testudo/src/nizk/bullet.rs

//! This module is an adaptation of code from the bulletproofs crate.
//! See NOTICE.md for more details
#![allow(non_snake_case)]
#![allow(clippy::type_complexity)]
#![allow(clippy::too_many_arguments)]
use crate::math::Math;
use crate::poseidon_transcript::PoseidonTranscript;

use super::super::errors::ProofVerifyError;
use super::super::group::{
  CompressGroupElement, CompressedGroup, DecompressGroupElement, GroupElement,
  VartimeMultiscalarMul,
};
use super::super::scalar::Scalar;
use ark_ff::Field;
use ark_serialize::*;
use ark_std::{One, Zero};
use core::iter;
use std::ops::MulAssign;

#[derive(Debug, CanonicalSerialize, CanonicalDeserialize)]
pub struct BulletReductionProof {
  L_vec: Vec<CompressedGroup>,
  R_vec: Vec<CompressedGroup>,
}

impl BulletReductionProof {
  /// Create an inner-product proof.
  ///
  /// The proof is created with respect to the bases \\(G\\).
  ///
  /// The `transcript` is passed in as a parameter so that the
  /// challenges depend on the *entire* transcript (including parent
  /// protocols).
  ///
  /// The lengths of the vectors must all be the same, and must all be
  /// either 0 or a power of 2.
  pub fn prove(
    transcript: &mut PoseidonTranscript,
    Q: &GroupElement,
    G_vec: &[GroupElement],
    H: &GroupElement,
    a_vec: &[Scalar],
    b_vec: &[Scalar],
    blind: &Scalar,
    blinds_vec: &[(Scalar, Scalar)],
  ) -> (
    BulletReductionProof,
    GroupElement,
    Scalar,
    Scalar,
    GroupElement,
    Scalar,
  ) {
    // Create slices G, H, a, b backed by their respective
    // vectors.  This lets us reslice as we compress the lengths
    // of the vectors in the main loop below.
    let mut G = &mut G_vec.to_owned()[..];
    let mut a = &mut a_vec.to_owned()[..];
    let mut b = &mut b_vec.to_owned()[..];

    // All of the input vectors must have a length that is a power of two.
    let mut n = G.len();
    assert!(n.is_power_of_two());
    let lg_n = n.log_2();

    // All of the input vectors must have the same length.
    assert_eq!(G.len(), n);
    assert_eq!(a.len(), n);
    assert_eq!(b.len(), n);
    assert_eq!(blinds_vec.len(), 2 * lg_n);

    let mut L_vec = Vec::with_capacity(lg_n);
    let mut R_vec = Vec::with_capacity(lg_n);
    let mut blinds_iter = blinds_vec.iter();
    let mut blind_fin = *blind;

    while n != 1 {
      n /= 2;
      let (a_L, a_R) = a.split_at_mut(n);
      let (b_L, b_R) = b.split_at_mut(n);
      let (G_L, G_R) = G.split_at_mut(n);

      let c_L = inner_product(a_L, b_R);
      let c_R = inner_product(a_R, b_L);

      let (blind_L, blind_R) = blinds_iter.next().unwrap();

      let L = GroupElement::vartime_multiscalar_mul(
        a_L
          .iter()
          .chain(iter::once(&c_L))
          .chain(iter::once(blind_L))
          .map(|s| *s)
          .collect::<Vec<Scalar>>()
          .as_slice(),
        G_R
          .iter()
          .chain(iter::once(Q))
          .chain(iter::once(H))
          .map(|p| *p)
          .collect::<Vec<GroupElement>>()
          .as_slice(),
      );

      let R = GroupElement::vartime_multiscalar_mul(
        a_R
          .iter()
          .chain(iter::once(&c_R))
          .chain(iter::once(blind_R))
          .map(|s| *s)
          .collect::<Vec<Scalar>>()
          .as_slice(),
        G_L
          .iter()
          .chain(iter::once(Q))
          .chain(iter::once(H))
          .map(|p| *p)
          .collect::<Vec<GroupElement>>()
          .as_slice(),
      );

      transcript.append_point(&L.compress());
      transcript.append_point(&R.compress());

      let u = transcript.challenge_scalar();
      let u_inv = u.inverse().unwrap();

      for i in 0..n {
        a_L[i] = a_L[i] * u + u_inv * a_R[i];
        b_L[i] = b_L[i] * u_inv + u * b_R[i];
        G_L[i] = GroupElement::vartime_multiscalar_mul(&[u_inv, u], &[G_L[i], G_R[i]]);
      }

      blind_fin = blind_fin + u * u * blind_L + u_inv * u_inv * blind_R;

      L_vec.push(L.compress());
      R_vec.push(R.compress());

      a = a_L;
      b = b_L;
      G = G_L;
    }

    let Gamma_hat =
      GroupElement::vartime_multiscalar_mul(&[a[0], a[0] * b[0], blind_fin], &[G[0], *Q, *H]);

    (
      BulletReductionProof { L_vec, R_vec },
      Gamma_hat,
      a[0],
      b[0],
      G[0],
      blind_fin,
    )
  }

  /// Computes three vectors of verification scalars \\([u\_{i}^{2}]\\), \\([u\_{i}^{-2}]\\) and \\([s\_{i}]\\) for combined multiscalar multiplication
  /// in a parent protocol. See [inner product protocol notes](index.html#verification-equation) for details.
  /// The verifier must provide the input length \\(n\\) explicitly to avoid unbounded allocation within the inner product proof.
  fn verification_scalars(
    &self,
    n: usize,
    transcript: &mut PoseidonTranscript,
  ) -> Result<(Vec<Scalar>, Vec<Scalar>, Vec<Scalar>), ProofVerifyError> {
    let lg_n = self.L_vec.len();
    if lg_n >= 32 {
      // 4 billion multiplications should be enough for anyone
      // and this check prevents overflow in 1<<lg_n below.
      return Err(ProofVerifyError::InternalError);
    }
    if n != (1 << lg_n) {
      return Err(ProofVerifyError::InternalError);
    }

    // 1. Recompute x_k,...,x_1 based on the proof transcript
    let mut challenges = Vec::with_capacity(lg_n);
    for (L, R) in self.L_vec.iter().zip(self.R_vec.iter()) {
      transcript.append_point(L);
      transcript.append_point(R);
      challenges.push(transcript.challenge_scalar());
    }

    // 2. Compute 1/(u_k...u_1) and 1/u_k, ..., 1/u_1
    let mut challenges_inv: Vec<Scalar> = challenges.clone();

    ark_ff::fields::batch_inversion(&mut challenges_inv);
    let mut allinv: Scalar = Scalar::one();
    for c in challenges.iter().filter(|s| !s.is_zero()) {
      allinv.mul_assign(c);
    }
    allinv = allinv.inverse().unwrap();

    // 3. Compute u_i^2 and (1/u_i)^2
    for i in 0..lg_n {
      challenges[i] = challenges[i].square();
      challenges_inv[i] = challenges_inv[i].square();
    }
    let challenges_sq = challenges;
    let challenges_inv_sq = challenges_inv;

    // 4. Compute s values inductively.
    let mut s = Vec::with_capacity(n);
    s.push(allinv);
    for i in 1..n {
      let lg_i = (32 - 1 - (i as u32).leading_zeros()) as usize;
      let k = 1 << lg_i;
      // The challenges are stored in "creation order" as [u_k,...,u_1],
      // so u_{lg(i)+1} = is indexed by (lg_n-1) - lg_i
      let u_lg_i_sq = challenges_sq[(lg_n - 1) - lg_i];
      s.push(s[i - k] * u_lg_i_sq);
    }

    Ok((challenges_sq, challenges_inv_sq, s))
  }

  /// This method is for testing that proof generation work,
  /// but for efficiency the actual protocols would use `verification_scalars`
  /// method to combine inner product verification with other checks
  /// in a single multiscalar multiplication.
  pub fn verify(
    &self,
    n: usize,
    a: &[Scalar],
    transcript: &mut PoseidonTranscript,
    Gamma: &GroupElement,
    G: &[GroupElement],
  ) -> Result<(GroupElement, GroupElement, Scalar), ProofVerifyError> {
    let (u_sq, u_inv_sq, s) = self.verification_scalars(n, transcript)?;

    let Ls = self
      .L_vec
      .iter()
      .map(|p| GroupElement::decompress(p).ok_or(ProofVerifyError::InternalError))
      .collect::<Result<Vec<_>, _>>()?;

    let Rs = self
      .R_vec
      .iter()
      .map(|p| GroupElement::decompress(p).ok_or(ProofVerifyError::InternalError))
      .collect::<Result<Vec<_>, _>>()?;

    let G_hat = GroupElement::vartime_multiscalar_mul(s.as_slice(), G);
    let a_hat = inner_product(a, &s);

    let Gamma_hat = GroupElement::vartime_multiscalar_mul(
      u_sq
        .iter()
        .chain(u_inv_sq.iter())
        .chain(iter::once(&Scalar::one()))
        .map(|s| *s)
        .collect::<Vec<Scalar>>()
        .as_slice(),
      Ls.iter()
        .chain(Rs.iter())
        .chain(iter::once(Gamma))
        .map(|p| *p)
        .collect::<Vec<GroupElement>>()
        .as_slice(),
    );

    Ok((G_hat, Gamma_hat, a_hat))
  }
}

/// Computes an inner product of two vectors
/// \\[
///    {\langle {\mathbf{a}}, {\mathbf{b}} \rangle} = \sum\_{i=0}^{n-1} a\_i \cdot b\_i.
/// \\]
/// Panics if the lengths of \\(\mathbf{a}\\) and \\(\mathbf{b}\\) are not equal.
pub fn inner_product(a: &[Scalar], b: &[Scalar]) -> Scalar {
  assert!(
    a.len() == b.len(),
    "inner_product(a,b): lengths of vectors do not match"
  );
  let mut out = Scalar::zero();
  for i in 0..a.len() {
    out += a[i] * b[i];
  }
  out
}