Implement small_multiexp() in arithmetic.rs

src/arithmetic.rs

@@ -180,6 +180,39 @@ fn multiexp_serial<C: CurveAffine>(coeffs: &[C::Scalar], bases: &[C], acc: &mut
     }
 }
 
+/// Performs a small multi-exponentiation operation.
+/// Uses the double-and-add algorithm with doublings shared across points.
+
+pub fn small_multiexp<C: CurveAffine>(coeffs: &[C::Scalar], bases: &[C]) -> C::Projective {
+    // Gets the bit at position `i`. Bits are numbered from 0 (least significant) to 7 (most significant).
+    fn get_bit_at(byte: u8, i: usize) -> bool {
+        if i < 8 {
+            ((byte >> i) & 1u8) != 0
+        } else {
+            false
+        }
+    }
+
+    let coeffs: Vec<[u8; 32]> = coeffs.iter().map(|a| a.to_bytes()).collect();
+    let mut acc = C::Projective::zero();
+
+    // for byte idx
+    for byte_idx in (0..32).rev() {
+        // for bit idx
+        for bit_idx in (0..8).rev() {
+            acc = acc.double();
+            // for each coeff
+            for coeff_idx in 0..coeffs.len() {
+                if get_bit_at(coeffs[coeff_idx][byte_idx], bit_idx) {
+                    acc = acc + &bases[coeff_idx].to_projective();
+                }
+            }
+        }
+    }
+
+    acc
+}
+
 /// Performs a multi-exponentiation operation.
 ///
 /// This function will panic if coeffs and bases have a different length.

src/poly/commitment/prover.rs

@@ -1,7 +1,7 @@
 use super::super::{Coeff, Polynomial};
 use super::{Blind, OpeningProof, Params};
 use crate::arithmetic::{
-    best_multiexp, compute_inner_product, get_challenge_scalar, parallelize, Challenge, Curve,
+    best_multiexp, compute_inner_product, get_challenge_scalar, small_multiexp, Challenge, Curve,
     CurveAffine, Field,
 };
 use crate::transcript::Hasher;
@@ -220,15 +220,11 @@ fn parallel_generator_collapse<C: CurveAffine>(
     challenge_inv: C::Scalar,
 ) {
     let len = g.len() / 2;
-    let (mut g_lo, g_hi) = g.split_at_mut(len);
+    let (g_lo, g_hi) = g.split_at_mut(len);
 
-    parallelize(&mut g_lo, |g_lo, start| {
-        let g_hi = &g_hi[start..];
-        let mut tmp = Vec::with_capacity(g_lo.len());
-        for (g_lo, g_hi) in g_lo.iter().zip(g_hi.iter()) {
-            // TODO: could use multiexp
-            tmp.push(((*g_lo) * challenge_inv) + &((*g_hi) * challenge));
-        }
-        C::Projective::batch_to_affine(&tmp, g_lo);
-    });
+    let mut tmp = Vec::with_capacity(g_lo.len());
+    for (g_lo, g_hi) in g_lo.iter().zip(g_hi.iter()) {
+        tmp.push(small_multiexp(&[challenge_inv, challenge], &[*g_lo, *g_hi]));
+    }
+    C::Projective::batch_to_affine(&tmp, g_lo);
 }