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// Copyright 2015-2023 Brian Smith.
//
// Permission to use, copy, modify, and/or distribute this software for any
// purpose with or without fee is hereby granted, provided that the above
// copyright notice and this permission notice appear in all copies.
//
// THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHORS DISCLAIM ALL WARRANTIES
// WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY
// SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
// WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
// OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
// CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
use super::{BoxedLimbs, Elem, PublicModulus, Unencoded, N0};
use crate::{
bits::BitLength,
cpu, error,
limb::{self, Limb, LimbMask, LIMB_BITS},
polyfill::LeadingZerosStripped,
};
use core::marker::PhantomData;
/// The x86 implementation of `bn_mul_mont`, at least, requires at least 4
/// limbs. For a long time we have required 4 limbs for all targets, though
/// this may be unnecessary. TODO: Replace this with
/// `n.len() < 256 / LIMB_BITS` so that 32-bit and 64-bit platforms behave the
/// same.
pub const MODULUS_MIN_LIMBS: usize = 4;
pub const MODULUS_MAX_LIMBS: usize = super::super::BIGINT_MODULUS_MAX_LIMBS;
/// The modulus *m* for a ring ℤ/mℤ, along with the precomputed values needed
/// for efficient Montgomery multiplication modulo *m*. The value must be odd
/// and larger than 2. The larger-than-1 requirement is imposed, at least, by
/// the modular inversion code.
pub struct OwnedModulus<M> {
limbs: BoxedLimbs<M>, // Also `value >= 3`.
// n0 * N == -1 (mod r).
//
// r == 2**(N0::LIMBS_USED * LIMB_BITS) and LG_LITTLE_R == lg(r). This
// ensures that we can do integer division by |r| by simply ignoring
// `N0::LIMBS_USED` limbs. Similarly, we can calculate values modulo `r` by
// just looking at the lowest `N0::LIMBS_USED` limbs. This is what makes
// Montgomery multiplication efficient.
//
// As shown in Algorithm 1 of "Fast Prime Field Elliptic Curve Cryptography
// with 256 Bit Primes" by Shay Gueron and Vlad Krasnov, in the loop of a
// multi-limb Montgomery multiplication of a * b (mod n), given the
// unreduced product t == a * b, we repeatedly calculate:
//
// t1 := t % r |t1| is |t|'s lowest limb (see previous paragraph).
// t2 := t1*n0*n
// t3 := t + t2
// t := t3 / r copy all limbs of |t3| except the lowest to |t|.
//
// In the last step, it would only make sense to ignore the lowest limb of
// |t3| if it were zero. The middle steps ensure that this is the case:
//
// t3 == 0 (mod r)
// t + t2 == 0 (mod r)
// t + t1*n0*n == 0 (mod r)
// t1*n0*n == -t (mod r)
// t*n0*n == -t (mod r)
// n0*n == -1 (mod r)
// n0 == -1/n (mod r)
//
// Thus, in each iteration of the loop, we multiply by the constant factor
// n0, the negative inverse of n (mod r).
//
// TODO(perf): Not all 32-bit platforms actually make use of n0[1]. For the
// ones that don't, we could use a shorter `R` value and use faster `Limb`
// calculations instead of double-precision `u64` calculations.
n0: N0,
len_bits: BitLength,
}
impl<M: PublicModulus> Clone for OwnedModulus<M> {
fn clone(&self) -> Self {
Self {
limbs: self.limbs.clone(),
n0: self.n0,
len_bits: self.len_bits,
}
}
}
impl<M> OwnedModulus<M> {
pub(crate) fn from_be_bytes(input: untrusted::Input) -> Result<Self, error::KeyRejected> {
let n = BoxedLimbs::positive_minimal_width_from_be_bytes(input)?;
if n.len() > MODULUS_MAX_LIMBS {
return Err(error::KeyRejected::too_large());
}
if n.len() < MODULUS_MIN_LIMBS {
return Err(error::KeyRejected::unexpected_error());
}
if limb::limbs_are_even_constant_time(&n) != LimbMask::False {
return Err(error::KeyRejected::invalid_component());
}
if limb::limbs_less_than_limb_constant_time(&n, 3) != LimbMask::False {
return Err(error::KeyRejected::unexpected_error());
}
// n_mod_r = n % r. As explained in the documentation for `n0`, this is
// done by taking the lowest `N0::LIMBS_USED` limbs of `n`.
#[allow(clippy::useless_conversion)]
let n0 = {
prefixed_extern! {
fn bn_neg_inv_mod_r_u64(n: u64) -> u64;
}
// XXX: u64::from isn't guaranteed to be constant time.
let mut n_mod_r: u64 = u64::from(n[0]);
if N0::LIMBS_USED == 2 {
// XXX: If we use `<< LIMB_BITS` here then 64-bit builds
// fail to compile because of `deny(exceeding_bitshifts)`.
debug_assert_eq!(LIMB_BITS, 32);
n_mod_r |= u64::from(n[1]) << 32;
}
N0::precalculated(unsafe { bn_neg_inv_mod_r_u64(n_mod_r) })
};
let len_bits = limb::limbs_minimal_bits(&n);
Ok(Self {
limbs: n,
n0,
len_bits,
})
}
pub fn verify_less_than<L>(&self, l: &Modulus<L>) -> Result<(), error::Unspecified> {
if self.len_bits() > l.len_bits()
|| (self.limbs.len() == l.limbs().len()
&& limb::limbs_less_than_limbs_consttime(&self.limbs, l.limbs()) != LimbMask::True)
{
return Err(error::Unspecified);
}
Ok(())
}
pub fn to_elem<L>(&self, l: &Modulus<L>) -> Result<Elem<L, Unencoded>, error::Unspecified> {
self.verify_less_than(l)?;
let mut limbs = BoxedLimbs::zero(l.limbs.len());
limbs[..self.limbs.len()].copy_from_slice(&self.limbs);
Ok(Elem {
limbs,
encoding: PhantomData,
})
}
pub(crate) fn modulus(&self, cpu_features: cpu::Features) -> Modulus<M> {
Modulus {
limbs: &self.limbs,
n0: self.n0,
len_bits: self.len_bits,
m: PhantomData,
cpu_features,
}
}
pub fn len_bits(&self) -> BitLength {
self.len_bits
}
}
impl<M: PublicModulus> OwnedModulus<M> {
pub fn be_bytes(&self) -> LeadingZerosStripped<impl ExactSizeIterator<Item = u8> + Clone + '_> {
LeadingZerosStripped::new(limb::unstripped_be_bytes(&self.limbs))
}
}
pub struct Modulus<'a, M> {
limbs: &'a [Limb],
n0: N0,
len_bits: BitLength,
m: PhantomData<M>,
cpu_features: cpu::Features,
}
impl<M> Modulus<'_, M> {
pub(super) fn oneR(&self, out: &mut [Limb]) {
assert_eq!(self.limbs.len(), out.len());
let r = self.limbs.len() * LIMB_BITS;
// out = 2**r - m where m = self.
limb::limbs_negative_odd(out, self.limbs);
let lg_m = self.len_bits().as_bits();
let leading_zero_bits_in_m = r - lg_m;
// When m's length is a multiple of LIMB_BITS, which is the case we
// most want to optimize for, then we already have
// out == 2**r - m == 2**r (mod m).
if leading_zero_bits_in_m != 0 {
debug_assert!(leading_zero_bits_in_m < LIMB_BITS);
// Correct out to 2**(lg m) (mod m). `limbs_negative_odd` flipped
// all the leading zero bits to ones. Flip them back.
*out.last_mut().unwrap() &= (!0) >> leading_zero_bits_in_m;
// Now we have out == 2**(lg m) (mod m). Keep doubling until we get
// to 2**r (mod m).
for _ in 0..leading_zero_bits_in_m {
limb::limbs_double_mod(out, self.limbs)
}
}
// Now out == 2**r (mod m) == 1*R.
}
// TODO: XXX Avoid duplication with `Modulus`.
pub(super) fn zero<E>(&self) -> Elem<M, E> {
Elem {
limbs: BoxedLimbs::zero(self.limbs.len()),
encoding: PhantomData,
}
}
#[inline]
pub(super) fn limbs(&self) -> &[Limb] {
self.limbs
}
#[inline]
pub(super) fn n0(&self) -> &N0 {
&self.n0
}
pub fn len_bits(&self) -> BitLength {
self.len_bits
}
#[inline]
pub(crate) fn cpu_features(&self) -> cpu::Features {
self.cpu_features
}
}