spartan2 0.8.0

High-speed zkSNARKs without trusted setup
Documentation 
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// Copyright (c) Microsoft Corporation.
// SPDX-License-Identifier: MIT
// This file is part of the Spartan2 project.
// See the LICENSE file in the project root for full license information.
// Source repository: https://github.com/Microsoft/Spartan2

//! Support for generating R1CS from Bellpepper
pub mod r1cs;
pub mod shape_cs;
pub mod solver;
pub mod test_r1cs;
pub mod test_shape_cs;

#[cfg(test)]
mod tests {
  use crate::{
    bellpepper::{
      solver::SatisfyingAssignment,
      test_r1cs::{TestSpartanShape, TestSpartanWitness},
      test_shape_cs::TestShapeCS,
    },
    provider::PallasHyraxEngine,
    traits::Engine,
  };
  use bellpepper_core::{ConstraintSystem, SynthesisError, num::AllocatedNum};
  use ff::PrimeField;

  fn synthesize_alloc_bit<Fr: PrimeField, CS: ConstraintSystem<Fr>>(
    cs: &mut CS,
  ) -> Result<(), SynthesisError> {
    // get two bits as input and check that they are indeed bits
    let a = AllocatedNum::alloc(cs.namespace(|| "a"), || Ok(Fr::ONE))?;
    let _ = a.inputize(cs.namespace(|| "a is input"));
    cs.enforce(
      || "check a is 0 or 1",
      |lc| lc + CS::one() - a.get_variable(),
      |lc| lc + a.get_variable(),
      |lc| lc,
    );
    let b = AllocatedNum::alloc(cs.namespace(|| "b"), || Ok(Fr::ONE))?;
    let _ = b.inputize(cs.namespace(|| "b is input"));
    cs.enforce(
      || "check b is 0 or 1",
      |lc| lc + CS::one() - b.get_variable(),
      |lc| lc + b.get_variable(),
      |lc| lc,
    );
    Ok(())
  }

  fn test_alloc_bit_with<E: Engine>() {
    // First create the shape
    let mut cs: TestShapeCS<E> = TestShapeCS::new();
    let _ = synthesize_alloc_bit(&mut cs);
    let (shape, ck, _vk) = cs.r1cs_shape().unwrap();

    // Now get the assignment
    let mut cs = SatisfyingAssignment::<E>::new();
    let _ = synthesize_alloc_bit(&mut cs);
    let (inst, witness) = cs.r1cs_instance_and_witness(&shape, &ck, true).unwrap();

    // Make sure that this is satisfiable
    assert!(shape.is_sat(&ck, &inst, &witness).is_ok());
  }

  #[test]
  fn test_alloc_bit() {
    test_alloc_bit_with::<PallasHyraxEngine>();
  }

  // ------------------------------------------------------------
  // Multi-round circuit test
  // ------------------------------------------------------------
  use crate::{
    bellpepper::{
      r1cs::{MultiRoundSpartanShape, MultiRoundSpartanWitness},
      shape_cs::ShapeCS,
    },
    traits::{circuit::MultiRoundCircuit, transcript::TranscriptEngineTrait},
  };

  #[derive(Clone)]
  struct TwoRoundBitsCircuit;

  impl<E: Engine> MultiRoundCircuit<E> for TwoRoundBitsCircuit {
    fn num_challenges(&self, _round_index: usize) -> Result<usize, SynthesisError> {
      Ok(0)
    }

    fn rounds<CS: ConstraintSystem<E::Scalar>>(
      &self,
      cs: &mut CS,
      round_index: usize,
      _prior_round_vars: &[Vec<AllocatedNum<E::Scalar>>],
      _prev_challenges: &[Vec<AllocatedNum<E::Scalar>>],
      _challenges: Option<&[E::Scalar]>,
    ) -> Result<(Vec<AllocatedNum<E::Scalar>>, Vec<AllocatedNum<E::Scalar>>), SynthesisError> {
      // Allocate a single bit set to 1 and enforce it is boolean
      let bit = AllocatedNum::alloc(cs.namespace(|| format!("bit_{round_index}")), || {
        Ok(<E::Scalar as ff::Field>::ONE)
      })?;
      cs.enforce(
        || format!("bit_boolean_{round_index}"),
        |lc| lc + bit.get_variable(),
        |lc| lc + CS::one() - bit.get_variable(),
        |lc| lc,
      );
      Ok((vec![bit], vec![]))
    }

    fn num_rounds(&self) -> usize {
      2
    }
  }

  fn test_multiround_bits_with<E: Engine>() {
    let circuit = TwoRoundBitsCircuit;

    // Generate shape
    let (shape, ck, _vk) =
      <ShapeCS<E> as MultiRoundSpartanShape<E>>::multiround_r1cs_shape(&circuit).unwrap();

    // Initialize witness state
    let mut state = SatisfyingAssignment::<E>::initialize_multiround_witness(&shape).unwrap();
    let mut transcript = <E as Engine>::TE::new(b"test");

    // Process each round
    let num_rounds = <TwoRoundBitsCircuit as MultiRoundCircuit<E>>::num_rounds(&circuit);
    for r in 0..num_rounds {
      let _ = SatisfyingAssignment::<E>::process_round(
        &mut state,
        &shape,
        &ck,
        &circuit,
        r,
        &mut transcript,
      )
      .unwrap();
    }

    // Finalize
    let (instance, witness) =
      SatisfyingAssignment::<E>::finalize_multiround_witness(&mut state, &shape).unwrap();

    // Convert to regular instance/shape for satisfiability check
    let regular_shape = shape.to_regular_shape();
    let regular_instance = instance.to_regular_instance().unwrap();

    let sat_res = regular_shape.is_sat(&ck, &regular_instance, &witness);
    assert!(sat_res.is_ok());
  }

  #[test]
  fn test_multiround_bits() {
    test_multiround_bits_with::<PallasHyraxEngine>();
  }

  // ------------------------------------------------------------
  // Multi-round permutation circuit test
  // ------------------------------------------------------------
  use ff::Field;

  #[derive(Clone)]
  struct TwoRoundPermutationCircuit;

  impl<E: Engine> MultiRoundCircuit<E> for TwoRoundPermutationCircuit {
    fn num_challenges(&self, round_index: usize) -> Result<usize, SynthesisError> {
      if round_index >= 2 {
        return Err(SynthesisError::Unsatisfiable);
      }
      Ok(match round_index {
        0 => 1, // one challenges after the first round
        1 => 0, // no challenges in the second round
        _ => 0, // no challenges in other rounds
      })
    }

    fn rounds<CS: ConstraintSystem<E::Scalar>>(
      &self,
      cs: &mut CS,
      round_index: usize,
      prior_round_vars: &[Vec<AllocatedNum<E::Scalar>>],
      _prev_challenges: &[Vec<AllocatedNum<E::Scalar>>],
      challenges: Option<&[E::Scalar]>,
    ) -> Result<(Vec<AllocatedNum<E::Scalar>>, Vec<AllocatedNum<E::Scalar>>), SynthesisError> {
      match round_index {
        // ---------------- Round 0 ----------------
        0 => {
          // Allocate six witness values (a..f). The first three (a,b,c) are a permutation of the
          // second three (d,e,f). We use distinct constants 1,2,3 but shuffle the order.
          let one = E::Scalar::from(1u64);
          let two = E::Scalar::from(2u64);
          let three = E::Scalar::from(3u64);

          let a = AllocatedNum::alloc(cs.namespace(|| "a"), || Ok(one))?;
          let b = AllocatedNum::alloc(cs.namespace(|| "b"), || Ok(two))?;
          let c = AllocatedNum::alloc(cs.namespace(|| "c"), || Ok(three))?;

          // Permuted copy
          let d = AllocatedNum::alloc(cs.namespace(|| "d"), || Ok(three))?;
          let e = AllocatedNum::alloc(cs.namespace(|| "e"), || Ok(one))?;
          let f = AllocatedNum::alloc(cs.namespace(|| "f"), || Ok(two))?;

          Ok((vec![a, b, c, d, e, f], vec![]))
        }
        // ---------------- Round 1 ----------------
        1 => {
          // Retrieve variables from round 0
          let round0_vars = &prior_round_vars[0];
          let a = &round0_vars[0];
          let b = &round0_vars[1];
          let c = &round0_vars[2];
          let d = &round0_vars[3];
          let e = &round0_vars[4];
          let f = &round0_vars[5];

          // Verifier-supplied challenge r for this round
          let r_val = challenges.map(|v| v[0]).unwrap_or(E::Scalar::ZERO);
          let r = AllocatedNum::alloc_input(cs.namespace(|| "r"), || Ok(r_val))?;

          // Helper closure to create (x - r)
          let sub_r = |cs: &mut CS, name: &'static str, x: &AllocatedNum<E::Scalar>| {
            let val = x.get_value().zip(r.get_value()).map(|(xv, rv)| xv - rv);
            AllocatedNum::alloc(cs.namespace(|| name), || {
              val.ok_or(SynthesisError::AssignmentMissing)
            })
          };

          let diff_a = sub_r(cs, "diff_a", a)?;
          let diff_b = sub_r(cs, "diff_b", b)?;
          let diff_c = sub_r(cs, "diff_c", c)?;
          let diff_d = sub_r(cs, "diff_d", d)?;
          let diff_e = sub_r(cs, "diff_e", e)?;
          let diff_f = sub_r(cs, "diff_f", f)?;

          // Enforce diff_i = x_i - r for each x in {a..f}
          let enforce_sub = |label: &'static str,
                             cs: &mut CS,
                             x: &AllocatedNum<E::Scalar>,
                             diff: &AllocatedNum<E::Scalar>| {
            cs.enforce(
              || label,
              |lc| lc + x.get_variable() - r.get_variable(),
              |lc| lc + CS::one(),
              |lc| lc + diff.get_variable(),
            );
          };
          enforce_sub("a_minus_r", cs, a, &diff_a);
          enforce_sub("b_minus_r", cs, b, &diff_b);
          enforce_sub("c_minus_r", cs, c, &diff_c);
          enforce_sub("d_minus_r", cs, d, &diff_d);
          enforce_sub("e_minus_r", cs, e, &diff_e);
          enforce_sub("f_minus_r", cs, f, &diff_f);

          // Compute lhs = (diff_a * diff_b) * diff_c
          let lhs_ab = AllocatedNum::alloc(cs.namespace(|| "lhs_ab"), || {
            diff_a
              .get_value()
              .zip(diff_b.get_value())
              .map(|(x, y)| x * y)
              .ok_or(SynthesisError::AssignmentMissing)
          })?;
          cs.enforce(
            || "lhs_ab_mul",
            |lc| lc + diff_a.get_variable(),
            |lc| lc + diff_b.get_variable(),
            |lc| lc + lhs_ab.get_variable(),
          );

          let lhs = AllocatedNum::alloc(cs.namespace(|| "lhs"), || {
            lhs_ab
              .get_value()
              .zip(diff_c.get_value())
              .map(|(x, y)| x * y)
              .ok_or(SynthesisError::AssignmentMissing)
          })?;
          cs.enforce(
            || "lhs_mul",
            |lc| lc + lhs_ab.get_variable(),
            |lc| lc + diff_c.get_variable(),
            |lc| lc + lhs.get_variable(),
          );

          // Compute rhs = (diff_d * diff_e) * diff_f
          let rhs_de = AllocatedNum::alloc(cs.namespace(|| "rhs_de"), || {
            diff_d
              .get_value()
              .zip(diff_e.get_value())
              .map(|(x, y)| x * y)
              .ok_or(SynthesisError::AssignmentMissing)
          })?;
          cs.enforce(
            || "rhs_de_mul",
            |lc| lc + diff_d.get_variable(),
            |lc| lc + diff_e.get_variable(),
            |lc| lc + rhs_de.get_variable(),
          );

          let rhs = AllocatedNum::alloc(cs.namespace(|| "rhs"), || {
            rhs_de
              .get_value()
              .zip(diff_f.get_value())
              .map(|(x, y)| x * y)
              .ok_or(SynthesisError::AssignmentMissing)
          })?;
          cs.enforce(
            || "rhs_mul",
            |lc| lc + rhs_de.get_variable(),
            |lc| lc + diff_f.get_variable(),
            |lc| lc + rhs.get_variable(),
          );

          // Enforce equality lhs = rhs
          cs.enforce(
            || "lhs_eq_rhs",
            |lc| lc + lhs.get_variable(),
            |lc| lc + CS::one(),
            |lc| lc + rhs.get_variable(),
          );

          Ok((vec![lhs, rhs], vec![r]))
        }
        _ => Err(SynthesisError::Unsatisfiable),
      }
    }

    fn num_rounds(&self) -> usize {
      2
    }
  }

  fn test_multiround_permutation_with<E: Engine>() {
    let circuit = TwoRoundPermutationCircuit;

    // Generate shape
    let (shape, ck, _vk) =
      <ShapeCS<E> as MultiRoundSpartanShape<E>>::multiround_r1cs_shape(&circuit).unwrap();

    // Initialize witness state
    let mut state = SatisfyingAssignment::<E>::initialize_multiround_witness(&shape).unwrap();
    let mut transcript = <E as Engine>::TE::new(b"test");

    // Process each round
    let num_rounds = <TwoRoundPermutationCircuit as MultiRoundCircuit<E>>::num_rounds(&circuit);
    for r in 0..num_rounds {
      let _ = SatisfyingAssignment::<E>::process_round(
        &mut state,
        &shape,
        &ck,
        &circuit,
        r,
        &mut transcript,
      )
      .unwrap();
    }

    // Finalize
    let (instance, witness) =
      SatisfyingAssignment::<E>::finalize_multiround_witness(&mut state, &shape).unwrap();

    // Convert to regular instance/shape for satisfiability check
    let regular_shape = shape.to_regular_shape();
    let regular_instance = instance.to_regular_instance().unwrap();

    let sat_res = regular_shape.is_sat(&ck, &regular_instance, &witness);
    assert!(sat_res.is_ok());
  }

  #[test]
  fn test_multiround_permutation() {
    test_multiround_permutation_with::<PallasHyraxEngine>();
  }
}