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This commit is contained in:
Jean-Philippe Bossuat
2024-12-31 15:30:57 +01:00
parent c65522099b
commit 8d84727fae
17 changed files with 422 additions and 363 deletions
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24
benches/ntt.rs
View File

@@ -3,25 +3,25 @@ use math::{modulus::prime::Prime,dft::ntt::Table};
use math::dft::DFT;
fn forward_inplace(c: &mut Criterion) {
fn runner<T: DFT<u64> + 'static>(prime_instance: Prime<u64>, nth_root: u64) -> Box<dyn FnMut()> {
fn runner(prime_instance: Prime<u64>, nth_root: u64) -> Box<dyn FnMut()> {
let ntt_table: Table<u64> = Table::<u64>::new(prime_instance, nth_root);
let mut a: Vec<u64> = vec![0; (nth_root >> 1) as usize];
for i in 0..a.len(){
a[i] = i as u64;
}
Box::new(move || {
ntt_table.forward_inplace(&mut a)
ntt_table.forward_inplace::<false>(&mut a)
})
}
let mut b: criterion::BenchmarkGroup<'_, criterion::measurement::WallTime> = c.benchmark_group("forward_inplace");
for log_nth_root in 11..18 {
let mut prime_instance: Prime<u64> = Prime::<u64>::new(0x1fffffffffe00001, 1);
let prime_instance: Prime<u64> = Prime::<u64>::new(0x1fffffffffe00001, 1);
let runners = [
("prime", {
runner::<Table<u64>>(prime_instance, 1<<log_nth_root)
runner(prime_instance, 1<<log_nth_root)
}),
];
for (name, mut runner) in runners {
@@ -32,7 +32,7 @@ fn forward_inplace(c: &mut Criterion) {
}
fn forward_inplace_lazy(c: &mut Criterion) {
fn runner<T: DFT<u64> + 'static>(prime_instance: Prime<u64>, nth_root: u64) -> Box<dyn FnMut()> {
fn runner(prime_instance: Prime<u64>, nth_root: u64) -> Box<dyn FnMut()> {
let ntt_table: Table<u64> = Table::<u64>::new(prime_instance, nth_root);
let mut a: Vec<u64> = vec![0; (nth_root >> 1) as usize];
for i in 0..a.len(){
@@ -50,7 +50,7 @@ fn forward_inplace_lazy(c: &mut Criterion) {
let runners = [
("prime", {
runner::<Table<u64>>(prime_instance, 1<<log_nth_root)
runner(prime_instance, 1<<log_nth_root)
}),
];
for (name, mut runner) in runners {
@@ -61,14 +61,14 @@ fn forward_inplace_lazy(c: &mut Criterion) {
}
fn backward_inplace(c: &mut Criterion) {
fn runner<T: DFT<u64> + 'static>(prime_instance: Prime<u64>, nth_root: u64) -> Box<dyn FnMut()> {
fn runner(prime_instance: Prime<u64>, nth_root: u64) -> Box<dyn FnMut()> {
let ntt_table: Table<u64> = Table::<u64>::new(prime_instance, nth_root);
let mut a: Vec<u64> = vec![0; (nth_root >> 1) as usize];
for i in 0..a.len(){
a[i] = i as u64;
}
Box::new(move || {
ntt_table.backward_inplace(&mut a)
ntt_table.backward_inplace::<false>(&mut a)
})
}
@@ -79,7 +79,7 @@ fn backward_inplace(c: &mut Criterion) {
let runners = [
("prime", {
runner::<Table<u64>>(prime_instance, 1<<log_nth_root)
runner(prime_instance, 1<<log_nth_root)
}),
];
for (name, mut runner) in runners {
@@ -90,14 +90,14 @@ fn backward_inplace(c: &mut Criterion) {
}
fn backward_inplace_lazy(c: &mut Criterion) {
fn runner<T: DFT<u64> + 'static>(prime_instance: Prime<u64>, nth_root: u64) -> Box<dyn FnMut()> {
fn runner(prime_instance: Prime<u64>, nth_root: u64) -> Box<dyn FnMut()> {
let ntt_table: Table<u64> = Table::<u64>::new(prime_instance, nth_root);
let mut a: Vec<u64> = vec![0; (nth_root >> 1) as usize];
for i in 0..a.len(){
a[i] = i as u64;
}
Box::new(move || {
ntt_table.backward_inplace_lazy(&mut a)
ntt_table.backward_inplace::<true>(&mut a)
})
}
@@ -108,7 +108,7 @@ fn backward_inplace_lazy(c: &mut Criterion) {
let runners = [
("prime", {
runner::<Table<u64>>(prime_instance, 1<<log_nth_root)
runner(prime_instance, 1<<log_nth_root)
}),
];
for (name, mut runner) in runners {

50
benches/operations.rs
View File

@@ -1,12 +1,12 @@
use criterion::{criterion_group, criterion_main, BenchmarkId, Criterion};
use math::ring::Ring;
use math::modulus::Operations;
use math::modulus::VecOperations;
use math::modulus::montgomery::Montgomery;
use math::modulus::{NONE, ONCE};
use math::modulus::{BARRETT, ONCE};
const CHUNK: usize= 8;
fn add_vec_unary(c: &mut Criterion) {
fn vec_add_unary(c: &mut Criterion) {
fn runner(r: Ring<u64>) -> Box<dyn FnMut()> {
let mut p0: math::poly::Poly<u64> = r.new_poly();
@@ -16,7 +16,7 @@ fn add_vec_unary(c: &mut Criterion) {
p1.0[i] = i as u64;
}
Box::new(move || {
r.modulus.add_vec_unary_assign::<CHUNK, ONCE>(&p0.0, &mut p1.0);
r.modulus.vec_add_unary_assign::<CHUNK, ONCE>(&p0.0, &mut p1.0);
})
}
@@ -39,17 +39,17 @@ fn add_vec_unary(c: &mut Criterion) {
}
}
fn mul_vec_montgomery_external_unary_assign(c: &mut Criterion) {
fn vec_mul_montgomery_external_unary_assign(c: &mut Criterion) {
fn runner(r: Ring<u64>) -> Box<dyn FnMut()> {
let mut p0: math::poly::Poly<Montgomery<u64>> = r.new_poly_montgomery();
let mut p0: math::poly::Poly<Montgomery<u64>> = r.new_poly();
let mut p1: math::poly::Poly<u64> = r.new_poly();
for i in 0..p0.n(){
p0.0[i] = r.modulus.montgomery.prepare::<ONCE>(i as u64);
p1.0[i] = i as u64;
}
Box::new(move || {
r.modulus.mul_vec_montgomery_external_unary_assign::<CHUNK, NONE>(&p0.0, &mut p1.0);
r.modulus.vec_mul_montgomery_external_unary_assign::<CHUNK, ONCE>(&p0.0, &mut p1.0);
})
}
@@ -72,5 +72,39 @@ fn mul_vec_montgomery_external_unary_assign(c: &mut Criterion) {
}
}
criterion_group!(benches, add_vec_unary, mul_vec_montgomery_external_unary_assign);
fn vec_mul_montgomery_external_binary_assign(c: &mut Criterion) {
fn runner(r: Ring<u64>) -> Box<dyn FnMut()> {
let mut p0: math::poly::Poly<Montgomery<u64>> = r.new_poly();
let mut p1: math::poly::Poly<u64> = r.new_poly();
let mut p2: math::poly::Poly<u64> = r.new_poly();
for i in 0..p0.n(){
p0.0[i] = r.modulus.montgomery.prepare::<ONCE>(i as u64);
p1.0[i] = i as u64;
}
Box::new(move || {
r.modulus.vec_mul_montgomery_external_binary_assign::<CHUNK,ONCE>(&p0.0, & p1.0, &mut p2.0);
})
}
let mut b: criterion::BenchmarkGroup<'_, criterion::measurement::WallTime> = c.benchmark_group("mul_vec_montgomery_external_binary_assign");
for log_n in 11..17 {
let n: usize = 1<<log_n as usize;
let q_base: u64 = 0x1fffffffffe00001u64;
let q_power: usize = 1usize;
let r: Ring<u64> = Ring::<u64>::new(n, q_base, q_power);
let runners = [
("prime", {
runner(r)
}),
];
for (name, mut runner) in runners {
let id = BenchmarkId::new(name, n);
b.bench_with_input(id, &(), |b, _| b.iter(&mut runner));
}
}
}
criterion_group!(benches, vec_add_unary, vec_mul_montgomery_external_unary_assign, vec_mul_montgomery_external_binary_assign);
criterion_main!(benches);

4
examples/main.rs
View File

@@ -28,11 +28,11 @@ fn main() {
println!("{:?}", a);
ntt_table.forward_inplace(&mut a);
ntt_table.forward_inplace::<false>(&mut a);
println!("{:?}", a);
ntt_table.backward_inplace(&mut a);
ntt_table.backward_inplace::<false>(&mut a);
println!("{:?}", a);

174
src/dft/ntt.rs
View File

@@ -1,5 +1,5 @@
use crate::modulus::montgomery::Montgomery;
use crate::modulus::shoup::Shoup;
use crate::modulus::barrett::Barrett;
use crate::modulus::prime::Prime;
use crate::modulus::ReduceOnce;
use crate::modulus::WordOps;
@@ -9,8 +9,9 @@ use itertools::izip;
pub struct Table<O>{
prime:Prime<O>,
psi_forward_rev:Vec<Shoup<u64>>,
psi_backward_rev: Vec<Shoup<u64>>,
psi: O,
psi_forward_rev:Vec<Barrett<u64>>,
psi_backward_rev: Vec<Barrett<u64>>,
q:O,
two_q:O,
four_q:O,
@@ -26,11 +27,11 @@ impl Table< u64> {
let psi_mont: Montgomery<u64> = prime.montgomery.prepare::<ONCE>(psi);
let psi_inv_mont: Montgomery<u64> = prime.montgomery.pow(psi_mont, prime.phi-1);
let mut psi_forward_rev: Vec<Shoup<u64>> = vec![Shoup(0, 0); (nth_root >> 1) as usize];
let mut psi_backward_rev: Vec<Shoup<u64>> = vec![Shoup(0, 0); (nth_root >> 1) as usize];
let mut psi_forward_rev: Vec<Barrett<u64>> = vec![Barrett(0, 0); (nth_root >> 1) as usize];
let mut psi_backward_rev: Vec<Barrett<u64>> = vec![Barrett(0, 0); (nth_root >> 1) as usize];
psi_forward_rev[0] = prime.shoup.prepare(1);
psi_backward_rev[0] = prime.shoup.prepare(1);
psi_forward_rev[0] = prime.barrett.prepare(1);
psi_backward_rev[0] = prime.barrett.prepare(1);
let log_nth_root_half: u32 = (nth_root>>1).log2() as _;
@@ -44,14 +45,15 @@ impl Table< u64> {
prime.montgomery.mul_external_assign::<ONCE>(psi_mont, &mut powers_forward);
prime.montgomery.mul_external_assign::<ONCE>(psi_inv_mont, &mut powers_backward);
psi_forward_rev[i_rev] = prime.shoup.prepare(powers_forward);
psi_backward_rev[i_rev] = prime.shoup.prepare(powers_backward);
psi_forward_rev[i_rev] = prime.barrett.prepare(powers_forward);
psi_backward_rev[i_rev] = prime.barrett.prepare(powers_backward);
}
let q: u64 = prime.q();
Self{
prime: prime,
psi:psi,
psi_forward_rev: psi_forward_rev,
psi_backward_rev: psi_backward_rev,
q:q,
@@ -59,65 +61,60 @@ impl Table< u64> {
four_q:q<<2,
}
}
// Returns n^-1 mod q in Montgomery.
fn inv(&self, n:u64) -> Montgomery<u64>{
self.prime.montgomery.pow(self.prime.montgomery.prepare::<ONCE>(n), self.prime.phi-1)
}
}
impl DFT<u64> for Table<u64>{
fn forward_inplace(&self, a: &mut [u64]){
self.forward_inplace(a)
self.forward_inplace::<false>(a)
}
fn forward_inplace_lazy(&self, a: &mut [u64]){
self.forward_inplace_lazy(a)
self.forward_inplace::<true>(a)
}
fn backward_inplace(&self, a: &mut [u64]){
self.backward_inplace(a)
self.backward_inplace::<false>(a)
}
fn backward_inplace_lazy(&self, a: &mut [u64]){
self.backward_inplace_lazy(a)
self.backward_inplace::<true>(a)
}
}
impl Table<u64>{
pub fn forward_inplace_lazy(&self, a: &mut [u64]){
self.forward_inplace_core::<true>(a);
pub fn forward_inplace<const LAZY:bool>(&self, a: &mut [u64]){
self.forward_inplace_core::<LAZY, 0, 0>(a);
}
pub fn forward_inplace(&self, a: &mut [u64]){
self.forward_inplace_core::<false>(a);
}
pub fn forward_inplace_core<const LAZY: bool>(&self, a: &mut [u64]) {
pub fn forward_inplace_core<const LAZY: bool, const SKIPSTART: u8, const SKIPEND: u8>(&self, a: &mut [u64]) {
let n: usize = a.len();
assert!(n & n-1 == 0, "invalid x.len()= {} must be a power of two", n);
let log_n: u32 = usize::BITS - ((n as usize)-1).leading_zeros();
for layer in 0..log_n {
let start: u32 = SKIPSTART as u32;
let end: u32 = log_n - (SKIPEND as u32);
for layer in start..end {
let (m, size) = (1 << layer, 1 << (log_n - layer - 1));
let t: usize = 2*size;
if layer == log_n - 1 {
if LAZY{
izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
let (a, b) = a.split_at_mut(size);
self.dit::<false>(&mut a[0], &mut b[0], *psi);
self.dit_inplace::<false>(&mut a[0], &mut b[0], *psi);
debug_assert!(a[0] < self.two_q, "forward_inplace_core::<LAZY=true> output {} > {} (2q-1)", a[0], self.two_q-1);
debug_assert!(b[0] < self.two_q, "forward_inplace_core::<LAZY=true> output {} > {} (2q-1)", b[0], self.two_q-1);
});
}else{
izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
let (a, b) = a.split_at_mut(size);
self.dit::<true>(&mut a[0], &mut b[0], *psi);
self.prime.shoup.reduce_assign(&mut a[0]);
self.prime.shoup.reduce_assign(&mut b[0]);
self.dit_inplace::<true>(&mut a[0], &mut b[0], *psi);
self.prime.barrett.reduce_assign(&mut a[0]);
self.prime.barrett.reduce_assign(&mut b[0]);
debug_assert!(a[0] < self.q, "forward_inplace_core::<LAZY=false> output {} > {} (q-1)", a[0], self.q-1);
debug_assert!(b[0] < self.q, "forward_inplace_core::<LAZY=false> output {} > {} (q-1)", b[0], self.q-1);
});
@@ -127,31 +124,31 @@ impl Table<u64>{
izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
let (a, b) = a.split_at_mut(size);
izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
self.dit::<true>(&mut a[0], &mut b[0], *psi);
self.dit::<true>(&mut a[1], &mut b[1], *psi);
self.dit::<true>(&mut a[2], &mut b[2], *psi);
self.dit::<true>(&mut a[3], &mut b[3], *psi);
self.dit::<true>(&mut a[4], &mut b[4], *psi);
self.dit::<true>(&mut a[5], &mut b[5], *psi);
self.dit::<true>(&mut a[6], &mut b[6], *psi);
self.dit::<true>(&mut a[7], &mut b[7], *psi);
self.dit_inplace::<true>(&mut a[0], &mut b[0], *psi);
self.dit_inplace::<true>(&mut a[1], &mut b[1], *psi);
self.dit_inplace::<true>(&mut a[2], &mut b[2], *psi);
self.dit_inplace::<true>(&mut a[3], &mut b[3], *psi);
self.dit_inplace::<true>(&mut a[4], &mut b[4], *psi);
self.dit_inplace::<true>(&mut a[5], &mut b[5], *psi);
self.dit_inplace::<true>(&mut a[6], &mut b[6], *psi);
self.dit_inplace::<true>(&mut a[7], &mut b[7], *psi);
});
});
}else{
izip!(a.chunks_exact_mut(t), &self.psi_forward_rev[m..]).for_each(|(a, psi)| {
let (a, b) = a.split_at_mut(size);
izip!(a, b).for_each(|(a, b)| self.dit::<true>(a, b, *psi));
izip!(a, b).for_each(|(a, b)| self.dit_inplace::<true>(a, b, *psi));
});
}
}
}
#[inline(always)]
fn dit<const LAZY: bool>(&self, a: &mut u64, b: &mut u64, t: Shoup<u64>) {
fn dit_inplace<const LAZY: bool>(&self, a: &mut u64, b: &mut u64, t: Barrett<u64>) {
debug_assert!(*a < self.four_q, "a:{} q:{}", a, self.four_q);
debug_assert!(*b < self.four_q, "b:{} q:{}", b, self.four_q);
a.reduce_once_assign(self.two_q);
let bt: u64 = self.prime.shoup.mul_external_lazy(t, *b);
let bt: u64 = self.prime.barrett.mul_external_lazy(t, *b);
*b = a.wrapping_add(self.two_q-bt);
*a = a.wrapping_add(bt);
if !LAZY {
@@ -160,39 +157,38 @@ impl Table<u64>{
}
}
pub fn backward_inplace_lazy(&self, a: &mut [u64]){
self.backward_inplace_core::<true>(a);
pub fn backward_inplace<const LAZY:bool>(&self, a: &mut [u64]){
self.backward_inplace_core::<LAZY, 0, 0>(a);
}
pub fn backward_inplace(&self, a: &mut [u64]){
self.backward_inplace_core::<false>(a);
}
pub fn backward_inplace_core<const LAZY:bool>(&self, a: &mut [u64]) {
pub fn backward_inplace_core<const LAZY:bool, const SKIPSTART: u8, const SKIPEND: u8>(&self, a: &mut [u64]) {
let n: usize = a.len();
assert!(n & n-1 == 0, "invalid x.len()= {} must be a power of two", n);
let log_n = usize::BITS - ((n as usize)-1).leading_zeros();
for layer in (0..log_n).rev() {
let start: u32 = SKIPEND as u32;
let end: u32 = log_n - (SKIPSTART as u32);
for layer in (start..end).rev() {
let (m, size) = (1 << layer, 1 << (log_n - layer - 1));
let t: usize = 2*size;
if layer == 0 {
let n_inv: Shoup<u64> = self.prime.shoup.prepare(self.prime.inv(n as u64));
let psi: Shoup<u64> = self.prime.shoup.prepare(self.prime.shoup.mul_external(n_inv, self.psi_backward_rev[1].0));
let n_inv: Barrett<u64> = self.prime.barrett.prepare(self.prime.inv(n as u64));
let psi: Barrett<u64> = self.prime.barrett.prepare(self.prime.barrett.mul_external(n_inv, self.psi_backward_rev[1].0));
izip!(a.chunks_exact_mut(2 * size)).for_each(
|a| {
let (a, b) = a.split_at_mut(size);
izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
self.dif_last::<LAZY>(&mut a[0], &mut b[0], psi, n_inv);
self.dif_last::<LAZY>(&mut a[1], &mut b[1], psi, n_inv);
self.dif_last::<LAZY>(&mut a[2], &mut b[2], psi, n_inv);
self.dif_last::<LAZY>(&mut a[3], &mut b[3], psi, n_inv);
self.dif_last::<LAZY>(&mut a[4], &mut b[4], psi, n_inv);
self.dif_last::<LAZY>(&mut a[5], &mut b[5], psi, n_inv);
self.dif_last::<LAZY>(&mut a[6], &mut b[6], psi, n_inv);
self.dif_last::<LAZY>(&mut a[7], &mut b[7], psi, n_inv);
self.dif_last_inplace::<LAZY>(&mut a[0], &mut b[0], psi, n_inv);
self.dif_last_inplace::<LAZY>(&mut a[1], &mut b[1], psi, n_inv);
self.dif_last_inplace::<LAZY>(&mut a[2], &mut b[2], psi, n_inv);
self.dif_last_inplace::<LAZY>(&mut a[3], &mut b[3], psi, n_inv);
self.dif_last_inplace::<LAZY>(&mut a[4], &mut b[4], psi, n_inv);
self.dif_last_inplace::<LAZY>(&mut a[5], &mut b[5], psi, n_inv);
self.dif_last_inplace::<LAZY>(&mut a[6], &mut b[6], psi, n_inv);
self.dif_last_inplace::<LAZY>(&mut a[7], &mut b[7], psi, n_inv);
});
},
);
@@ -202,14 +198,14 @@ impl Table<u64>{
|(a, psi)| {
let (a, b) = a.split_at_mut(size);
izip!(a.chunks_exact_mut(8), b.chunks_exact_mut(8)).for_each(|(a, b)| {
self.dif::<true>(&mut a[0], &mut b[0], *psi);
self.dif::<true>(&mut a[1], &mut b[1], *psi);
self.dif::<true>(&mut a[2], &mut b[2], *psi);
self.dif::<true>(&mut a[3], &mut b[3], *psi);
self.dif::<true>(&mut a[4], &mut b[4], *psi);
self.dif::<true>(&mut a[5], &mut b[5], *psi);
self.dif::<true>(&mut a[6], &mut b[6], *psi);
self.dif::<true>(&mut a[7], &mut b[7], *psi);
self.dif_inplace::<true>(&mut a[0], &mut b[0], *psi);
self.dif_inplace::<true>(&mut a[1], &mut b[1], *psi);
self.dif_inplace::<true>(&mut a[2], &mut b[2], *psi);
self.dif_inplace::<true>(&mut a[3], &mut b[3], *psi);
self.dif_inplace::<true>(&mut a[4], &mut b[4], *psi);
self.dif_inplace::<true>(&mut a[5], &mut b[5], *psi);
self.dif_inplace::<true>(&mut a[6], &mut b[6], *psi);
self.dif_inplace::<true>(&mut a[7], &mut b[7], *psi);
});
},
);
@@ -217,7 +213,7 @@ impl Table<u64>{
izip!(a.chunks_exact_mut(2 * size), &self.psi_backward_rev[m..]).for_each(
|(a, psi)| {
let (a, b) = a.split_at_mut(size);
izip!(a, b).for_each(|(a, b)| self.dif::<true>(a, b, *psi));
izip!(a, b).for_each(|(a, b)| self.dif_inplace::<true>(a, b, *psi));
},
);
}
@@ -225,10 +221,10 @@ impl Table<u64>{
}
#[inline(always)]
fn dif<const LAZY: bool>(&self, a: &mut u64, b: &mut u64, t: Shoup<u64>) {
debug_assert!(*a < self.two_q);
debug_assert!(*b < self.two_q);
let d: u64 = self.prime.shoup.mul_external_lazy(t, *a + self.two_q - *b);
fn dif_inplace<const LAZY: bool>(&self, a: &mut u64, b: &mut u64, t: Barrett<u64>) {
debug_assert!(*a < self.two_q, "a:{} q:{}", a, self.four_q);
debug_assert!(*b < self.two_q, "b:{} q:{}", b, self.four_q);
let d: u64 = self.prime.barrett.mul_external_lazy(t, *a + self.two_q - *b);
*a = a.wrapping_add(*b);
a.reduce_once_assign(self.two_q);
*b = d;
@@ -238,17 +234,41 @@ impl Table<u64>{
}
}
fn dif_last<const LAZY:bool>(&self, a: &mut u64, b: &mut u64, psi: Shoup<u64>, n_inv: Shoup<u64>){
fn dif_last_inplace<const LAZY:bool>(&self, a: &mut u64, b: &mut u64, psi: Barrett<u64>, n_inv: Barrett<u64>){
debug_assert!(*a < self.two_q);
debug_assert!(*b < self.two_q);
if LAZY{
let d: u64 = self.prime.shoup.mul_external_lazy(psi, *a + self.two_q - *b);
*a = self.prime.shoup.mul_external_lazy(n_inv, *a + *b);
let d: u64 = self.prime.barrett.mul_external_lazy(psi, *a + self.two_q - *b);
*a = self.prime.barrett.mul_external_lazy(n_inv, *a + *b);
*b = d;
}else{
let d: u64 = self.prime.shoup.mul_external(psi, *a + self.two_q - *b);
*a = self.prime.shoup.mul_external(n_inv, *a + *b);
let d: u64 = self.prime.barrett.mul_external(psi, *a + self.two_q - *b);
*a = self.prime.barrett.mul_external(n_inv, *a + *b);
*b = d;
}
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_ntt() {
let q_base: u64 = 0x800000000004001;
let q_power: usize = 1;
let prime_instance: Prime<u64> = Prime::<u64>::new(q_base, q_power);
let n: u64 = 32;
let two_nth_root: u64 = n<<1;
let ntt_table: Table<u64> = Table::<u64>::new(prime_instance, two_nth_root);
let mut a: Vec<u64> = vec![0; n as usize];
for i in 0..a.len(){
a[i] = i as u64;
}
let b: Vec<u64> = a.clone();
ntt_table.forward_inplace::<false>(&mut a);
ntt_table.backward_inplace::<false>(&mut a);
assert!(a == b);
}
}

88
src/modulus.rs
View File

@@ -1,7 +1,6 @@
pub mod prime;
pub mod barrett;
pub mod montgomery;
pub mod shoup;
pub mod impl_u64;
pub type REDUCEMOD = u8;
@@ -55,75 +54,64 @@ pub trait ReduceOnce<O>{
fn reduce_once(&self, q:O) -> O;
}
impl ReduceOnce<u64> for u64{
#[inline(always)]
fn reduce_once_constant_time_assign(&mut self, q: u64){
debug_assert!(q < 0x8000000000000000, "2q >= 2^64");
*self -= (q.wrapping_sub(*self)>>63)*q;
}
pub trait WordOperations<O>{
#[inline(always)]
fn reduce_once_constant_time(&self, q:u64) -> u64{
debug_assert!(q < 0x8000000000000000, "2q >= 2^64");
self - (q.wrapping_sub(*self)>>63)*q
}
// Applies a parameterized modular reduction.
fn word_reduce_assign<const REDUCE:REDUCEMOD>(&self, x: &mut O);
#[inline(always)]
fn reduce_once_assign(&mut self, q: u64){
debug_assert!(q < 0x8000000000000000, "2q >= 2^64");
*self = *self.min(&mut self.wrapping_sub(q))
}
#[inline(always)]
fn reduce_once(&self, q:u64) -> u64{
debug_assert!(q < 0x8000000000000000, "2q >= 2^64");
*self.min(&mut self.wrapping_sub(q))
}
}
pub trait Operations<O>{
// Assigns a + b to c.
fn add_binary_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b:&O, c: &mut O);
fn word_add_binary_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b:&O, c: &mut O);
// Assigns a + b to b.
fn add_unary_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b: &mut O);
// Assigns a[i] + b[i] to c[i]
fn add_vec_binary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b:&[O], c: &mut [O]);
// Assigns a[i] + b[i] to b[i]
fn add_vec_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b: &mut [O]);
fn word_add_unary_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b: &mut O);
// Assigns a - b to c.
fn sub_binary_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b:&O, c: &mut O);
fn word_sub_binary_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b:&O, c: &mut O);
// Assigns b - a to b.
fn sub_unary_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b: &mut O);
// Assigns a[i] - b[i] to c[i]
fn sub_vec_binary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b:&[O], c: &mut [O]);
// Assigns a[i] - b[i] to b[i]
fn sub_vec_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b: &mut [O]);
fn word_sub_unary_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b: &mut O);
// Assigns -a to a.
fn neg_assign<const REDUCE:REDUCEMOD>(&self, a:&mut O);
fn word_neg_assign<const REDUCE:REDUCEMOD>(&self, a:&mut O);
// Assigns -a[i] to a[i].
fn neg_vec_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &mut [O]);
// Assigns a * 2^64 to b.
fn word_prepare_montgomery_assign<const REDUCE:REDUCEMOD>(&self, a: &O, b: &mut montgomery::Montgomery<O>);
// Assigns a * b to c.
fn mul_montgomery_external_binary_assign<const REDUCE:REDUCEMOD>(&self, a:&montgomery::Montgomery<O>, b:&O, c: &mut O);
fn word_mul_montgomery_external_binary_assign<const REDUCE:REDUCEMOD>(&self, a:&montgomery::Montgomery<O>, b:&O, c: &mut O);
// Assigns a * b to b.
fn mul_montgomery_external_unary_assign<const REDUCE:REDUCEMOD>(&self, a:&montgomery::Montgomery<O>, b:&mut O);
fn word_mul_montgomery_external_unary_assign<const REDUCE:REDUCEMOD>(&self, a:&montgomery::Montgomery<O>, b:&mut O);
}
pub trait VecOperations<O>{
// Applies a parameterized modular reduction.
fn vec_reduce_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, x: &mut [O]);
// Assigns a[i] + b[i] to c[i]
fn vec_add_binary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b:&[O], c: &mut [O]);
// Assigns a[i] + b[i] to b[i]
fn vec_add_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b: &mut [O]);
// Assigns a[i] - b[i] to c[i]
fn vec_sub_binary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b:&[O], c: &mut [O]);
// Assigns a[i] - b[i] to b[i]
fn vec_sub_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b: &mut [O]);
// Assigns -a[i] to a[i].
fn vec_neg_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &mut [O]);
// Assigns a * 2^64 to b.
fn vec_prepare_montgomery_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[O], b: &mut [montgomery::Montgomery<O>]);
// Assigns a[i] * b[i] to c[i].
fn mul_vec_montgomery_external_binary_assign<const CHUNK:usize,const REDUCE:REDUCEMOD>(&self, a:&[montgomery::Montgomery<O>], b:&[O], c: &mut [O]);
fn vec_mul_montgomery_external_binary_assign<const CHUNK:usize,const REDUCE:REDUCEMOD>(&self, a:&[montgomery::Montgomery<O>], b:&[O], c: &mut [O]);
// Assigns a[i] * b[i] to b[i].
fn mul_vec_montgomery_external_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a:&[montgomery::Montgomery<O>], b:&mut [O]);
fn vec_mul_montgomery_external_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a:&[montgomery::Montgomery<O>], b:&mut [O]);
}

17
src/modulus/barrett.rs
View File

@@ -1,8 +1,25 @@
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub struct Barrett<O>(pub O, pub O);
impl<O> Barrett<O> {
#[inline(always)]
pub fn value(&self) -> &O {
&self.0
}
#[inline(always)]
pub fn quotient(&self) -> &O {
&self.1
}
}
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub struct BarrettPrecomp<O>{
pub q: O,
pub lo:O,
pub hi:O,
pub one: Barrett<O>,
}
impl<O> BarrettPrecomp<O>{

45
src/modulus/impl_u64/barrett.rs
View File

@@ -1,15 +1,30 @@
use crate::modulus::barrett::BarrettPrecomp;
use crate::modulus::barrett::{Barrett, BarrettPrecomp};
use crate::modulus::ReduceOnce;
use num_bigint::BigUint;
use num_traits::cast::ToPrimitive;
impl BarrettPrecomp<u64>{
pub fn new(q: u64) -> BarrettPrecomp<u64> {
let big_r: BigUint = (BigUint::from(1 as usize)<<((u64::BITS<<1) as usize)) / BigUint::from(q);
let lo: u64 = (&big_r & BigUint::from(u64::MAX)).to_u64().unwrap();
let hi: u64 = (big_r >> u64::BITS).to_u64().unwrap();
Self{q, lo, hi}
let mut precomp: BarrettPrecomp<u64> = Self{q, lo, hi, one:Barrett(0,0)};
precomp.one = precomp.prepare(1);
precomp
}
#[inline(always)]
pub fn one(&self) -> Barrett<u64> {
self.one
}
#[inline(always)]
pub fn prepare(&self, v: u64) -> Barrett<u64> {
debug_assert!(v < self.q);
let quotient: u64 = (((v as u128) << 64) / self.q as u128) as _;
Barrett(v, quotient)
}
/// Returns lhs mod q.
@@ -40,4 +55,30 @@ impl BarrettPrecomp<u64>{
let (_, mhi) = lhs.widening_mul(self.hi);
*lhs = *lhs - mhi.wrapping_mul(self.q)
}
#[inline(always)]
pub fn mul_external(&self, lhs: Barrett<u64>, rhs: u64) -> u64 {
let mut r: u64 = self.mul_external_lazy(lhs, rhs);
r.reduce_once_assign(self.q);
r
}
#[inline(always)]
pub fn mul_external_assign(&self, lhs: Barrett<u64>, rhs: &mut u64){
self.mul_external_lazy_assign(lhs, rhs);
rhs.reduce_once_assign(self.q);
}
#[inline(always)]
pub fn mul_external_lazy(&self, lhs: Barrett<u64>, rhs: u64) -> u64 {
let mut r: u64 = rhs;
self.mul_external_lazy_assign(lhs, &mut r);
r
}
#[inline(always)]
pub fn mul_external_lazy_assign(&self, lhs: Barrett<u64>, rhs: &mut u64){
let t: u64 = ((*lhs.quotient() as u128 * *rhs as u128) >> 64) as _;
*rhs = (rhs.wrapping_mul(*lhs.value())).wrapping_sub(self.q.wrapping_mul(t));
}
}

29
src/modulus/impl_u64/mod.rs
View File

@@ -1,5 +1,32 @@
pub mod prime;
pub mod barrett;
pub mod montgomery;
pub mod shoup;
pub mod operations;
use crate::modulus::ReduceOnce;
impl ReduceOnce<u64> for u64{
#[inline(always)]
fn reduce_once_constant_time_assign(&mut self, q: u64){
debug_assert!(q < 0x8000000000000000, "2q >= 2^64");
*self -= (q.wrapping_sub(*self)>>63)*q;
}
#[inline(always)]
fn reduce_once_constant_time(&self, q:u64) -> u64{
debug_assert!(q < 0x8000000000000000, "2q >= 2^64");
self - (q.wrapping_sub(*self)>>63)*q
}
#[inline(always)]
fn reduce_once_assign(&mut self, q: u64){
debug_assert!(q < 0x8000000000000000, "2q >= 2^64");
*self = *self.min(&mut self.wrapping_sub(q))
}
#[inline(always)]
fn reduce_once(&self, q:u64) -> u64{
debug_assert!(q < 0x8000000000000000, "2q >= 2^64");
*self.min(&mut self.wrapping_sub(q))
}
}

49
src/modulus/impl_u64/montgomery.rs
View File

@@ -26,12 +26,12 @@ impl MontgomeryPrecomp<u64>{
four_q: q<<2,
barrett: BarrettPrecomp::new(q),
q_inv: q_inv,
one: Montgomery(0),
minus_one: Montgomery(0),
one: 0,
minus_one:0,
};
precomp.one = precomp.prepare::<ONCE>(1);
precomp.minus_one = Montgomery(q-precomp.one.value());
precomp.minus_one = q-precomp.one;
precomp
}
@@ -71,7 +71,7 @@ impl MontgomeryPrecomp<u64>{
TWICE=>{x.reduce_once_assign(self.two_q)},
FOURTIMES =>{x.reduce_once_assign(self.four_q)},
BARRETT =>{self.barrett.reduce_assign(x)},
BARRETTLAZY =>{self.barrett.reduce_assign(x)},
BARRETTLAZY =>{self.barrett.reduce_lazy_assign(x)},
_ => unreachable!("invalid REDUCE argument")
}
}
@@ -79,7 +79,7 @@ impl MontgomeryPrecomp<u64>{
/// Returns lhs * 2^64 mod q as a Montgomery<u64>.
#[inline(always)]
pub fn prepare<const REDUCE:REDUCEMOD>(&self, lhs: u64) -> Montgomery<u64>{
let mut rhs = Montgomery(0);
let mut rhs: u64 = 0;
self.prepare_assign::<REDUCE>(lhs, &mut rhs);
rhs
}
@@ -88,8 +88,8 @@ impl MontgomeryPrecomp<u64>{
#[inline(always)]
pub fn prepare_assign<const REDUCE:REDUCEMOD>(&self, lhs: u64, rhs: &mut Montgomery<u64>){
let (_, mhi) = lhs.widening_mul(*self.barrett.value_lo());
*rhs = Montgomery((lhs.wrapping_mul(*self.barrett.value_hi()).wrapping_add(mhi)).wrapping_mul(self.q).wrapping_neg());
self.reduce_assign::<REDUCE>(rhs.value_mut());
*rhs = (lhs.wrapping_mul(*self.barrett.value_hi()).wrapping_add(mhi)).wrapping_mul(self.q).wrapping_neg();
self.reduce_assign::<REDUCE>(rhs);
}
/// Returns lhs * (2^64)^-1 mod q as a u64.
@@ -103,7 +103,7 @@ impl MontgomeryPrecomp<u64>{
/// Assigns lhs * (2^64)^-1 mod q to rhs.
#[inline(always)]
pub fn unprepare_assign<const REDUCE:REDUCEMOD>(&self, lhs: Montgomery<u64>, rhs: &mut u64){
let (_, r) = self.q.widening_mul(lhs.value().wrapping_mul(self.q_inv));
let (_, r) = self.q.widening_mul(lhs.wrapping_mul(self.q_inv));
*rhs = self.reduce::<REDUCE>(self.q.wrapping_sub(r));
}
@@ -118,7 +118,7 @@ impl MontgomeryPrecomp<u64>{
/// Assigns lhs * rhs * (2^{64})^-1 mod q to rhs.
#[inline(always)]
pub fn mul_external_assign<const REDUCE:REDUCEMOD>(&self, lhs: Montgomery<u64>, rhs: &mut u64){
let (mlo, mhi) = lhs.value().widening_mul(*rhs);
let (mlo, mhi) = lhs.widening_mul(*rhs);
let (_, hhi) = self.q.widening_mul(mlo.wrapping_mul(self.q_inv));
*rhs = self.reduce::<REDUCE>(mhi.wrapping_sub(hhi).wrapping_add(self.q));
}
@@ -126,31 +126,31 @@ impl MontgomeryPrecomp<u64>{
/// Returns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1].
#[inline(always)]
pub fn mul_internal<const REDUCE:REDUCEMOD>(&self, lhs: Montgomery<u64>, rhs: Montgomery<u64>) -> Montgomery<u64>{
Montgomery(self.mul_external::<REDUCE>(lhs, *rhs.value()))
self.mul_external::<REDUCE>(lhs, rhs)
}
/// Assigns lhs * rhs * (2^{64})^-1 mod q to rhs.
#[inline(always)]
pub fn mul_internal_assign<const REDUCE:REDUCEMOD>(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
self.mul_external_assign::<REDUCE>(lhs, rhs.value_mut());
self.mul_external_assign::<REDUCE>(lhs, rhs);
}
#[inline(always)]
pub fn add_internal(&self, lhs: Montgomery<u64>, rhs: Montgomery<u64>) -> Montgomery<u64>{
Montgomery(self.barrett.reduce(rhs.value() + lhs.value()))
self.barrett.reduce(rhs + lhs)
}
/// Assigns lhs + rhs to rhs.
#[inline(always)]
pub fn add_internal_lazy_assign(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
*rhs.value_mut() += lhs.value()
*rhs += lhs
}
/// Assigns lhs + rhs - q if (lhs + rhs) >= q to rhs.
#[inline(always)]
pub fn add_internal_reduce_once_assign<const LAZY:bool>(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
self.add_internal_lazy_assign(lhs, rhs);
rhs.value_mut().reduce_once_assign(self.q);
rhs.reduce_once_assign(self.q);
}
/// Returns lhs mod q in range [0, 2q-1].
@@ -173,30 +173,11 @@ impl MontgomeryPrecomp<u64>{
i >>= 1;
}
y.value_mut().reduce_once_assign(self.q);
y.reduce_once_assign(self.q);
y
}
}
/// Returns x^exponent mod q.
/// This function internally instantiate a new MontgomeryPrecomp<u64>
/// To be used when called only a few times and if there
/// is no Prime instantiated with q.
fn pow(x:u64, exponent:u64, q:u64) -> u64{
let montgomery: MontgomeryPrecomp<u64> = MontgomeryPrecomp::<u64>::new(q);
let mut y_mont: Montgomery<u64> = montgomery.one();
let mut x_mont: Montgomery<u64> = montgomery.prepare::<ONCE>(x);
while exponent > 0{
if exponent & 1 == 1{
montgomery.mul_internal_assign::<ONCE>(x_mont, &mut y_mont);
}
montgomery.mul_internal_assign::<ONCE>(x_mont, &mut x_mont);
}
montgomery.unprepare::<ONCE>(y_mont)
}
#[cfg(test)]
mod tests {
use crate::modulus::montgomery;

129
src/modulus/impl_u64/operations.rs
View File

@@ -1,84 +1,121 @@
use crate::modulus::Operations;
use crate::modulus::{WordOperations, VecOperations};
use crate::modulus::prime::Prime;
use crate::modulus::ReduceOnce;
use crate::modulus::montgomery::Montgomery;
use crate::modulus::{REDUCEMOD, NONE, ONCE, BARRETT, BARRETTLAZY};
use crate::modulus::REDUCEMOD;
use crate::{apply_unary, apply_binary, apply_ternary};
use itertools::izip;
impl Operations<u64> for Prime<u64>{
impl WordOperations<u64> for Prime<u64>{
/// Applies a modular reduction on x based on REDUCE:
/// - LAZY: no modular reduction.
/// - ONCE: subtracts q if x >= q.
/// - TWO: subtracts 2q if x >= 2q.
/// - FOUR: subtracts 4q if x >= 4q.
/// - BARRETT: maps x to x mod q using Barrett reduction.
/// - BARRETTLAZY: maps x to x mod q using Barrett reduction with values in [0, 2q-1].
#[inline(always)]
fn word_reduce_assign<const REDUCE:REDUCEMOD>(&self, x: &mut u64){
self.montgomery.reduce_assign::<REDUCE>(x);
}
#[inline(always)]
fn add_binary_assign<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &u64, c: &mut u64){
fn word_add_binary_assign<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &u64, c: &mut u64){
*c = a.wrapping_add(*b);
self.montgomery.reduce_assign::<REDUCE>(c);
self.word_reduce_assign::<REDUCE>(c);
}
#[inline(always)]
fn add_unary_assign<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &mut u64){
fn word_add_unary_assign<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &mut u64){
*b = a.wrapping_add(*b);
self.montgomery.reduce_assign::<REDUCE>(b);
self.word_reduce_assign::<REDUCE>(b);
}
#[inline(always)]
fn add_vec_binary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&[u64], c:&mut [u64]){
apply_ternary!(self, Self::add_binary_assign::<REDUCE>, a, b, c, CHUNK);
}
#[inline(always)]
fn add_vec_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&mut [u64]){
apply_binary!(self, Self::add_unary_assign::<REDUCE>, a, b, CHUNK);
}
#[inline(always)]
fn sub_binary_assign<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &u64, c: &mut u64){
fn word_sub_binary_assign<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &u64, c: &mut u64){
*c = a.wrapping_add(self.q.wrapping_sub(*b)).reduce_once(self.q);
}
#[inline(always)]
fn sub_unary_assign<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &mut u64){
fn word_sub_unary_assign<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &mut u64){
*b = a.wrapping_add(self.q.wrapping_sub(*b)).reduce_once(self.q);
}
#[inline(always)]
fn sub_vec_binary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&[u64], c:&mut [u64]){
apply_ternary!(self, Self::sub_binary_assign::<REDUCE>, a, b, c, CHUNK);
}
#[inline(always)]
fn sub_vec_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&mut [u64]){
apply_binary!(self, Self::sub_unary_assign::<REDUCE>, a, b, CHUNK);
}
#[inline(always)]
fn neg_assign<const REDUCE:REDUCEMOD>(&self, a: &mut u64){
fn word_neg_assign<const REDUCE:REDUCEMOD>(&self, a: &mut u64){
*a = self.q.wrapping_sub(*a);
self.montgomery.reduce_assign::<REDUCE>(a)
self.word_reduce_assign::<REDUCE>(a)
}
#[inline(always)]
fn neg_vec_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &mut [u64]){
apply_unary!(self, Self::neg_assign::<REDUCE>, a, CHUNK);
fn word_prepare_montgomery_assign<const REDUCE:REDUCEMOD>(&self, a: &u64, b: &mut Montgomery<u64>){
self.montgomery.prepare_assign::<REDUCE>(*a, b);
}
#[inline(always)]
fn mul_montgomery_external_binary_assign<const REDUCE:REDUCEMOD>(&self, a:& Montgomery<u64>, b:&u64, c: &mut u64){
fn word_mul_montgomery_external_binary_assign<const REDUCE:REDUCEMOD>(&self, a: &Montgomery<u64>, b:&u64, c: &mut u64){
*c = self.montgomery.mul_external::<REDUCE>(*a, *b);
}
#[inline(always)]
fn mul_montgomery_external_unary_assign<const REDUCE:REDUCEMOD>(&self, lhs:&Montgomery<u64>, rhs:&mut u64){
*rhs = self.montgomery.mul_external::<REDUCE>(*lhs, *rhs);
}
#[inline(always)]
fn mul_vec_montgomery_external_binary_assign<const CHUNK:usize,const REDUCE:REDUCEMOD>(&self, a:& [Montgomery<u64>], b:&[u64], c: &mut [u64]){
apply_ternary!(self, Self::mul_montgomery_external_binary_assign::<REDUCE>, a, b, c, CHUNK);
}
#[inline(always)]
fn mul_vec_montgomery_external_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a:&[Montgomery<u64>], b:&mut [u64]){
apply_binary!(self, Self::mul_montgomery_external_unary_assign::<REDUCE>, a, b, CHUNK);
fn word_mul_montgomery_external_unary_assign<const REDUCE:REDUCEMOD>(&self, lhs:&Montgomery<u64>, rhs:&mut u64){
self.montgomery.mul_external_assign::<REDUCE>(*lhs, rhs);
}
}
impl VecOperations<u64> for Prime<u64>{
/// Applies a modular reduction on x based on REDUCE:
/// - LAZY: no modular reduction.
/// - ONCE: subtracts q if x >= q.
/// - TWO: subtracts 2q if x >= 2q.
/// - FOUR: subtracts 4q if x >= 4q.
/// - BARRETT: maps x to x mod q using Barrett reduction.
/// - BARRETTLAZY: maps x to x mod q using Barrett reduction with values in [0, 2q-1].
#[inline(always)]
fn vec_reduce_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, x: &mut [u64]){
apply_unary!(self, Self::word_reduce_assign::<REDUCE>, x, CHUNK);
}
#[inline(always)]
fn vec_add_binary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&[u64], c:&mut [u64]){
apply_ternary!(self, Self::word_add_binary_assign::<REDUCE>, a, b, c, CHUNK);
}
#[inline(always)]
fn vec_add_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&mut [u64]){
apply_binary!(self, Self::word_add_unary_assign::<REDUCE>, a, b, CHUNK);
}
#[inline(always)]
fn vec_sub_binary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&[u64], c:&mut [u64]){
apply_ternary!(self, Self::word_sub_binary_assign::<REDUCE>, a, b, c, CHUNK);
}
#[inline(always)]
fn vec_sub_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b:&mut [u64]){
apply_binary!(self, Self::word_sub_unary_assign::<REDUCE>, a, b, CHUNK);
}
#[inline(always)]
fn vec_neg_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &mut [u64]){
apply_unary!(self, Self::word_neg_assign::<REDUCE>, a, CHUNK);
}
#[inline(always)]
fn vec_prepare_montgomery_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a: &[u64], b: &mut [Montgomery<u64>]){
apply_binary!(self, Self::word_prepare_montgomery_assign::<REDUCE>, a, b, CHUNK);
}
#[inline(always)]
fn vec_mul_montgomery_external_binary_assign<const CHUNK:usize,const REDUCE:REDUCEMOD>(&self, a:& [Montgomery<u64>], b:&[u64], c: &mut [u64]){
apply_ternary!(self, Self::word_mul_montgomery_external_binary_assign::<REDUCE>, a, b, c, CHUNK);
}
#[inline(always)]
fn vec_mul_montgomery_external_unary_assign<const CHUNK:usize, const REDUCE:REDUCEMOD>(&self, a:& [Montgomery<u64>], b:&mut [u64]){
apply_binary!(self, Self::word_mul_montgomery_external_unary_assign::<REDUCE>, a, b, CHUNK);
}
}

16
src/modulus/impl_u64/prime.rs
View File

@@ -1,6 +1,6 @@
use crate::modulus::prime::Prime;
use crate::modulus::montgomery::{Montgomery, MontgomeryPrecomp};
use crate::modulus::shoup::{ShoupPrecomp};
use crate::modulus::barrett::BarrettPrecomp;
use crate::modulus::ONCE;
use primality_test::is_prime;
use prime_factorization::Factorization;
@@ -34,11 +34,13 @@ impl Prime<u64>{
let mut prime: Prime<u64> = Self {
q:q,
two_q:q<<1,
four_q:q<<2,
q_base:q_base,
q_power:q_power,
factors: Vec::new(),
montgomery:MontgomeryPrecomp::new(q),
shoup:ShoupPrecomp::new(q),
barrett:BarrettPrecomp::new(q),
phi:phi,
};
@@ -101,7 +103,7 @@ impl Prime<u64>{
for &factor in &self.factors{
if Pow(candidate, (self.q_base-1)/factor, self.q_base) == 1{
if pow(candidate, (self.q_base-1)/factor, self.q_base) == 1{
not_found = true;
break
}
@@ -124,7 +126,7 @@ impl Prime<u64>{
let psi: u64 = self.primitive_root();
// nth primitive root mod q_base: psi_nth^(prime.q_base-1)/nth_root mod q_base
let psi_nth_q_base: u64 = Pow(psi, (self.q_base-1)/nth_root, self.q_base);
let psi_nth_q_base: u64 = pow(psi, (self.q_base-1)/nth_root, self.q_base);
// lifts nth primitive root mod q_base to q = q_base^q_power
let psi_nth_q: u64 = self.hensel_lift(psi_nth_q_base, nth_root);
@@ -171,7 +173,7 @@ impl Prime<u64>{
/// Returns (psi + a * q_base)^{nth_root} = 1 mod q = q_base^q_power given psi^{nth_root} = 1 mod q_base.
/// Panics if psi^{nth_root} != 1 mod q_base.
fn hensel_lift(&self, psi: u64, nth_root: u64) -> u64{
assert!(Pow(psi, nth_root, self.q_base)==1, "invalid argument psi: psi^nth_root = {} != 1", Pow(psi, nth_root, self.q_base));
assert!(pow(psi, nth_root, self.q_base)==1, "invalid argument psi: psi^nth_root = {} != 1", pow(psi, nth_root, self.q_base));
let mut psi_mont: Montgomery<u64> = self.montgomery.prepare::<ONCE>(psi);
let nth_root_mont: Montgomery<u64> = self.montgomery.prepare::<ONCE>(nth_root);
@@ -180,7 +182,7 @@ impl Prime<u64>{
let psi_pow: Montgomery<u64> = self.montgomery.pow(psi_mont, nth_root-1);
let num: Montgomery<u64> = Montgomery(self.montgomery.one().value() + self.q - self.montgomery.mul_internal::<ONCE>(psi_pow, psi_mont).value());
let num: Montgomery<u64> = self.montgomery.one() + self.q - self.montgomery.mul_internal::<ONCE>(psi_pow, psi_mont);
let mut den: Montgomery<u64> = self.montgomery.mul_internal::<ONCE>(nth_root_mont, psi_pow);
@@ -197,7 +199,7 @@ impl Prime<u64>{
/// This function internally instantiate a new MontgomeryPrecomp<u64>
/// To be used when called only a few times and if there
/// is no Prime instantiated with q.
pub fn Pow(x:u64, exponent:u64, q:u64) -> u64{
pub fn pow(x:u64, exponent:u64, q:u64) -> u64{
let montgomery: MontgomeryPrecomp<u64> = MontgomeryPrecomp::<u64>::new(q);
let mut y_mont: Montgomery<u64> = montgomery.one();
let mut x_mont: Montgomery<u64> = montgomery.prepare::<ONCE>(x);

60
src/modulus/impl_u64/shoup.rs
View File

@@ -1,60 +0,0 @@
use crate::modulus::ReduceOnce;
use crate::modulus::shoup::{ShoupPrecomp, Shoup};
impl ShoupPrecomp<u64>{
pub fn new(q: u64) -> Self {
let mut precomp: ShoupPrecomp<u64> = Self{q:q, one:Shoup(0,0)};
precomp.one = precomp.prepare(1);
precomp
}
#[inline(always)]
pub fn one(&self) -> Shoup<u64> {
self.one
}
#[inline(always)]
pub fn prepare(&self, v: u64) -> Shoup<u64> {
debug_assert!(v < self.q);
let quotient: u64 = (((v as u128) << 64) / self.q as u128) as _;
Shoup(v, quotient)
}
#[inline(always)]
pub fn mul_external(&self, lhs: Shoup<u64>, rhs: u64) -> u64 {
let mut r: u64 = self.mul_external_lazy(lhs, rhs);
r.reduce_once_assign(self.q);
r
}
#[inline(always)]
pub fn mul_external_assign(&self, lhs: Shoup<u64>, rhs: &mut u64){
self.mul_external_lazy_assign(lhs, rhs);
rhs.reduce_once_assign(self.q);
}
#[inline(always)]
pub fn mul_external_lazy(&self, lhs: Shoup<u64>, rhs: u64) -> u64 {
let mut r: u64 = rhs;
self.mul_external_lazy_assign(lhs, &mut r);
r
}
#[inline(always)]
pub fn mul_external_lazy_assign(&self, lhs: Shoup<u64>, rhs: &mut u64){
let t: u64 = ((*lhs.quotient() as u128 * *rhs as u128) >> 64) as _;
*rhs = (rhs.wrapping_mul(*lhs.value())).wrapping_sub(self.q.wrapping_mul(t));
}
#[inline(always)]
pub fn reduce_assign(&self, rhs: &mut u64){
self.reduce_assign_lazy(rhs);
rhs.reduce_once_assign(self.q);
}
#[inline(always)]
pub fn reduce_assign_lazy(&self, rhs: &mut u64){
*rhs = rhs.wrapping_sub(self.q.wrapping_mul(((self.one.1 as u128 * *rhs as u128) >> 64) as _))
}
}

30
src/modulus/montgomery.rs
View File

@@ -2,35 +2,7 @@ use crate::modulus::barrett::BarrettPrecomp;
/// Montgomery is a generic struct storing
/// an element in the Montgomery domain.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub struct Montgomery<O>(pub O);
/// Implements helper methods on the struct Montgomery<O>.
impl<O> Montgomery<O>{
#[inline(always)]
pub fn new(lhs: O) -> Self{
Self(lhs)
}
#[inline(always)]
pub fn value(&self) -> &O{
&self.0
}
pub fn value_mut(&mut self) -> &mut O{
&mut self.0
}
}
/// Default instantiation.
impl<O> Default for Montgomery<O> where O:Default {
fn default() -> Self {
Self {
0: O::default(),
}
}
}
pub type Montgomery<O> = O;
/// MontgomeryPrecomp is a generic struct storing
/// precomputations for Montgomery arithmetic.

6
src/modulus/prime.rs
View File

@@ -1,14 +1,16 @@
use crate::modulus::montgomery::MontgomeryPrecomp;
use crate::modulus::shoup::ShoupPrecomp;
use crate::modulus::barrett::BarrettPrecomp;
#[derive(Clone, Debug, PartialEq, Eq)]
pub struct Prime<O> {
pub q: O, /// q_base^q_powers
pub two_q: O,
pub four_q: O,
pub q_base: O,
pub q_power: usize,
pub factors: Vec<O>, /// distinct factors of q-1
pub montgomery: MontgomeryPrecomp<O>,
pub shoup:ShoupPrecomp<O>,
pub barrett:BarrettPrecomp<O>,
pub phi: O,
}

22
src/modulus/shoup.rs
View File

@@ -1,22 +0,0 @@
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub struct Shoup<O>(pub O, pub O);
impl<O> Shoup<O> {
#[inline(always)]
pub fn value(&self) -> &O {
&self.0
}
#[inline(always)]
pub fn quotient(&self) -> &O {
&self.1
}
}
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub struct ShoupPrecomp<O>{
pub q: O,
pub one: Shoup<O>,
}

3
src/ring/impl_u64/automorphism.rs
View File

@@ -5,7 +5,7 @@ use crate::poly::Poly;
/// Returns a lookup table for the automorphism X^{i} -> X^{i * k mod nth_root}.
/// Method will panic if n or nth_root are not power-of-two.
/// Method will panic if gal_el is not coprime with nth_root.
pub fn automorphism_index_ntt(n: usize, nth_root:u64, gal_el: u64) -> (Vec<u64>){
pub fn automorphism_index_ntt(n: usize, nth_root:u64, gal_el: u64) -> Vec<u64>{
assert!(n&(n-1) != 0, "invalid n={}: not a power-of-two", n);
assert!(nth_root&(nth_root-1) != 0, "invalid nth_root={}: not a power-of-two", n);
assert!(gal_el & 1 == 1, "invalid gal_el={}: not coprime with nth_root={}", gal_el, nth_root);
@@ -39,6 +39,5 @@ impl Ring<u64>{
let i_out: u64 = gal_el_i & mask;
b_vec[i_out as usize] = ai * (sign^1) | (q - ai) * sign
});
}
}

37
src/ring/impl_u64/ring.rs
View File

@@ -1,7 +1,6 @@
use crate::ring::Ring;
use crate::dft::ntt::Table;
use crate::modulus::prime::Prime;
use crate::modulus::montgomery::Montgomery;
use crate::poly::Poly;
impl Ring<u64>{
@@ -18,15 +17,37 @@ impl Ring<u64>{
return self.n
}
fn new_poly_core<O>(&self) -> Poly<O> where O: Default + Clone {
Poly::<O>::new(self.n())
}
pub fn new_poly(&self) -> Poly<u64>{
self.new_poly_core::<u64>()
Poly::<u64>::new(self.n())
}
pub fn new_poly_montgomery(&self) -> Poly<Montgomery<u64>>{
self.new_poly_core::<Montgomery<u64>>()
pub fn ntt_inplace<const LAZY:bool>(&self, poly: &mut Poly<u64>){
match LAZY{
true => self.dft.forward_inplace_lazy(&mut poly.0),
false => self.dft.forward_inplace(&mut poly.0)
}
}
pub fn intt_inplace<const LAZY:bool>(&self, poly: &mut Poly<u64>){
match LAZY{
true => self.dft.forward_inplace_lazy(&mut poly.0),
false => self.dft.forward_inplace(&mut poly.0)
}
}
pub fn ntt<const LAZY:bool>(&self, poly_in: &Poly<u64>, poly_out: &mut Poly<u64>){
poly_out.0.copy_from_slice(&poly_in.0);
match LAZY{
true => self.dft.backward_inplace_lazy(&mut poly_out.0),
false => self.dft.backward_inplace(&mut poly_out.0)
}
}
pub fn intt<const LAZY:bool>(&self, poly_in: &Poly<u64>, poly_out: &mut Poly<u64>){
poly_out.0.copy_from_slice(&poly_in.0);
match LAZY{
true => self.dft.backward_inplace_lazy(&mut poly_out.0),
false => self.dft.backward_inplace(&mut poly_out.0)
}
}
}