p3_mds/
coset_mds.rs

1use alloc::vec::Vec;
2
3use p3_field::{Algebra, Field, TwoAdicField};
4use p3_symmetric::Permutation;
5use p3_util::{log2_strict_usize, reverse_slice_index_bits};
6
7use crate::MdsPermutation;
8use crate::butterflies::{bowers_g_layer, bowers_g_t_layer};
9
10/// A Reed-Solomon based MDS permutation.
11///
12/// An MDS permutation which works by interpreting the input as evaluations of a polynomial over a
13/// power-of-two subgroup, and computing evaluations over a coset of that subgroup. This can be
14/// viewed as returning the parity elements of a systematic Reed-Solomon code. Since Reed-Solomon
15/// codes are MDS, this is an MDS permutation.
16#[derive(Clone, Debug)]
17pub struct CosetMds<F, const N: usize> {
18    fft_twiddles: Vec<F>,
19    ifft_twiddles: Vec<F>,
20    weights: [F; N],
21}
22
23impl<F, const N: usize> Default for CosetMds<F, N>
24where
25    F: TwoAdicField,
26{
27    fn default() -> Self {
28        let log_n = log2_strict_usize(N);
29
30        let root = F::two_adic_generator(log_n);
31        let root_inv = root.inverse();
32        let mut fft_twiddles: Vec<F> = root.powers().collect_n(N / 2);
33        let mut ifft_twiddles: Vec<F> = root_inv.powers().collect_n(N / 2);
34        reverse_slice_index_bits(&mut fft_twiddles);
35        reverse_slice_index_bits(&mut ifft_twiddles);
36
37        let shift = F::GENERATOR;
38        let mut weights: [F; N] = shift.powers().collect_n(N).try_into().unwrap();
39        reverse_slice_index_bits(&mut weights);
40        Self {
41            fft_twiddles,
42            ifft_twiddles,
43            weights,
44        }
45    }
46}
47
48impl<F: TwoAdicField, A: Algebra<F>, const N: usize> Permutation<[A; N]> for CosetMds<F, N> {
49    fn permute_mut(&self, values: &mut [A; N]) {
50        // Inverse DFT, except we skip bit reversal and rescaling by 1/N.
51        bowers_g_t(values, &self.ifft_twiddles);
52
53        // Multiply by powers of the coset shift (see default coset LDE impl for an explanation)
54        for (value, weight) in values.iter_mut().zip(self.weights) {
55            *value = value.clone() * weight;
56        }
57
58        // DFT, assuming bit-reversed input.
59        bowers_g(values, &self.fft_twiddles);
60    }
61}
62
63impl<F: TwoAdicField, A: Algebra<F>, const N: usize> MdsPermutation<A, N> for CosetMds<F, N> {}
64
65/// Executes the Bowers G network. This is like a DFT, except it assumes the input is in
66/// bit-reversed order.
67#[inline]
68fn bowers_g<F: Field, A: Algebra<F>, const N: usize>(values: &mut [A; N], twiddles: &[F]) {
69    let log_n = log2_strict_usize(N);
70    for log_half_block_size in 0..log_n {
71        bowers_g_layer(values, log_half_block_size, twiddles);
72    }
73}
74
75/// Executes the Bowers G^T network. This is like an inverse DFT, except we skip rescaling by
76/// `1/N`, and the output is bit-reversed.
77#[inline]
78fn bowers_g_t<F: Field, A: Algebra<F>, const N: usize>(values: &mut [A; N], twiddles: &[F]) {
79    let log_n = log2_strict_usize(N);
80    for log_half_block_size in (0..log_n).rev() {
81        bowers_g_t_layer(values, log_half_block_size, twiddles);
82    }
83}
84
85#[cfg(test)]
86mod tests {
87    use p3_baby_bear::BabyBear;
88    use p3_dft::{NaiveDft, TwoAdicSubgroupDft};
89    use p3_field::{Field, PrimeCharacteristicRing};
90    use p3_symmetric::Permutation;
91    use rand::rngs::SmallRng;
92    use rand::{Rng, SeedableRng};
93
94    use crate::coset_mds::CosetMds;
95
96    #[test]
97    fn matches_naive() {
98        type F = BabyBear;
99        const N: usize = 8;
100
101        let mut rng = SmallRng::seed_from_u64(1);
102        let mut arr: [F; N] = rng.random();
103
104        let shift = F::GENERATOR;
105        let mut coset_lde_naive = NaiveDft.coset_lde(arr.to_vec(), 0, shift);
106        coset_lde_naive
107            .iter_mut()
108            .for_each(|x| *x *= F::from_u8(N as u8));
109        CosetMds::default().permute_mut(&mut arr);
110        assert_eq!(coset_lde_naive, arr);
111    }
112}
p3_mds/coset_mds.rs

p3_mds/
coset_mds.rs
