testudo/src/bullet.rs

#![allow(non_snake_case)]

use super::errors::ProofVerifyError;
use super::group::{CompressedGroup, GroupElement, VartimeMultiscalarMul};
use super::math::Math;
use super::scalar::Scalar;
use super::transcript::ProofTranscript;
use merlin::Transcript;
use serde::{Deserialize, Serialize};
use std::iter;

#[derive(Debug, Serialize, Deserialize)]
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 Transcript,
    Q: &GroupElement,
    G_vec: &Vec<GroupElement>,
    H: &GroupElement,
    a_vec: &Vec<Scalar>,
    b_vec: &Vec<Scalar>,
    blind: &Scalar,
    blinds_vec: &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.clone()[..];
    let mut a = &mut a_vec.clone()[..];
    let mut b = &mut b_vec.clone()[..];

    // 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.log2();

    let G_factors: Vec<Scalar> = iter::repeat(Scalar::one()).take(n).collect();

    // 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!(G_factors.len(), n);
    assert_eq!(blinds_vec.len(), 2 * lg_n);

    //transcript.innerproduct_domain_sep(n as u64);

    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 = 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)),
        G_R.iter().chain(iter::once(Q)).chain(iter::once(H)),
      );

      let R = GroupElement::vartime_multiscalar_mul(
        a_R
          .iter()
          .chain(iter::once(&c_R))
          .chain(iter::once(blind_R)),
        G_L.iter().chain(iter::once(Q)).chain(iter::once(H)),
      );

      transcript.append_point(b"L", &L.compress());
      transcript.append_point(b"R", &R.compress());

      let u = transcript.challenge_scalar(b"u");
      let u_inv = u.invert().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 + blind_L * &u * &u + blind_R * &u_inv * &u_inv;

      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: L_vec,
        R_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 Transcript,
  ) -> 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);
    }
    if n != (1 << lg_n) {
      return Err(ProofVerifyError);
    }

    // 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(b"L", L);
      transcript.append_point(b"R", R);
      challenges.push(transcript.challenge_scalar(b"u"));
    }

    // 2. Compute 1/(u_k...u_1) and 1/u_k, ..., 1/u_1
    let mut challenges_inv = challenges.clone();
    let allinv = Scalar::batch_invert(&mut challenges_inv);

    // 3. Compute u_i^2 and (1/u_i)^2
    for i in 0..lg_n {
      challenges[i] = challenges[i] * challenges[i];
      challenges_inv[i] = challenges_inv[i] * challenges_inv[i];
    }
    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: &Vec<Scalar>,
    transcript: &mut Transcript,
    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| p.decompress().ok_or(ProofVerifyError))
      .collect::<Result<Vec<_>, _>>()?;

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

    let G_hat = GroupElement::vartime_multiscalar_mul(s.iter(), G.iter());
    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())),
      Ls.iter().chain(Rs.iter()).chain(iter::once(Gamma)),
    );

    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 {
  let mut out = Scalar::zero();
  if a.len() != b.len() {
    panic!("inner_product(a,b): lengths of vectors do not match");
  }
  for i in 0..a.len() {
    out += a[i] * b[i];
  }
  out
}