ipa.rs

// 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

//! Inner Product Argument (IPA) implementation
use crate::{
  errors::SpartanError,
  provider::traits::{DlogGroup, DlogGroupExt},
  traits::{
    Engine,
    transcript::{TranscriptEngineTrait, TranscriptReprTrait},
  },
};
use core::fmt::Debug;
use ff::Field;
use rayon::prelude::*;
use serde::{Deserialize, Serialize};

/// computes the inner product of two vectors.
pub(crate) fn inner_product<T: Field + Send + Sync>(a: &[T], b: &[T]) -> T {
  assert_eq!(a.len(), b.len());
  a.iter()
    .zip(b.iter())
    .fold(T::ZERO, |acc, (ai, bi)| acc + *ai * *bi)
}

/// An inner product instance consists of a commitment to a vector `a` and another vector `b`
/// and the claim that c = <a, b>.
pub struct InnerProductInstance<E: Engine> {
  pub(crate) comm_a_vec: E::GE,
  pub(crate) b_vec: Vec<E::Scalar>,
  pub(crate) comm_c: E::GE,
}

/// Holds witness for the inner product instance.
pub struct InnerProductWitness<E: Engine> {
  pub(crate) a_vec: Vec<E::Scalar>,
  pub(crate) r_a: E::Scalar, // blind for the commitment to a_vec
  pub(crate) r_c: E::Scalar, // blind for the commitment to c
}

impl<E: Engine> InnerProductInstance<E>
where
  E::GE: DlogGroup,
{
  /// Creates a new inner product instance
  pub fn new(comm_a_vec: &E::GE, b_vec: &[E::Scalar], comm_c: &E::GE) -> Self {
    InnerProductInstance {
      comm_a_vec: *comm_a_vec,
      b_vec: b_vec.to_vec(),
      comm_c: *comm_c,
    }
  }
}

impl<E: Engine> TranscriptReprTrait<E::GE> for InnerProductInstance<E>
where
  E::GE: DlogGroup,
{
  fn to_transcript_bytes(&self) -> Vec<u8> {
    // we do not need to include self.b_vec as in our context it is produced from the transcript
    [
      self.comm_a_vec.to_transcript_bytes(),
      self.comm_c.to_transcript_bytes(),
    ]
    .concat()
  }
}

impl<E: Engine> InnerProductWitness<E> {
  /// Creates a new inner product witness
  pub fn new(a_vec: &[E::Scalar], r_a: &E::Scalar, r_c: &E::Scalar) -> Self {
    InnerProductWitness {
      a_vec: a_vec.to_vec(),
      r_a: *r_a,
      r_c: *r_c,
    }
  }
}

// Instance: C_a, C_c, b_vec
// Witness: a_vec, r_a, c, r_c
// Sat if: C_x = Com(x, r_x), C_c = Com(c, r_c), and y = <a_vec, b_vec>
//
// P: samples d_vec, r_\beta, r_\delta, and sends:
// \delta \gets Com(d_vec, r_delta)
// \beta \gets Com(<b_vec, d_vec>, r_beta)
//
// V: sends a challenge r
//
// P: sends
// z_vec \gets r * a_vec + d_vec
// z_\delta \gets r * r_a + r_\delta
// z_\beta \gets r * r_c + r_\beta
//
// V: checks
// r * Comm_a + delta =? Com(z_vec, z_\delta)
// r * Comm_c + beta =? Com(<z_vec, b_vec>, z_\beta)
//
/// An inner product argument using a linear-sized argument
#[derive(Clone, Debug, Serialize, Deserialize)]
#[serde(bound = "")]
pub struct InnerProductArgumentLinear<E: Engine>
where
  E::GE: DlogGroupExt,
{
  delta: E::GE,
  beta: E::GE,
  z_vec: Vec<E::Scalar>,
  z_delta: E::Scalar,
  z_beta: E::Scalar,
}

impl<E: Engine> InnerProductArgumentLinear<E>
where
  E::GE: DlogGroupExt,
{
  fn protocol_name() -> &'static [u8] {
    b"inner product argument (linear)"
  }

  /// Proves the inner product argument
  pub fn prove(
    ck: &[<E::GE as DlogGroup>::AffineGroupElement],
    h: &E::GE,
    ck_c: &<E::GE as DlogGroup>::AffineGroupElement,
    h_c: &E::GE,
    U: &InnerProductInstance<E>,
    W: &InnerProductWitness<E>,
    transcript: &mut E::TE,
  ) -> Result<Self, SpartanError> {
    transcript.dom_sep(Self::protocol_name());

    // absorb the instance in the transcript
    transcript.absorb(b"U", U);

    // produce randomness for the proofs using fast CSPRNG
    let mut rng = rand::thread_rng();
    let d_vec = (0..U.b_vec.len())
      .map(|_| E::Scalar::random(&mut rng))
      .collect::<Vec<E::Scalar>>();
    let r_delta = E::Scalar::random(&mut rng);
    let r_beta = E::Scalar::random(&mut rng);

    let delta = E::GE::vartime_multiscalar_mul(&d_vec, &ck[0..d_vec.len()], true)? + *h * r_delta;
    let beta = E::GE::group(ck_c) * inner_product(&U.b_vec, &d_vec) + *h_c * r_beta;

    transcript.absorb(b"delta", &delta);
    transcript.absorb(b"beta", &beta);

    let r = transcript.squeeze(b"r")?;

    let z_vec = (0..d_vec.len())
      .into_par_iter()
      .map(|i| r * W.a_vec[i] + d_vec[i])
      .collect::<Vec<E::Scalar>>();

    let z_delta = r * W.r_a + r_delta;
    let z_beta = r * W.r_c + r_beta;

    Ok(Self {
      delta,
      z_vec,
      z_delta,
      beta,
      z_beta,
    })
  }

  /// Verifies the inner product argument
  pub fn verify(
    &self,
    ck: &[<E::GE as DlogGroup>::AffineGroupElement],
    h: &E::GE,
    ck_c: &<E::GE as DlogGroup>::AffineGroupElement,
    h_c: &E::GE,
    n: usize,
    U: &InnerProductInstance<E>,
    transcript: &mut E::TE,
  ) -> Result<(), SpartanError> {
    transcript.dom_sep(Self::protocol_name());

    // absorb the instance in the transcript
    transcript.absorb(b"U", U);

    transcript.absorb(b"delta", &self.delta);
    transcript.absorb(b"beta", &self.beta);

    let r = transcript.squeeze(b"r")?;

    if self.z_vec.len() != n || ck.len() < self.z_vec.len() {
      return Err(SpartanError::InvalidInputLength {
        reason: format!(
          "Inner product argument verify: Expected {} elements in z_vec, got {}",
          n,
          self.z_vec.len()
        ),
      });
    }

    if U.comm_a_vec * r + self.delta
      != E::GE::vartime_multiscalar_mul(&self.z_vec, &ck[0..self.z_vec.len()], true)?
        + *h * self.z_delta
    {
      return Err(SpartanError::InvalidPCS {
        reason: "Inner product argument verify: First equation failed".to_string(),
      });
    }

    if U.comm_c * r + self.beta
      != E::GE::group(ck_c) * inner_product(&self.z_vec, &U.b_vec) + *h_c * self.z_beta
    {
      return Err(SpartanError::InvalidPCS {
        reason: "Inner product argument verify: Second equation failed".to_string(),
      });
    }

    Ok(())
  }
}