From 2f8e67acd6f441030654d941af5a78cc81b2830e Mon Sep 17 00:00:00 2001 From: kilic Date: Wed, 29 Nov 2023 15:08:05 +0300 Subject: [PATCH] Booth encoding (#106) * booth encoding baseline * working msm with booth encoding * tidy * apply suggestions & remove leftovers --- src/msm.rs | 298 ++++++++++++++++++++++++++++++++++++++++++++++++----- 1 file changed, 272 insertions(+), 26 deletions(-) diff --git a/src/msm.rs b/src/msm.rs index de30be55..cf6ed4d4 100644 --- a/src/msm.rs +++ b/src/msm.rs @@ -1,9 +1,55 @@ +use std::ops::Neg; + use ff::PrimeField; use group::Group; use pasta_curves::arithmetic::CurveAffine; use crate::multicore; +fn get_booth_index(window_index: usize, window_size: usize, el: &[u8]) -> i32 { + // Booth encoding: + // * step by `window` size + // * slice by size of `window + 1`` + // * each window overlap by 1 bit + // * append a zero bit to the least significant end + // Indexing rule for example window size 3 where we slice by 4 bits: + // `[0, +1, +1, +2, +2, +3, +3, +4, -4, -3, -3 -2, -2, -1, -1, 0]`` + // So we can reduce the bucket size without preprocessing scalars + // and remembering them as in classic signed digit encoding + + let skip_bits = (window_index * window_size).saturating_sub(1); + let skip_bytes = skip_bits / 8; + + // fill into a u32 + let mut v: [u8; 4] = [0; 4]; + for (dst, src) in v.iter_mut().zip(el.iter().skip(skip_bytes)) { + *dst = *src + } + let mut tmp = u32::from_le_bytes(v); + + // pad with one 0 if slicing the least significant window + if window_index == 0 { + tmp <<= 1; + } + + // remove further bits + tmp >>= skip_bits - (skip_bytes * 8); + // apply the booth window + tmp &= (1 << (window_size + 1)) - 1; + + let sign = tmp & (1 << window_size) == 0; + + // div ceil by 2 + tmp = (tmp + 1) >> 1; + + // find the booth action index + if sign { + tmp as i32 + } else { + ((!(tmp - 1) & ((1 << window_size) - 1)) as i32).neg() + } +} + pub fn multiexp_serial(coeffs: &[C::Scalar], bases: &[C], acc: &mut C::Curve) { let coeffs: Vec<_> = coeffs.iter().map(|a| a.to_repr()).collect(); @@ -15,29 +61,9 @@ pub fn multiexp_serial(coeffs: &[C::Scalar], bases: &[C], acc: & (f64::from(bases.len() as u32)).ln().ceil() as usize }; - fn get_at(segment: usize, c: usize, bytes: &F::Repr) -> usize { - let skip_bits = segment * c; - let skip_bytes = skip_bits / 8; - - if skip_bytes >= 32 { - return 0; - } - - let mut v = [0; 8]; - for (v, o) in v.iter_mut().zip(bytes.as_ref()[skip_bytes..].iter()) { - *v = *o; - } + let number_of_windows = C::Scalar::NUM_BITS as usize / c + 1; - let mut tmp = u64::from_le_bytes(v); - tmp >>= skip_bits - (skip_bytes * 8); - tmp %= 1 << c; - - tmp as usize - } - - let segments = (256 / c) + 1; - - for current_segment in (0..segments).rev() { + for current_window in (0..number_of_windows).rev() { for _ in 0..c { *acc = acc.double(); } @@ -73,12 +99,15 @@ pub fn multiexp_serial(coeffs: &[C::Scalar], bases: &[C], acc: & } } - let mut buckets: Vec> = vec![Bucket::None; (1 << c) - 1]; + let mut buckets: Vec> = vec![Bucket::None; 1 << (c - 1)]; for (coeff, base) in coeffs.iter().zip(bases.iter()) { - let coeff = get_at::(current_segment, c, coeff); - if coeff != 0 { - buckets[coeff - 1].add_assign(base); + let coeff = get_booth_index(current_window as usize, c, coeff.as_ref()); + if coeff.is_positive() { + buckets[coeff as usize - 1].add_assign(base); + } + if coeff.is_negative() { + buckets[coeff.unsigned_abs() as usize - 1].add_assign(&base.neg()); } } @@ -151,3 +180,220 @@ pub fn best_multiexp(coeffs: &[C::Scalar], bases: &[C]) -> C::Cu acc } } + +#[cfg(test)] +mod test { + + use std::ops::Neg; + + use crate::{ + bn256::{Fr, G1Affine, G1}, + multicore, + }; + use ark_std::{end_timer, start_timer}; + use ff::{Field, PrimeField}; + use group::{Curve, Group}; + use pasta_curves::arithmetic::CurveAffine; + use rand_core::OsRng; + + // keeping older implementation it here for baseline comparision, debugging & benchmarking + fn best_multiexp(coeffs: &[C::Scalar], bases: &[C]) -> C::Curve { + assert_eq!(coeffs.len(), bases.len()); + + let num_threads = multicore::current_num_threads(); + if coeffs.len() > num_threads { + let chunk = coeffs.len() / num_threads; + let num_chunks = coeffs.chunks(chunk).len(); + let mut results = vec![C::Curve::identity(); num_chunks]; + multicore::scope(|scope| { + let chunk = coeffs.len() / num_threads; + + for ((coeffs, bases), acc) in coeffs + .chunks(chunk) + .zip(bases.chunks(chunk)) + .zip(results.iter_mut()) + { + scope.spawn(move |_| { + multiexp_serial(coeffs, bases, acc); + }); + } + }); + results.iter().fold(C::Curve::identity(), |a, b| a + b) + } else { + let mut acc = C::Curve::identity(); + multiexp_serial(coeffs, bases, &mut acc); + acc + } + } + + // keeping older implementation it here for baseline comparision, debugging & benchmarking + fn multiexp_serial(coeffs: &[C::Scalar], bases: &[C], acc: &mut C::Curve) { + let coeffs: Vec<_> = coeffs.iter().map(|a| a.to_repr()).collect(); + + let c = if bases.len() < 4 { + 1 + } else if bases.len() < 32 { + 3 + } else { + (f64::from(bases.len() as u32)).ln().ceil() as usize + }; + + fn get_at(segment: usize, c: usize, bytes: &F::Repr) -> usize { + let skip_bits = segment * c; + let skip_bytes = skip_bits / 8; + + if skip_bytes >= 32 { + return 0; + } + + let mut v = [0; 8]; + for (v, o) in v.iter_mut().zip(bytes.as_ref()[skip_bytes..].iter()) { + *v = *o; + } + + let mut tmp = u64::from_le_bytes(v); + tmp >>= skip_bits - (skip_bytes * 8); + tmp %= 1 << c; + + tmp as usize + } + + let segments = (256 / c) + 1; + + for current_segment in (0..segments).rev() { + for _ in 0..c { + *acc = acc.double(); + } + + #[derive(Clone, Copy)] + enum Bucket { + None, + Affine(C), + Projective(C::Curve), + } + + impl Bucket { + fn add_assign(&mut self, other: &C) { + *self = match *self { + Bucket::None => Bucket::Affine(*other), + Bucket::Affine(a) => Bucket::Projective(a + *other), + Bucket::Projective(mut a) => { + a += *other; + Bucket::Projective(a) + } + } + } + + fn add(self, mut other: C::Curve) -> C::Curve { + match self { + Bucket::None => other, + Bucket::Affine(a) => { + other += a; + other + } + Bucket::Projective(a) => other + a, + } + } + } + + let mut buckets: Vec> = vec![Bucket::None; (1 << c) - 1]; + + for (coeff, base) in coeffs.iter().zip(bases.iter()) { + let coeff = get_at::(current_segment, c, coeff); + if coeff != 0 { + buckets[coeff - 1].add_assign(base); + } + } + + // Summation by parts + // e.g. 3a + 2b + 1c = a + + // (a) + b + + // ((a) + b) + c + let mut running_sum = C::Curve::identity(); + for exp in buckets.into_iter().rev() { + running_sum = exp.add(running_sum); + *acc += &running_sum; + } + } + } + + #[test] + fn test_booth_encoding() { + fn mul(scalar: &Fr, point: &G1Affine, window: usize) -> G1Affine { + let u = scalar.to_repr(); + let n = Fr::NUM_BITS as usize / window + 1; + + let table = (0..=1 << (window - 1)) + .map(|i| point * Fr::from(i as u64)) + .collect::>(); + + let mut acc = G1::identity(); + for i in (0..n).rev() { + for _ in 0..window { + acc = acc.double(); + } + + let idx = super::get_booth_index(i as usize, window, u.as_ref()); + + if idx.is_negative() { + acc += table[idx.unsigned_abs() as usize].neg(); + } + if idx.is_positive() { + acc += table[idx.unsigned_abs() as usize]; + } + } + + acc.to_affine() + } + + let (scalars, points): (Vec<_>, Vec<_>) = (0..10) + .map(|_| { + let scalar = Fr::random(OsRng); + let point = G1Affine::random(OsRng); + (scalar, point) + }) + .unzip(); + + for window in 1..10 { + for (scalar, point) in scalars.iter().zip(points.iter()) { + let c0 = mul(scalar, point, window); + let c1 = point * scalar; + assert_eq!(c0, c1.to_affine()); + } + } + } + + fn run_msm_cross(min_k: usize, max_k: usize) { + let points = (0..1 << max_k) + .map(|_| C::Curve::random(OsRng)) + .collect::>(); + let mut affine_points = vec![C::identity(); 1 << max_k]; + C::Curve::batch_normalize(&points[..], &mut affine_points[..]); + let points = affine_points; + + let scalars = (0..1 << max_k) + .map(|_| C::Scalar::random(OsRng)) + .collect::>(); + + for k in min_k..=max_k { + let points = &points[..1 << k]; + let scalars = &scalars[..1 << k]; + + let t0 = start_timer!(|| format!("w/ booth k={}", k)); + let e0 = super::best_multiexp(scalars, points); + end_timer!(t0); + + let t1 = start_timer!(|| format!("w/o booth k={}", k)); + let e1 = best_multiexp(scalars, points); + end_timer!(t1); + + assert_eq!(e0, e1); + } + } + + #[test] + fn test_msm_cross() { + run_msm_cross::(10, 18); + // run_msm_cross::(19, 23); + } +}