snarkvm-algorithms 0.2.2

// Copyright (C) 2019-2021 Aleo Systems Inc.
// This file is part of the snarkVM library.

// The snarkVM library is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// The snarkVM library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with the snarkVM library. If not, see <https://www.gnu.org/licenses/>.

use snarkvm_curves::traits::{AffineCurve, ProjectiveCurve};
use snarkvm_fields::{FieldParameters, One, PrimeField, Zero};
use snarkvm_utilities::biginteger::BigInteger;

#[cfg(feature = "parallel")]
use rayon::prelude::*;

pub struct VariableBaseMSM;

impl VariableBaseMSM {
    fn msm_inner<G: AffineCurve>(bases: &[G], scalars: &[<G::ScalarField as PrimeField>::BigInteger]) -> G::Projective {
        let c = if scalars.len() < 32 {
            3
        } else {
            (2.0 / 3.0 * (f64::from(scalars.len() as u32)).log2() + 2.0).ceil() as usize
        };

        let num_bits = <G::ScalarField as PrimeField>::Parameters::MODULUS_BITS as usize;
        let fr_one = G::ScalarField::one().into_repr();

        let zero = G::zero().into_projective();
        let window_starts: Vec<_> = (0..num_bits).step_by(c).collect();

        // Each window is of size `c`.
        // We divide up the bits 0..num_bits into windows of size `c`, and
        // in parallel process each such window.
        let window_sums: Vec<_> = cfg_into_iter!(window_starts)
            .map(|w_start| {
                let mut res = zero;
                // We don't need the "zero" bucket, so we only have 2^c - 1 buckets
                let mut buckets = vec![zero; (1 << c) - 1];
                scalars
                    .iter()
                    .zip(bases)
                    .filter(|(s, _)| !s.is_zero())
                    .for_each(|(&scalar, base)| {
                        if scalar == fr_one {
                            // We only process unit scalars once in the first window.
                            if w_start == 0 {
                                res.add_assign_mixed(base);
                            }
                        } else {
                            let mut scalar = scalar;

                            // We right-shift by w_start, thus getting rid of the
                            // lower bits.
                            scalar.divn(w_start as u32);

                            // We mod the remaining bits by the window size.
                            let scalar = scalar.as_ref()[0] % (1 << c);

                            // If the scalar is non-zero, we update the corresponding
                            // bucket.
                            // (Recall that `buckets` doesn't have a zero bucket.)
                            if scalar != 0 {
                                buckets[(scalar - 1) as usize].add_assign_mixed(&base);
                            }
                        }
                    });
                G::Projective::batch_normalization(&mut buckets);

                let mut running_sum = G::Projective::zero();
                for b in buckets.into_iter().map(|g| g.into_affine()).rev() {
                    running_sum.add_assign_mixed(&b);
                    res += &running_sum;
                }

                res
            })
            .collect();

        // We store the sum for the lowest window.
        let lowest = window_sums.first().unwrap();

        // We're traversing windows from high to low.
        window_sums[1..].iter().rev().fold(zero, |mut total, sum_i| {
            total += sum_i;
            for _ in 0..c {
                total.double_in_place();
            }
            total
        }) + lowest
    }

    pub fn multi_scalar_mul<G: AffineCurve>(
        bases: &[G],
        scalars: &[<G::ScalarField as PrimeField>::BigInteger],
    ) -> G::Projective {
        Self::msm_inner(bases, scalars)
    }
}