n: usize) -> Self;
+
+  /// Returns the vector length that can be committed
+  fn len(&self) -> usize;
+
+  /// Commits to a vector using the commitment key
+  fn commit(&self, v: &[G::Scalar]) -> Self::Commitment;
+
+  /// Splits the commitment key into two pieces at a specified point
+  fn split_at(&self, n: usize) -> (Self, Self)
+  where
+    Self: Sized;
+
+  /// Combines two commitment keys into one
+  fn combine(&self, other: &Self) -> Self;
+
+  /// Folds the two commitment keys into one using the provided weights
+  fn fold(&self, w1: &G::Scalar, w2: &G::Scalar) -> Self;
+
+  /// Scales the commitment key using the provided scalar
+  fn scale(&self, r: &G::Scalar) -> Self;
+
+  /// Reinterprets commitments as commitment keys
+  fn reinterpret_commitments_as_gens(c: &[Self::CompressedCommitment]) -> Result<Self, NovaError>
+  where
+    Self: Sized;
+}
+
+/// Defines basic operations on commitments
+pub trait CommitmentOps<Rhs = Self, Output = Self>:
+  Add<Rhs, Output = Output> + AddAssign<Rhs>
+{
+}
+
+impl<T, Rhs, Output> CommitmentOps<Rhs, Output> for T where
+  T: Add<Rhs, Output = Output> + AddAssign<Rhs>
+{
+}
+
+/// A helper trait for references with a commitment operation
+pub trait CommitmentOpsOwned<Rhs = Self, Output = Self>:
+  for<'r> CommitmentOps<&'r Rhs, Output>
+{
+}
+impl<T, Rhs, Output> CommitmentOpsOwned<Rhs, Output> for T where
+  T: for<'r> CommitmentOps<&'r Rhs, Output>
+{
+}
+
+/// A helper trait for types implementing a multiplication of a commitment with a scalar
+pub trait ScalarMul<Rhs, Output = Self>: Mul<Rhs, Output = Output> + MulAssign<Rhs> {}
+
+impl<T, Rhs, Output> ScalarMul<Rhs, Output> for T where T: Mul<Rhs, Output = Output> + MulAssign<Rhs>
+{}
+
+/// This trait defines the behavior of the commitment
+pub trait CommitmentTrait<G: Group>:
+  Clone
+  + Copy
+  + Debug
+  + Default
+  + PartialEq
+  + Eq
+  + Send
+  + Sync
+  + Serialize
+  + for<'de> Deserialize<'de>
+  + AbsorbInROTrait<G>
+  + AppendToTranscriptTrait
+  + CommitmentOps
+  + CommitmentOpsOwned
+  + ScalarMul<G::Scalar>
+{
+  /// Holds the type of the compressed commitment
+  type CompressedCommitment;
+
+  /// Compresses self into a compressed commitment
+  fn compress(&self) -> Self::CompressedCommitment;
+
+  /// Returns the coordinate representation of the commitment
+  fn to_coordinates(&self) -> (G::Base, G::Base, bool);
+}
+
+/// This trait defines the behavior of a compressed commitment
+pub trait CompressedCommitmentTrait<C: CompressedGroup>:
+  Clone
+  + Debug
+  + PartialEq
+  + Eq
+  + Send
+  + Sync
+  + Serialize
+  + for<'de> Deserialize<'de>
+  + AppendToTranscriptTrait
+{
+  /// Holds the type of the commitment that can be decompressed into
+  type Commitment;
+
+  /// Decompresses self into a commitment
+  fn decompress(&self) -> Result<Self::Commitment, NovaError>;
+}
+
+/// A trait that ties different pieces of the commitment generation together
+pub trait CommitmentEngineTrait<G: Group>:
+  Clone + Send + Sync + Serialize + for<'de> Deserialize<'de>
+{
+  /// Holds the type of the commitment key
+  type CommitmentGens: CommitmentGensTrait<
+    G,
+    Commitment = Self::Commitment,
+    CompressedCommitment = Self::CompressedCommitment,
+  >;
+
+  /// Holds the type of the commitment
+  type Commitment: CommitmentTrait<G, CompressedCommitment = Self::CompressedCommitment>;
+
+  /// Holds the type of the compressed commitment
+  type CompressedCommitment: CompressedCommitmentTrait<
+    G::CompressedGroupElement,
+    Commitment = Self::Commitment,
+  >;
+
+  /// Commits to the provided vector using the provided generators
+  fn commit(gens: &Self::CommitmentGens, v: &[G::Scalar]) -> Self::Commitment;
+}

src/traits/evaluation.rs

@@ -0,0 +1,46 @@
+//! This module defines a collection of traits that define the behavior of a polynomial evaluation engine
+//! A vector of size N is treated as a multilinear polynomial in \log{N} variables,
+//! and a commitment provided by the commitment engine is treated as a multilinear polynomial commitment
+use crate::{
+  errors::NovaError,
+  traits::{commitment::CommitmentEngineTrait, Group},
+};
+use merlin::Transcript;
+use serde::{Deserialize, Serialize};
+
+/// A trait that ties different pieces of the commitment evaluation together
+pub trait EvaluationEngineTrait<G: Group>:
+  Clone + Send + Sync + Serialize + for<'de> Deserialize<'de>
+{
+  /// A type that holds the associated commitment engine
+  type CE: CommitmentEngineTrait<G>;
+
+  /// A type that holds generators
+  type EvaluationGens: Clone + Send + Sync + Serialize + for<'de> Deserialize<'de>;
+
+  /// A type that holds the evaluation argument
+  type EvaluationArgument: Clone + Send + Sync + Serialize + for<'de> Deserialize<'de>;
+
+  /// A method to perform any additional setup needed to produce proofs of evaluations
+  fn setup(gens: &<Self::CE as CommitmentEngineTrait<G>>::CommitmentGens) -> Self::EvaluationGens;
+
+  /// A method to prove evaluations of a batch of polynomials
+  fn prove_batch(
+    gens: &Self::EvaluationGens,
+    transcript: &mut Transcript,
+    comm: &[<Self::CE as CommitmentEngineTrait<G>>::Commitment],
+    polys: &[Vec<G::Scalar>],
+    points: &[Vec<G::Scalar>],
+    evals: &[G::Scalar],
+  ) -> Result<Self::EvaluationArgument, NovaError>;
+
+  /// A method to verify purported evaluations of a batch of polynomials
+  fn verify_batch(
+    gens: &Self::EvaluationGens,
+    transcript: &mut Transcript,
+    comm: &[<Self::CE as CommitmentEngineTrait<G>>::Commitment],
+    points: &[Vec<G::Scalar>],
+    evals: &[G::Scalar],
+    arg: &Self::EvaluationArgument,
+  ) -> Result<(), NovaError>;
+}

src/traits/mod.rs

@@ -12,6 +12,10 @@ use merlin::Transcript;
 use num_bigint::BigInt;
 use serde::{Deserialize, Serialize};
 
+pub mod commitment;
+
+use commitment::CommitmentEngineTrait;
+
 /// Represents an element of a group
 /// This is currently tailored for an elliptic curve group
 pub trait Group:
@@ -47,7 +51,7 @@ pub trait Group:
     + for<'de> Deserialize<'de>;
 
   /// A type representing preprocessed group element
-  type PreprocessedGroupElement: Clone + Send + Sync + Serialize + for<'de> Deserialize<'de>;
+  type PreprocessedGroupElement: Clone + Debug + Send + Sync + Serialize + for<'de> Deserialize<'de>;
 
   /// A type that represents a hash function that consumes elements
   /// from the base field and squeezes out elements of the scalar field
@@ -56,6 +60,9 @@ pub trait Group:
   /// An alternate implementation of Self::RO in the circuit model
   type ROCircuit: ROCircuitTrait<Self::Base> + Serialize + for<'de> Deserialize<'de>;
 
+  /// A type that defines a commitment engine over scalars in the group
+  type CE: CommitmentEngineTrait<Self> + Serialize + for<'de> Deserialize<'de>;
+
   /// A method to compute a multiexponentation
   fn vartime_multiscalar_mul(
     scalars: &[Self::Scalar],
@@ -212,4 +219,5 @@ impl<F: PrimeField> AppendToTranscriptTrait for [F] {
 }
 
 pub mod circuit;
+pub mod evaluation;
 pub mod snark;