mirror of
https://github.com/pezkuwichain/bizinikiwi-bn.git
synced 2026-06-14 09:51:04 +00:00
Sean Bowe
409 lines
9.5 KiB
Rust
409 lines
9.5 KiB
Rust
use std::cmp::Ordering;
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use rand::Rng;
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use rustc_serialize::{Encodable, Encoder, Decodable, Decoder};
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use byteorder::{ByteOrder, BigEndian};
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/// 256-bit, stack allocated biginteger for use in prime field
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/// arithmetic.
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#[derive(Copy, Clone, Debug, PartialEq, Eq)]
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#[repr(C)]
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pub struct U256(pub [u64; 4]);
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impl Encodable for U256 {
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fn encode<S: Encoder>(&self, s: &mut S) -> Result<(), S::Error> {
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let mut buf = [0; 32];
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BigEndian::write_u64(&mut buf[0..], self.0[3]);
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BigEndian::write_u64(&mut buf[8..], self.0[2]);
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BigEndian::write_u64(&mut buf[16..], self.0[1]);
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BigEndian::write_u64(&mut buf[24..], self.0[0]);
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for i in 0..32 {
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try!(s.emit_u8(buf[i]));
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}
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Ok(())
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}
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}
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impl Decodable for U256 {
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fn decode<S: Decoder>(s: &mut S) -> Result<U256, S::Error> {
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let mut buf = [0; 32];
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for i in 0..32 {
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buf[i] = try!(s.read_u8());
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}
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let mut n = [0; 4];
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n[3] = BigEndian::read_u64(&buf[0..]);
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n[2] = BigEndian::read_u64(&buf[8..]);
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n[1] = BigEndian::read_u64(&buf[16..]);
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n[0] = BigEndian::read_u64(&buf[24..]);
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Ok(U256(n))
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}
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}
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impl Ord for U256 {
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#[inline]
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fn cmp(&self, other: &U256) -> Ordering {
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for (a, b) in self.0.iter().zip(other.0.iter()).rev() {
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if *a < *b {
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return Ordering::Less;
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} else if *a > *b {
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return Ordering::Greater;
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}
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}
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return Ordering::Equal;
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}
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}
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impl PartialOrd for U256 {
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#[inline]
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fn partial_cmp(&self, other: &U256) -> Option<Ordering> {
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Some(self.cmp(other))
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}
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}
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impl U256 {
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#[inline]
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pub fn zero() -> U256 {
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U256([0, 0, 0, 0])
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}
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#[inline]
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pub fn one() -> U256 {
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U256([1, 0, 0, 0])
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}
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/// Produce a random number (mod `modulo`)
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pub fn random<R: Rng>(rng: &mut R, modulo: &U256) -> U256
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{
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let mut res;
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loop {
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res = U256(rng.gen());
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for (i, x) in modulo.bits().enumerate() {
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if !x {
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assert!(res.set_bit(255 - i, false));
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} else {
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break;
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}
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}
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if &res < modulo { break; }
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}
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res
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}
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pub fn is_zero(&self) -> bool {
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self.0[0] == 0 &&
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self.0[1] == 0 &&
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self.0[2] == 0 &&
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self.0[3] == 0
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}
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pub fn set_bit(&mut self, n: usize, to: bool) -> bool
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{
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if n >= 256 {
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false
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} else {
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let part = n / 64;
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let bit = n - (64 * part);
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if to {
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self.0[part] |= 1 << bit;
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} else {
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self.0[part] &= !(1 << bit);
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}
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true
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}
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}
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pub fn get_bit(&self, n: usize) -> Option<bool>
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{
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if n >= 256 {
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None
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} else {
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let part = n / 64;
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let bit = n - (64 * part);
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Some(self.0[part] & (1 << bit) > 0)
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}
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}
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/// Add `other` to `self` (mod `modulo`)
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pub fn add(&mut self, other: &U256, modulo: &U256) {
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add_nocarry(&mut self.0, &other.0);
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if *self >= *modulo {
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sub_noborrow(&mut self.0, &modulo.0);
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}
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}
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/// Subtract `other` from `self` (mod `modulo`)
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pub fn sub(&mut self, other: &U256, modulo: &U256) {
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if *self < *other {
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add_nocarry(&mut self.0, &modulo.0);
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}
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sub_noborrow(&mut self.0, &other.0);
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}
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/// Multiply `self` by `other` (mod `modulo`) via the Montgomery
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/// multiplication method.
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pub fn mul(&mut self, other: &U256, modulo: &U256, inv: u64) {
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mul_reduce(&mut self.0, &other.0, &modulo.0, inv);
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if *self >= *modulo {
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sub_noborrow(&mut self.0, &modulo.0);
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}
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}
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/// Turn `self` into its additive inverse (mod `modulo`)
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pub fn neg(&mut self, modulo: &U256) {
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if *self > Self::zero() {
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let mut tmp = modulo.0;
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sub_noborrow(&mut tmp, &self.0);
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self.0 = tmp;
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}
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}
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#[inline]
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pub fn is_even(&self) -> bool {
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self.0[0] & 1 == 0
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}
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/// Turn `self` into its multiplicative inverse (mod `modulo`)
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pub fn invert(&mut self, modulo: &U256) {
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// Guajardo Kumar Paar Pelzl
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// Efficient Software-Implementation of Finite Fields with Applications to Cryptography
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// Algorithm 16 (BEA for Inversion in Fp)
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let mut u = *self;
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let mut v = *modulo;
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let mut b = U256::one();
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let mut c = U256::zero();
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while u != U256::one() && v != U256::one() {
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while u.is_even() {
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div2(&mut u.0);
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if b.is_even() {
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div2(&mut b.0);
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} else {
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add_nocarry(&mut b.0, &modulo.0);
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div2(&mut b.0);
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}
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}
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while v.is_even() {
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div2(&mut v.0);
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if c.is_even() {
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div2(&mut c.0);
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} else {
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add_nocarry(&mut c.0, &modulo.0);
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div2(&mut c.0);
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}
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}
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if u >= v {
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sub_noborrow(&mut u.0, &v.0);
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b.sub(&c, modulo);
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} else {
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sub_noborrow(&mut v.0, &u.0);
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c.sub(&b, modulo);
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}
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}
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if u == U256::one() {
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self.0 = b.0;
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} else {
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self.0 = c.0;
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}
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}
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/// Return an Iterator<Item=bool> over all bits from
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/// MSB to LSB.
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pub fn bits(&self) -> BitIterator {
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BitIterator {
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int: &self,
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n: 256
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}
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}
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}
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pub struct BitIterator<'a> {
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int: &'a U256,
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n: usize
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}
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impl<'a> Iterator for BitIterator<'a> {
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type Item = bool;
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fn next(&mut self) -> Option<bool> {
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if self.n == 0 {
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None
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}
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else {
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self.n -= 1;
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self.int.get_bit(self.n)
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}
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}
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}
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/// Divide by two
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#[inline]
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fn div2(a: &mut [u64; 4]) {
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let mut t = a[3] << 63;
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a[3] = a[3] >> 1;
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let b = a[2] << 63;
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a[2] >>= 1;
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a[2] |= t;
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t = a[1] << 63;
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a[1] >>= 1;
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a[1] |= b;
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a[0] >>= 1;
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a[0] |= t;
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}
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#[inline(always)]
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fn split_u64(i: u64) -> (u64, u64) {
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(i >> 32, i & 0xFFFFFFFF)
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}
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#[inline(always)]
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fn combine_u64(hi: u64, lo: u64) -> u64 {
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(hi << 32) | lo
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}
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#[inline]
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fn add_nocarry(a: &mut [u64; 4], b: &[u64; 4]) {
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#[inline]
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fn adc(a: u64, b: u64, carry: &mut u64) -> u64 {
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let (a1, a0) = split_u64(a);
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let (b1, b0) = split_u64(b);
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let (c, r0) = split_u64(a0 + b0 + *carry);
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let (c, r1) = split_u64(a1 + b1 + c);
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*carry = c;
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combine_u64(r1, r0)
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}
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let mut carry = 0;
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for (a, b) in a.into_iter().zip(b.iter()) {
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*a = adc(*a, *b, &mut carry);
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}
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debug_assert!(0 == carry);
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}
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#[inline]
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fn sub_noborrow(a: &mut [u64; 4], b: &[u64; 4]) {
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#[inline]
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fn sbb(a: u64, b: u64, borrow: &mut u64) -> u64 {
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let (a1, a0) = split_u64(a);
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let (b1, b0) = split_u64(b);
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let (b, r0) = split_u64((1 << 32) + a0 - b0 - *borrow);
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let (b, r1) = split_u64((1 << 32) + a1 - b1 - ((b == 0) as u64));
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*borrow = (b == 0) as u64;
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combine_u64(r1, r0)
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}
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let mut borrow = 0;
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for (a, b) in a.into_iter().zip(b.iter()) {
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*a = sbb(*a, *b, &mut borrow);
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}
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debug_assert!(0 == borrow);
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}
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#[inline]
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fn mul_reduce(
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this: &mut [u64; 4],
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by: &[u64; 4],
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modulus: &[u64; 4],
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inv: u64
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)
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{
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fn mac_digit(acc: &mut [u64], b: &[u64], c: u64)
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{
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#[inline]
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fn mac_with_carry(a: u64, b: u64, c: u64, carry: &mut u64) -> u64 {
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let (b_hi, b_lo) = split_u64(b);
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let (c_hi, c_lo) = split_u64(c);
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let (a_hi, a_lo) = split_u64(a);
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let (carry_hi, carry_lo) = split_u64(*carry);
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let (x_hi, x_lo) = split_u64(b_lo * c_lo + a_lo + carry_lo);
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let (y_hi, y_lo) = split_u64(b_lo * c_hi);
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let (z_hi, z_lo) = split_u64(b_hi * c_lo);
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let (r_hi, r_lo) = split_u64(x_hi + y_lo + z_lo + a_hi + carry_hi);
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*carry = (b_hi * c_hi) + r_hi + y_hi + z_hi;
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combine_u64(r_lo, x_lo)
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}
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if c == 0 {
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return;
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}
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let mut b_iter = b.iter();
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let mut carry = 0;
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for ai in acc.iter_mut() {
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if let Some(bi) = b_iter.next() {
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*ai = mac_with_carry(*ai, *bi, c, &mut carry);
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} else if carry != 0 {
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*ai = mac_with_carry(*ai, 0, c, &mut carry);
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} else {
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break;
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}
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}
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debug_assert!(carry == 0);
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}
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// The Montgomery reduction here is based on Algorithm 14.32 in
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// Handbook of Applied Cryptography
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// <http://cacr.uwaterloo.ca/hac/about/chap14.pdf>.
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let mut res = [0; 2*4];
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for (i, xi) in this.iter().enumerate() {
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mac_digit(&mut res[i..], by, *xi);
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}
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for i in 0..4 {
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let k = inv.wrapping_mul(res[i]);
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mac_digit(&mut res[i..], modulus, k);
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}
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this.copy_from_slice(&res[4..]);
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}
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#[test]
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fn setting_bits() {
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let rng = &mut ::rand::thread_rng();
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let modulo = U256([0xffffffffffffffff; 4]);
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let a = U256::random(rng, &modulo);
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let mut e = U256::zero();
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for (i, b) in a.bits().enumerate() {
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assert!(e.set_bit(255 - i, b));
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}
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assert_eq!(a, e);
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}
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