From 402e7a5247a22b1e9313f1f1d1c1ff58f9e97951 Mon Sep 17 00:00:00 2001 From: kilic Date: Tue, 28 Nov 2023 20:28:21 +0300 Subject: [PATCH] tidy --- src/msm.rs | 432 +++++++++++++++++++++++++++-------------------------- 1 file changed, 223 insertions(+), 209 deletions(-) diff --git a/src/msm.rs b/src/msm.rs index 5c84e25c..0760d62d 100644 --- a/src/msm.rs +++ b/src/msm.rs @@ -1,105 +1,56 @@ -use ark_std::{end_timer, start_timer}; -use ff::{Field, PrimeField}; -use group::{Curve, Group}; -use pasta_curves::arithmetic::CurveAffine; -use rand_core::OsRng; - -use crate::{ - bn256::{Fr, G1Affine, G1}, - multicore, -}; - -pub 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 - }; +use std::ops::Neg; - fn get_at(segment: usize, c: usize, bytes: &F::Repr) -> usize { - let skip_bits = segment * c; - let skip_bytes = skip_bits / 8; +use ff::PrimeField; +use group::Group; +use pasta_curves::arithmetic::CurveAffine; - if skip_bytes >= 32 { - return 0; - } +use crate::multicore; - let mut v = [0; 8]; - for (v, o) in v.iter_mut().zip(bytes.as_ref()[skip_bytes..].iter()) { - *v = *o; - } +fn get_booth_index(window_index: usize, window_size: usize, el: &[u8]) -> i32 { + // Booth encoding: + // * step by `window`e 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 mut tmp = u64::from_le_bytes(v); - tmp >>= skip_bits - (skip_bytes * 8); - tmp %= 1 << c; + let skip_bits = (window_index * window_size).saturating_sub(1); + let skip_bytes = skip_bits / 8; - tmp as usize + // 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); - 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) - } - } - } + // pad with one 0 if windowing least significant window + if window_index == 0 { + tmp <<= 1; + } - 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, - } - } - } + // remove further bits + tmp >>= skip_bits - (skip_bytes * 8); + // apply the booth window + tmp &= (1 << (window_size + 1)) - 1; - let mut buckets: Vec> = vec![Bucket::None; (1 << c) - 1]; + let sign = tmp & (1 << window_size) == 0; - 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); - } - } + // div ceil by 2 + tmp = (tmp + 1) >> 1; - // 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; - } + // find the booth action index + if sign { + tmp as i32 + } else { + ((!tmp.saturating_sub(1) & ((1 << window_size) - 1)) as i32).neg() } } -pub fn multiexp_serial_2(coeffs: &[C::Scalar], bases: &[C], acc: &mut C::Curve) { +pub 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 { @@ -110,9 +61,9 @@ pub fn multiexp_serial_2(coeffs: &[C::Scalar], bases: &[C], acc: (f64::from(bases.len() as u32)).ln().ceil() as usize }; - let segments = (256 / c) + 1; + let number_of_windows = C::Scalar::NUM_BITS as usize / 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(); } @@ -151,13 +102,12 @@ pub fn multiexp_serial_2(coeffs: &[C::Scalar], bases: &[C], acc: let mut buckets: Vec> = vec![Bucket::None; 1 << (c - 1)]; for (coeff, base) in coeffs.iter().zip(bases.iter()) { - let coeff = get_booth_index(current_segment, c, coeff.as_ref()); + 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() { - let coeff = coeff.abs(); - buckets[coeff as usize - 1].add_assign(&base.neg()); + buckets[coeff.unsigned_abs() as usize - 1].add_assign(&base.neg()); } } @@ -231,150 +181,214 @@ pub fn best_multiexp(coeffs: &[C::Scalar], bases: &[C]) -> C::Cu } } -pub fn best_multiexp_2(coeffs: &[C::Scalar], bases: &[C]) -> C::Curve { - assert_eq!(coeffs.len(), bases.len()); +#[cfg(test)] +mod test { - 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; + use std::ops::Neg; - for ((coeffs, bases), acc) in coeffs - .chunks(chunk) - .zip(bases.chunks(chunk)) - .zip(results.iter_mut()) - { - scope.spawn(move |_| { - multiexp_serial_2(coeffs, bases, acc); - }); - } - }); - results.iter().fold(C::Curve::identity(), |a, b| a + b) - } else { - let mut acc = C::Curve::identity(); - multiexp_serial_2(coeffs, bases, &mut acc); - acc + 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 + } } -} -fn div_ceil(a: u32, b: u32) -> u32 { - a.checked_sub(1).map_or(0, |a| a / b + 1) -} + // 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(); -pub(crate) fn get_booth_index(segment: usize, window: usize, el: &[u8]) -> i32 { - let (skip_bits, pad) = match (segment * window).checked_sub(1) { - Some(skip_bits) => (skip_bits, false), - None => (0, true), - }; + let c = if bases.len() < 4 { + 1 + } else if bases.len() < 32 { + 3 + } else { + (f64::from(bases.len() as u32)).ln().ceil() as usize + }; - let skip_bytes = skip_bits / 8; - if skip_bytes >= 32 { - return 0; - } + fn get_at(segment: usize, c: usize, bytes: &F::Repr) -> usize { + let skip_bits = segment * c; + let skip_bytes = skip_bits / 8; - let mut v = [0; 4]; - for (v, o) in v.iter_mut().zip(el.iter().skip(skip_bytes)) { - *v = *o; - } - let mut tmp = u32::from_le_bytes(v); - if pad { - tmp <<= 1; // pad left with one 0 - } - tmp >>= skip_bits - (skip_bytes * 8); - tmp %= 1 << (window + 1); - // let bits = format!("T {:0>width$b}", tmp, width = window + 1); - // println!("{}", bits); - // tmp + if skip_bytes >= 32 { + return 0; + } - let sign = tmp & (1 << window) == 0; + let mut v = [0; 8]; + for (v, o) in v.iter_mut().zip(bytes.as_ref()[skip_bytes..].iter()) { + *v = *o; + } - let mask = (1 << window) - 1; + let mut tmp = u64::from_le_bytes(v); + tmp >>= skip_bits - (skip_bytes * 8); + tmp %= 1 << c; - if sign { - let idx = div_ceil(tmp, 2u32); - idx as i32 - } else { - let idx = !div_ceil(tmp, 2u32).saturating_sub(1) & mask; - -(idx as i32) - } -} - -#[test] -fn get_bucket_index() { - let window = 5; + tmp as usize + } - fn mul(a: Fr, b: Fr, window: usize) -> Fr { - let u = b.to_repr(); - let n = div_ceil(Fr::NUM_BITS, window as u32) + 1; - // let n = 10; + let segments = (256 / c) + 1; - let mut acc = Fr::ZERO; - for i in (0..n).rev() { - let idx = get_booth_index(i as usize, window, u.as_ref()); + for current_segment in (0..segments).rev() { + for _ in 0..c { + *acc = acc.double(); + } - let tmp = a * Fr::from(idx.abs() as u64); - // println!("{:?}", idx); - if idx.is_negative() { - acc -= tmp; + #[derive(Clone, Copy)] + enum Bucket { + None, + Affine(C), + Projective(C::Curve), } - if idx.is_positive() { - acc += tmp; + + 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, + } + } } - if i != 0 { - for _ in 0..window { - acc = acc.double(); + + 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); } } - } - acc + // 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; + } + } } - for _ in 0..10000 { - let a = Fr::random(OsRng); - let b = Fr::random(OsRng); - let c0 = mul(a, b, window); - let c1 = a * b; - assert_eq!(c0, c1); - } -} + #[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; -#[test] -fn test_msm_with_booth() { - // let n = 100; + let table = (0..=1 << (window - 1)) + .map(|i| point * Fr::from(i as u64)) + .collect::>(); - // let points = (0..n).map(|_| G1Affine::random(OsRng)).collect::>(); - // let scalars = (0..n).map(|_| Fr::random(OsRng)).collect::>(); + let mut acc = G1::identity(); + for i in (0..n).rev() { + for _ in 0..window { + acc = acc.double(); + } - // let mut e0 = G1::identity(); - // multiexp_serial(&scalars[..], &points[..], &mut e0); + let idx = super::get_booth_index(i as usize, window, u.as_ref()); - // let mut e1 = G1::identity(); - // multiexp_serial_2(&scalars[..], &points[..], &mut e1); - // assert_eq!(e0, e1); + if idx.is_negative() { + acc += table[idx.unsigned_abs() as usize].neg(); + } + if idx.is_positive() { + acc += table[idx.unsigned_abs() as usize]; + } + } - let n = 1 << 21; + acc.to_affine() + } - let points = (0..n).map(|_| G1Affine::random(OsRng)).collect::>(); - let scalars = (0..n).map(|_| Fr::random(OsRng)).collect::>(); + 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()); + } + } + } + + #[test] + fn test_msm_cross() { + let min_k = 10; + let max_k = 22; - let t0 = start_timer!(|| "zcash"); - let e0 = best_multiexp(&scalars[..], &points[..]); - end_timer!(t0); + let points = (0..1 << max_k) + .map(|_| G1Affine::random(OsRng)) + .collect::>(); - let t1 = start_timer!(|| "booth"); - let e1 = best_multiexp_2(&scalars[..], &points[..]); - end_timer!(t1); - assert_eq!(e0, e1); + let scalars = (0..1 << max_k) + .map(|_| Fr::random(OsRng)) + .collect::>(); - let t1 = start_timer!(|| "booth"); - let _e1 = best_multiexp_2(&scalars[..], &points[..]); - end_timer!(t1); + for k in min_k..=max_k { + let points = &points[..1 << k]; + let scalars = &scalars[..1 << k]; - let t0 = start_timer!(|| "zcash"); - let _e0 = best_multiexp(&scalars[..], &points[..]); - end_timer!(t0); + 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); + } + } }