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

* make Minroot example generic over the supported curve cycles

* upgrade version

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "nova-snark"
-version = "0.31.0"
+version = "0.32.0"
 authors = ["Srinath Setty <[email protected]>"]
 edition = "2021"
 description = "High-speed recursive arguments from folding schemes"

examples/minroot.rs

@@ -2,47 +2,54 @@
 //! iterations of the `MinRoot` function, thereby realizing a Nova-based verifiable delay function (VDF).
 //! We execute a configurable number of iterations of the `MinRoot` function per step of Nova's recursion.
 use bellpepper_core::{num::AllocatedNum, ConstraintSystem, SynthesisError};
-use ff::PrimeField;
+use ff::Field;
 use flate2::{write::ZlibEncoder, Compression};
 use nova_snark::{
-  provider::{PallasEngine, VestaEngine},
+  provider::{mlkzg::Bn256EngineKZG, GrumpkinEngine},
   traits::{
     circuit::{StepCircuit, TrivialCircuit},
-    snark::default_ck_hint,
-    Engine,
+    snark::RelaxedR1CSSNARKTrait,
+    Engine, Group,
   },
   CompressedSNARK, PublicParams, RecursiveSNARK,
 };
 use num_bigint::BigUint;
 use std::time::Instant;
 
-type E1 = PallasEngine;
-type E2 = VestaEngine;
+type E1 = Bn256EngineKZG;
+type E2 = GrumpkinEngine;
+type EE1 = nova_snark::provider::mlkzg::EvaluationEngine<E1>;
+type EE2 = nova_snark::provider::ipa_pc::EvaluationEngine<E2>;
+type S1 = nova_snark::spartan::snark::RelaxedR1CSSNARK<E1, EE1>; // non-preprocessing SNARK
+type S2 = nova_snark::spartan::snark::RelaxedR1CSSNARK<E2, EE2>; // non-preprocessing SNARK
 
 #[derive(Clone, Debug)]
-struct MinRootIteration<F: PrimeField> {
-  x_i: F,
-  y_i: F,
-  x_i_plus_1: F,
-  y_i_plus_1: F,
+struct MinRootIteration<G: Group> {
+  x_i: G::Scalar,
+  y_i: G::Scalar,
+  x_i_plus_1: G::Scalar,
+  y_i_plus_1: G::Scalar,
 }
 
-impl<F: PrimeField> MinRootIteration<F> {
+impl<G: Group> MinRootIteration<G> {
   // produces a sample non-deterministic advice, executing one invocation of MinRoot per step
-  fn new(num_iters: usize, x_0: &F, y_0: &F) -> (Vec<F>, Vec<Self>) {
-    // although this code is written generically, it is tailored to Pallas' scalar field
-    // (p - 3 / 5)
-    let exp = BigUint::parse_bytes(
-      b"23158417847463239084714197001737581570690445185553317903743794198714690358477",
-      10,
-    )
-    .unwrap();
+  fn new(num_iters: usize, x_0: &G::Scalar, y_0: &G::Scalar) -> (Vec<G::Scalar>, Vec<Self>) {
+    // exp = (p - 3 / 5), where p is the order of the group
+    // x^{exp} mod p provides the fifth root of x
+    let exp = {
+      let p = G::group_params().2.to_biguint().unwrap();
+      let two = BigUint::parse_bytes(b"2", 10).unwrap();
+      let three = BigUint::parse_bytes(b"3", 10).unwrap();
+      let five = BigUint::parse_bytes(b"5", 10).unwrap();
+      let five_inv = five.modpow(&(&p - &two), &p);
+      (&five_inv * (&p - &three)) % &p
+    };
 
     let mut res = Vec::new();
     let mut x_i = *x_0;
     let mut y_i = *y_0;
     for _i in 0..num_iters {
-      let x_i_plus_1 = (x_i + y_i).pow_vartime(exp.to_u64_digits()); // computes the fifth root of x_i + y_i
+      let x_i_plus_1 = (x_i + y_i).pow_vartime(&exp.to_u64_digits()); // computes the fifth root of x_i + y_i
 
       // sanity check
       if cfg!(debug_assertions) {
@@ -72,21 +79,21 @@ impl<F: PrimeField> MinRootIteration<F> {
 }
 
 #[derive(Clone, Debug)]
-struct MinRootCircuit<F: PrimeField> {
-  seq: Vec<MinRootIteration<F>>,
+struct MinRootCircuit<G: Group> {
+  seq: Vec<MinRootIteration<G>>,
 }
 
-impl<F: PrimeField> StepCircuit<F> for MinRootCircuit<F> {
+impl<G: Group> StepCircuit<G::Scalar> for MinRootCircuit<G> {
   fn arity(&self) -> usize {
     2
   }
 
-  fn synthesize<CS: ConstraintSystem<F>>(
+  fn synthesize<CS: ConstraintSystem<G::Scalar>>(
     &self,
     cs: &mut CS,
-    z: &[AllocatedNum<F>],
-  ) -> Result<Vec<AllocatedNum<F>>, SynthesisError> {
-    let mut z_out: Result<Vec<AllocatedNum<F>>, SynthesisError> =
+    z: &[AllocatedNum<G::Scalar>],
+  ) -> Result<Vec<AllocatedNum<G::Scalar>>, SynthesisError> {
+    let mut z_out: Result<Vec<AllocatedNum<G::Scalar>>, SynthesisError> =
       Err(SynthesisError::AssignmentMissing);
 
     // use the provided inputs
@@ -161,13 +168,13 @@ fn main() {
     let pp = PublicParams::<
       E1,
       E2,
-      MinRootCircuit<<E1 as Engine>::Scalar>,
+      MinRootCircuit<<E1 as Engine>::GE>,
       TrivialCircuit<<E2 as Engine>::Scalar>,
     >::setup(
       &circuit_primary,
       &circuit_secondary,
-      &*default_ck_hint(),
-      &*default_ck_hint(),
+      &*S1::ck_floor(),
+      &*S2::ck_floor(),
     );
     println!("PublicParams::setup, took {:?} ", start.elapsed());
 
@@ -190,7 +197,7 @@ fn main() {
     );
 
     // produce non-deterministic advice
-    let (z0_primary, minroot_iterations) = MinRootIteration::new(
+    let (z0_primary, minroot_iterations) = MinRootIteration::<<E1 as Engine>::GE>::new(
       num_iters_per_step * num_steps,
       &<E1 as Engine>::Scalar::zero(),
       &<E1 as Engine>::Scalar::one(),
@@ -210,7 +217,7 @@ fn main() {
 
     let z0_secondary = vec![<E2 as Engine>::Scalar::zero()];
 
-    type C1 = MinRootCircuit<<E1 as Engine>::Scalar>;
+    type C1 = MinRootCircuit<<E1 as Engine>::GE>;
     type C2 = TrivialCircuit<<E2 as Engine>::Scalar>;
     // produce a recursive SNARK
     println!("Generating a RecursiveSNARK...");
@@ -248,14 +255,10 @@ fn main() {
     assert!(res.is_ok());
 
     // produce a compressed SNARK
-    println!("Generating a CompressedSNARK using Spartan with IPA-PC...");
+    println!("Generating a CompressedSNARK using Spartan with multilinear KZG...");
     let (pk, vk) = CompressedSNARK::<_, _, _, _, S1, S2>::setup(&pp).unwrap();
 
     let start = Instant::now();
-    type EE1 = nova_snark::provider::ipa_pc::EvaluationEngine<E1>;
-    type EE2 = nova_snark::provider::ipa_pc::EvaluationEngine<E2>;
-    type S1 = nova_snark::spartan::snark::RelaxedR1CSSNARK<E1, EE1>;
-    type S2 = nova_snark::spartan::snark::RelaxedR1CSSNARK<E2, EE2>;
 
     let res = CompressedSNARK::<_, _, _, _, S1, S2>::prove(&pp, &pk, &recursive_snark);
     println!(