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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.
//! Multi-precision integers.
//!
//! # Modular Arithmetic.
//!
//! Modular arithmetic is done in finite commutative rings ℤ/mℤ for some
//! modulus *m*. We work in finite commutative rings instead of finite fields
//! because the RSA public modulus *n* is not prime, which means ℤ/nℤ contains
//! nonzero elements that have no multiplicative inverse, so ℤ/nℤ is not a
//! finite field.
//!
//! In some calculations we need to deal with multiple rings at once. For
//! example, RSA private key operations operate in the rings ℤ/nℤ, ℤ/pℤ, and
//! ℤ/qℤ. Types and functions dealing with such rings are all parameterized
//! over a type `M` to ensure that we don't wrongly mix up the math, e.g. by
//! multiplying an element of ℤ/pℤ by an element of ℤ/qℤ modulo q. This follows
//! the "unit" pattern described in [Static checking of units in Servo].
//!
//! `Elem` also uses the static unit checking pattern to statically track the
//! Montgomery factors that need to be canceled out in each value using it's
//! `E` parameter.
//!
//! [Static checking of units in Servo]:
//! https://blog.mozilla.org/research/2014/06/23/static-checking-of-units-in-servo/
use self::boxed_limbs::BoxedLimbs;
pub(crate) use self::{
modulus::{Modulus, OwnedModulus, MODULUS_MAX_LIMBS},
private_exponent::PrivateExponent,
};
use crate::{
arithmetic::montgomery::*,
bits::BitLength,
c, error,
limb::{self, Limb, LimbMask, LIMB_BITS},
};
use alloc::vec;
use core::{marker::PhantomData, num::NonZeroU64};
mod boxed_limbs;
mod modulus;
mod private_exponent;
pub trait PublicModulus {}
/// Elements of ℤ/mℤ for some modulus *m*.
//
// Defaulting `E` to `Unencoded` is a convenience for callers from outside this
// submodule. However, for maximum clarity, we always explicitly use
// `Unencoded` within the `bigint` submodule.
pub struct Elem<M, E = Unencoded> {
limbs: BoxedLimbs<M>,
/// The number of Montgomery factors that need to be canceled out from
/// `value` to get the actual value.
encoding: PhantomData<E>,
}
// TODO: `derive(Clone)` after https://github.com/rust-lang/rust/issues/26925
// is resolved or restrict `M: Clone` and `E: Clone`.
impl<M, E> Clone for Elem<M, E> {
fn clone(&self) -> Self {
Self {
limbs: self.limbs.clone(),
encoding: self.encoding,
}
}
}
impl<M, E> Elem<M, E> {
#[inline]
pub fn is_zero(&self) -> bool {
self.limbs.is_zero()
}
}
/// Does a Montgomery reduction on `limbs` assuming they are Montgomery-encoded ('R') and assuming
/// they are the same size as `m`, but perhaps not reduced mod `m`. The result will be
/// fully reduced mod `m`.
fn from_montgomery_amm<M>(limbs: BoxedLimbs<M>, m: &Modulus<M>) -> Elem<M, Unencoded> {
debug_assert_eq!(limbs.len(), m.limbs().len());
let mut limbs = limbs;
let mut one = [0; MODULUS_MAX_LIMBS];
one[0] = 1;
let one = &one[..m.limbs().len()];
limbs_mont_mul(&mut limbs, one, m.limbs(), m.n0(), m.cpu_features());
Elem {
limbs,
encoding: PhantomData,
}
}
#[cfg(any(test, not(target_arch = "x86_64")))]
impl<M> Elem<M, R> {
#[inline]
pub fn into_unencoded(self, m: &Modulus<M>) -> Elem<M, Unencoded> {
from_montgomery_amm(self.limbs, m)
}
}
impl<M> Elem<M, Unencoded> {
pub fn from_be_bytes_padded(
input: untrusted::Input,
m: &Modulus<M>,
) -> Result<Self, error::Unspecified> {
Ok(Self {
limbs: BoxedLimbs::from_be_bytes_padded_less_than(input, m)?,
encoding: PhantomData,
})
}
#[inline]
pub fn fill_be_bytes(&self, out: &mut [u8]) {
// See Falko Strenzke, "Manger's Attack revisited", ICICS 2010.
limb::big_endian_from_limbs(&self.limbs, out)
}
fn is_one(&self) -> bool {
limb::limbs_equal_limb_constant_time(&self.limbs, 1) == LimbMask::True
}
}
pub fn elem_mul<M, AF, BF>(
a: &Elem<M, AF>,
mut b: Elem<M, BF>,
m: &Modulus<M>,
) -> Elem<M, <(AF, BF) as ProductEncoding>::Output>
where
(AF, BF): ProductEncoding,
{
limbs_mont_mul(&mut b.limbs, &a.limbs, m.limbs(), m.n0(), m.cpu_features());
Elem {
limbs: b.limbs,
encoding: PhantomData,
}
}
// r *= 2.
fn elem_double<M, AF>(r: &mut Elem<M, AF>, m: &Modulus<M>) {
limb::limbs_double_mod(&mut r.limbs, m.limbs())
}
// TODO: This is currently unused, but we intend to eventually use this to
// reduce elements (x mod q) mod p in the RSA CRT. If/when we do so, we
// should update the testing so it is reflective of that usage, instead of
// the old usage.
pub fn elem_reduced_once<A, M>(
a: &Elem<A, Unencoded>,
m: &Modulus<M>,
other_modulus_len_bits: BitLength,
) -> Elem<M, Unencoded> {
assert_eq!(m.len_bits(), other_modulus_len_bits);
let mut r = a.limbs.clone();
limb::limbs_reduce_once_constant_time(&mut r, m.limbs());
Elem {
limbs: BoxedLimbs::new_unchecked(r.into_limbs()),
encoding: PhantomData,
}
}
#[inline]
pub fn elem_reduced<Larger, Smaller>(
a: &Elem<Larger, Unencoded>,
m: &Modulus<Smaller>,
other_prime_len_bits: BitLength,
) -> Elem<Smaller, RInverse> {
// This is stricter than required mathematically but this is what we
// guarantee and this is easier to check. The real requirement is that
// that `a < m*R` where `R` is the Montgomery `R` for `m`.
assert_eq!(other_prime_len_bits, m.len_bits());
// `limbs_from_mont_in_place` requires this.
assert_eq!(a.limbs.len(), m.limbs().len() * 2);
let mut tmp = [0; MODULUS_MAX_LIMBS];
let tmp = &mut tmp[..a.limbs.len()];
tmp.copy_from_slice(&a.limbs);
let mut r = m.zero();
limbs_from_mont_in_place(&mut r.limbs, tmp, m.limbs(), m.n0());
r
}
fn elem_squared<M, E>(
mut a: Elem<M, E>,
m: &Modulus<M>,
) -> Elem<M, <(E, E) as ProductEncoding>::Output>
where
(E, E): ProductEncoding,
{
limbs_mont_square(&mut a.limbs, m.limbs(), m.n0(), m.cpu_features());
Elem {
limbs: a.limbs,
encoding: PhantomData,
}
}
pub fn elem_widen<Larger, Smaller>(
a: Elem<Smaller, Unencoded>,
m: &Modulus<Larger>,
smaller_modulus_bits: BitLength,
) -> Result<Elem<Larger, Unencoded>, error::Unspecified> {
if smaller_modulus_bits >= m.len_bits() {
return Err(error::Unspecified);
}
let mut r = m.zero();
r.limbs[..a.limbs.len()].copy_from_slice(&a.limbs);
Ok(r)
}
// TODO: Document why this works for all Montgomery factors.
pub fn elem_add<M, E>(mut a: Elem<M, E>, b: Elem<M, E>, m: &Modulus<M>) -> Elem<M, E> {
limb::limbs_add_assign_mod(&mut a.limbs, &b.limbs, m.limbs());
a
}
// TODO: Document why this works for all Montgomery factors.
pub fn elem_sub<M, E>(mut a: Elem<M, E>, b: &Elem<M, E>, m: &Modulus<M>) -> Elem<M, E> {
prefixed_extern! {
// `r` and `a` may alias.
fn LIMBS_sub_mod(
r: *mut Limb,
a: *const Limb,
b: *const Limb,
m: *const Limb,
num_limbs: c::size_t,
);
}
unsafe {
LIMBS_sub_mod(
a.limbs.as_mut_ptr(),
a.limbs.as_ptr(),
b.limbs.as_ptr(),
m.limbs().as_ptr(),
m.limbs().len(),
);
}
a
}
// The value 1, Montgomery-encoded some number of times.
pub struct One<M, E>(Elem<M, E>);
impl<M> One<M, RR> {
// Returns RR = = R**2 (mod n) where R = 2**r is the smallest power of
// 2**LIMB_BITS such that R > m.
//
// Even though the assembly on some 32-bit platforms works with 64-bit
// values, using `LIMB_BITS` here, rather than `N0::LIMBS_USED * LIMB_BITS`,
// is correct because R**2 will still be a multiple of the latter as
// `N0::LIMBS_USED` is either one or two.
pub(crate) fn newRR(m: &Modulus<M>) -> Self {
// The number of limbs in the numbers involved.
let w = m.limbs().len();
// The length of the numbers involved, in bits. R = 2**r.
let r = w * LIMB_BITS;
let mut acc: Elem<M, R> = m.zero();
m.oneR(&mut acc.limbs);
// 2**t * R can be calculated by t doublings starting with R.
//
// Choose a t that divides r and where t doublings are cheaper than 1 squaring.
//
// We could choose other values of t than w. But if t < d then the exponentiation that
// follows would require multiplications. Normally d is 1 (i.e. the modulus length is a
// power of two: RSA 1024, 2048, 4097, 8192) or 3 (RSA 1536, 3072).
//
// XXX(perf): Currently t = w / 2 is slightly faster. TODO(perf): Optimize `elem_double`
// and re-run benchmarks to rebalance this.
let t = w;
let z = w.trailing_zeros();
let d = w >> z;
debug_assert_eq!(w, d * (1 << z));
debug_assert!(d <= t);
debug_assert!(t < r);
for _ in 0..t {
elem_double(&mut acc, m);
}
// Because t | r:
//
// MontExp(2**t * R, r / t)
// = (2**t)**(r / t) * R (mod m) by definition of MontExp.
// = (2**t)**(1/t * r) * R (mod m)
// = (2**(t * 1/t))**r * R (mod m)
// = (2**1)**r * R (mod m)
// = 2**r * R (mod m)
// = R * R (mod m)
// = RR
//
// Like BoringSSL, use t = w (`m.limbs.len()`) which ensures that the exponent is a power
// of two. Consequently, there will be no multiplications in the Montgomery exponentiation;
// there will only be lg(r / t) squarings.
//
// lg(r / t)
// = lg((w * 2**b) / t)
// = lg((t * 2**b) / t)
// = lg(2**b)
// = b
// TODO(MSRV:1.67): const B: u32 = LIMB_BITS.ilog2();
const B: u32 = if cfg!(target_pointer_width = "64") {
6
} else if cfg!(target_pointer_width = "32") {
5
} else {
panic!("unsupported target_pointer_width")
};
#[allow(clippy::assertions_on_constants)]
const _LIMB_BITS_IS_2_POW_B: () = assert!(LIMB_BITS == 1 << B);
debug_assert_eq!(r, t * (1 << B));
for _ in 0..B {
acc = elem_squared(acc, m);
}
Self(Elem {
limbs: acc.limbs,
encoding: PhantomData, // PhantomData<RR>
})
}
}
impl<M> One<M, RRR> {
pub(crate) fn newRRR(One(oneRR): One<M, RR>, m: &Modulus<M>) -> Self {
Self(elem_squared(oneRR, m))
}
}
impl<M, E> AsRef<Elem<M, E>> for One<M, E> {
fn as_ref(&self) -> &Elem<M, E> {
&self.0
}
}
impl<M: PublicModulus, E> Clone for One<M, E> {
fn clone(&self) -> Self {
Self(self.0.clone())
}
}
/// Calculates base**exponent (mod m).
///
/// The run time is a function of the number of limbs in `m` and the bit
/// length and Hamming Weight of `exponent`. The bounds on `m` are pretty
/// obvious but the bounds on `exponent` are less obvious. Callers should
/// document the bounds they place on the maximum value and maximum Hamming
/// weight of `exponent`.
// TODO: The test coverage needs to be expanded, e.g. test with the largest
// accepted exponent and with the most common values of 65537 and 3.
pub(crate) fn elem_exp_vartime<M>(
base: Elem<M, R>,
exponent: NonZeroU64,
m: &Modulus<M>,
) -> Elem<M, R> {
// Use what [Knuth] calls the "S-and-X binary method", i.e. variable-time
// square-and-multiply that scans the exponent from the most significant
// bit to the least significant bit (left-to-right). Left-to-right requires
// less storage compared to right-to-left scanning, at the cost of needing
// to compute `exponent.leading_zeros()`, which we assume to be cheap.
//
// As explained in [Knuth], exponentiation by squaring is the most
// efficient algorithm when the Hamming weight is 2 or less. It isn't the
// most efficient for all other, uncommon, exponent values but any
// suboptimality is bounded at least by the small bit length of `exponent`
// as enforced by its type.
//
// This implementation is slightly simplified by taking advantage of the
// fact that we require the exponent to be a positive integer.
//
// [Knuth]: The Art of Computer Programming, Volume 2: Seminumerical
// Algorithms (3rd Edition), Section 4.6.3.
let exponent = exponent.get();
let mut acc = base.clone();
let mut bit = 1 << (64 - 1 - exponent.leading_zeros());
debug_assert!((exponent & bit) != 0);
while bit > 1 {
bit >>= 1;
acc = elem_squared(acc, m);
if (exponent & bit) != 0 {
acc = elem_mul(&base, acc, m);
}
}
acc
}
#[cfg(not(target_arch = "x86_64"))]
pub fn elem_exp_consttime<M>(
base: Elem<M, R>,
exponent: &PrivateExponent,
m: &Modulus<M>,
) -> Result<Elem<M, Unencoded>, error::Unspecified> {
use crate::{bssl, limb::Window};
const WINDOW_BITS: usize = 5;
const TABLE_ENTRIES: usize = 1 << WINDOW_BITS;
let num_limbs = m.limbs().len();
let mut table = vec![0; TABLE_ENTRIES * num_limbs];
fn gather<M>(table: &[Limb], acc: &mut Elem<M, R>, i: Window) {
prefixed_extern! {
fn LIMBS_select_512_32(
r: *mut Limb,
table: *const Limb,
num_limbs: c::size_t,
i: Window,
) -> bssl::Result;
}
Result::from(unsafe {
LIMBS_select_512_32(acc.limbs.as_mut_ptr(), table.as_ptr(), acc.limbs.len(), i)
})
.unwrap();
}
fn power<M>(
table: &[Limb],
mut acc: Elem<M, R>,
m: &Modulus<M>,
i: Window,
mut tmp: Elem<M, R>,
) -> (Elem<M, R>, Elem<M, R>) {
for _ in 0..WINDOW_BITS {
acc = elem_squared(acc, m);
}
gather(table, &mut tmp, i);
let acc = elem_mul(&tmp, acc, m);
(acc, tmp)
}
fn entry(table: &[Limb], i: usize, num_limbs: usize) -> &[Limb] {
&table[(i * num_limbs)..][..num_limbs]
}
fn entry_mut(table: &mut [Limb], i: usize, num_limbs: usize) -> &mut [Limb] {
&mut table[(i * num_limbs)..][..num_limbs]
}
// table[0] = base**0 (i.e. 1).
m.oneR(entry_mut(&mut table, 0, num_limbs));
entry_mut(&mut table, 1, num_limbs).copy_from_slice(&base.limbs);
for i in 2..TABLE_ENTRIES {
let (src1, src2) = if i % 2 == 0 {
(i / 2, i / 2)
} else {
(i - 1, 1)
};
let (previous, rest) = table.split_at_mut(num_limbs * i);
let src1 = entry(previous, src1, num_limbs);
let src2 = entry(previous, src2, num_limbs);
let dst = entry_mut(rest, 0, num_limbs);
limbs_mont_product(dst, src1, src2, m.limbs(), m.n0(), m.cpu_features());
}
let tmp = m.zero();
let mut acc = Elem {
limbs: base.limbs,
encoding: PhantomData,
};
let (acc, _) = limb::fold_5_bit_windows(
exponent.limbs(),
|initial_window| {
gather(&table, &mut acc, initial_window);
(acc, tmp)
},
|(acc, tmp), window| power(&table, acc, m, window, tmp),
);
Ok(acc.into_unencoded(m))
}
#[cfg(target_arch = "x86_64")]
pub fn elem_exp_consttime<M>(
base: Elem<M, R>,
exponent: &PrivateExponent,
m: &Modulus<M>,
) -> Result<Elem<M, Unencoded>, error::Unspecified> {
use crate::{cpu, limb::LIMB_BYTES};
// Pretty much all the math here requires CPU feature detection to have
// been done. `cpu_features` isn't threaded through all the internal
// functions, so just make it clear that it has been done at this point.
let cpu_features = m.cpu_features();
// The x86_64 assembly was written under the assumption that the input data
// is aligned to `MOD_EXP_CTIME_ALIGN` bytes, which was/is 64 in OpenSSL.
// Similarly, OpenSSL uses the x86_64 assembly functions by giving it only
// inputs `tmp`, `am`, and `np` that immediately follow the table. All the
// awkwardness here stems from trying to use the assembly code like OpenSSL
// does.
use crate::limb::Window;
const WINDOW_BITS: usize = 5;
const TABLE_ENTRIES: usize = 1 << WINDOW_BITS;
let num_limbs = m.limbs().len();
const ALIGNMENT: usize = 64;
assert_eq!(ALIGNMENT % LIMB_BYTES, 0);
let mut table = vec![0; ((TABLE_ENTRIES + 3) * num_limbs) + ALIGNMENT];
let (table, state) = {
let misalignment = (table.as_ptr() as usize) % ALIGNMENT;
let table = &mut table[((ALIGNMENT - misalignment) / LIMB_BYTES)..];
assert_eq!((table.as_ptr() as usize) % ALIGNMENT, 0);
table.split_at_mut(TABLE_ENTRIES * num_limbs)
};
fn scatter(table: &mut [Limb], acc: &[Limb], i: Window, num_limbs: usize) {
prefixed_extern! {
fn bn_scatter5(a: *const Limb, a_len: c::size_t, table: *mut Limb, i: Window);
}
unsafe { bn_scatter5(acc.as_ptr(), num_limbs, table.as_mut_ptr(), i) }
}
fn gather(table: &[Limb], acc: &mut [Limb], i: Window, num_limbs: usize) {
prefixed_extern! {
fn bn_gather5(r: *mut Limb, a_len: c::size_t, table: *const Limb, i: Window);
}
unsafe { bn_gather5(acc.as_mut_ptr(), num_limbs, table.as_ptr(), i) }
}
fn limbs_mul_mont_gather5_amm(
table: &[Limb],
acc: &mut [Limb],
base: &[Limb],
m: &[Limb],
n0: &N0,
i: Window,
num_limbs: usize,
) {
prefixed_extern! {
fn bn_mul_mont_gather5(
rp: *mut Limb,
ap: *const Limb,
table: *const Limb,
np: *const Limb,
n0: &N0,
num: c::size_t,
power: Window,
);
}
unsafe {
bn_mul_mont_gather5(
acc.as_mut_ptr(),
base.as_ptr(),
table.as_ptr(),
m.as_ptr(),
n0,
num_limbs,
i,
);
}
}
fn power_amm(
table: &[Limb],
acc: &mut [Limb],
m_cached: &[Limb],
n0: &N0,
i: Window,
num_limbs: usize,
) {
prefixed_extern! {
fn bn_power5(
r: *mut Limb,
a: *const Limb,
table: *const Limb,
n: *const Limb,
n0: &N0,
num: c::size_t,
i: Window,
);
}
unsafe {
bn_power5(
acc.as_mut_ptr(),
acc.as_ptr(),
table.as_ptr(),
m_cached.as_ptr(),
n0,
num_limbs,
i,
);
}
}
// These are named `(tmp, am, np)` in BoringSSL.
let (acc, base_cached, m_cached): (&mut [Limb], &[Limb], &[Limb]) = {
let (acc, rest) = state.split_at_mut(num_limbs);
let (base_cached, rest) = rest.split_at_mut(num_limbs);
// Upstream, the input `base` is not Montgomery-encoded, so they compute a
// Montgomery-encoded copy and store it here.
base_cached.copy_from_slice(&base.limbs);
let m_cached = &mut rest[..num_limbs];
// "To improve cache locality" according to upstream.
m_cached.copy_from_slice(m.limbs());
(acc, base_cached, m_cached)
};
let n0 = m.n0();
// Fill in all the powers of 2 of `acc` into the table using only squaring and without any
// gathering, storing the last calculated power into `acc`.
fn scatter_powers_of_2(
table: &mut [Limb],
acc: &mut [Limb],
m_cached: &[Limb],
n0: &N0,
mut i: Window,
num_limbs: usize,
cpu_features: cpu::Features,
) {
loop {
scatter(table, acc, i, num_limbs);
i *= 2;
if i >= (TABLE_ENTRIES as Window) {
break;
}
limbs_mont_square(acc, m_cached, n0, cpu_features);
}
}
// All entries in `table` will be Montgomery encoded.
// acc = table[0] = base**0 (i.e. 1).
m.oneR(acc);
scatter(table, acc, 0, num_limbs);
// acc = base**1 (i.e. base).
acc.copy_from_slice(base_cached);
// Fill in entries 1, 2, 4, 8, 16.
scatter_powers_of_2(table, acc, m_cached, n0, 1, num_limbs, cpu_features);
// Fill in entries 3, 6, 12, 24; 5, 10, 20, 30; 7, 14, 28; 9, 18; 11, 22; 13, 26; 15, 30;
// 17; 19; 21; 23; 25; 27; 29; 31.
for i in (3..(TABLE_ENTRIES as Window)).step_by(2) {
limbs_mul_mont_gather5_amm(table, acc, base_cached, m_cached, n0, i - 1, num_limbs);
scatter_powers_of_2(table, acc, m_cached, n0, i, num_limbs, cpu_features);
}
let acc = limb::fold_5_bit_windows(
exponent.limbs(),
|initial_window| {
gather(table, acc, initial_window, num_limbs);
acc
},
|acc, window| {
power_amm(table, acc, m_cached, n0, window, num_limbs);
acc
},
);
let mut r_amm = base.limbs;
r_amm.copy_from_slice(acc);
Ok(from_montgomery_amm(r_amm, m))
}
/// Verified a == b**-1 (mod m), i.e. a**-1 == b (mod m).
pub fn verify_inverses_consttime<M>(
a: &Elem<M, R>,
b: Elem<M, Unencoded>,
m: &Modulus<M>,
) -> Result<(), error::Unspecified> {
if elem_mul(a, b, m).is_one() {
Ok(())
} else {
Err(error::Unspecified)
}
}
#[inline]
pub fn elem_verify_equal_consttime<M, E>(
a: &Elem<M, E>,
b: &Elem<M, E>,
) -> Result<(), error::Unspecified> {
if limb::limbs_equal_limbs_consttime(&a.limbs, &b.limbs) == LimbMask::True {
Ok(())
} else {
Err(error::Unspecified)
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::{cpu, test};
// Type-level representation of an arbitrary modulus.
struct M {}
impl PublicModulus for M {}
#[test]
fn test_elem_exp_consttime() {
let cpu_features = cpu::features();
test::run(
test_file!("../../crypto/fipsmodule/bn/test/mod_exp_tests.txt"),
|section, test_case| {
assert_eq!(section, "");
let m = consume_modulus::<M>(test_case, "M");
let m = m.modulus(cpu_features);
let expected_result = consume_elem(test_case, "ModExp", &m);
let base = consume_elem(test_case, "A", &m);
let e = {
let bytes = test_case.consume_bytes("E");
PrivateExponent::from_be_bytes_for_test_only(untrusted::Input::from(&bytes), &m)
.expect("valid exponent")
};
let base = into_encoded(base, &m);
let actual_result = elem_exp_consttime(base, &e, &m).unwrap();
assert_elem_eq(&actual_result, &expected_result);
Ok(())
},
)
}
// TODO: fn test_elem_exp_vartime() using
// "src/rsa/bigint_elem_exp_vartime_tests.txt". See that file for details.
// In the meantime, the function is tested indirectly via the RSA
// verification and signing tests.
#[test]
fn test_elem_mul() {
let cpu_features = cpu::features();
test::run(
test_file!("../../crypto/fipsmodule/bn/test/mod_mul_tests.txt"),
|section, test_case| {
assert_eq!(section, "");
let m = consume_modulus::<M>(test_case, "M");
let m = m.modulus(cpu_features);
let expected_result = consume_elem(test_case, "ModMul", &m);
let a = consume_elem(test_case, "A", &m);
let b = consume_elem(test_case, "B", &m);
let b = into_encoded(b, &m);
let a = into_encoded(a, &m);
let actual_result = elem_mul(&a, b, &m);
let actual_result = actual_result.into_unencoded(&m);
assert_elem_eq(&actual_result, &expected_result);
Ok(())
},
)
}
#[test]
fn test_elem_squared() {
let cpu_features = cpu::features();
test::run(
test_file!("bigint_elem_squared_tests.txt"),
|section, test_case| {
assert_eq!(section, "");
let m = consume_modulus::<M>(test_case, "M");
let m = m.modulus(cpu_features);
let expected_result = consume_elem(test_case, "ModSquare", &m);
let a = consume_elem(test_case, "A", &m);
let a = into_encoded(a, &m);
let actual_result = elem_squared(a, &m);
let actual_result = actual_result.into_unencoded(&m);
assert_elem_eq(&actual_result, &expected_result);
Ok(())
},
)
}
#[test]
fn test_elem_reduced() {
let cpu_features = cpu::features();
test::run(
test_file!("bigint_elem_reduced_tests.txt"),
|section, test_case| {
assert_eq!(section, "");
struct M {}
let m_ = consume_modulus::<M>(test_case, "M");
let m = m_.modulus(cpu_features);
let expected_result = consume_elem(test_case, "R", &m);
let a =
consume_elem_unchecked::<M>(test_case, "A", expected_result.limbs.len() * 2);
let other_modulus_len_bits = m_.len_bits();
let actual_result = elem_reduced(&a, &m, other_modulus_len_bits);
let oneRR = One::newRR(&m);
let actual_result = elem_mul(oneRR.as_ref(), actual_result, &m);
assert_elem_eq(&actual_result, &expected_result);
Ok(())
},
)
}
#[test]
fn test_elem_reduced_once() {
let cpu_features = cpu::features();
test::run(
test_file!("bigint_elem_reduced_once_tests.txt"),
|section, test_case| {
assert_eq!(section, "");
struct M {}
struct O {}
let m = consume_modulus::<M>(test_case, "m");
let m = m.modulus(cpu_features);
let a = consume_elem_unchecked::<O>(test_case, "a", m.limbs().len());
let expected_result = consume_elem::<M>(test_case, "r", &m);
let other_modulus_len_bits = m.len_bits();
let actual_result = elem_reduced_once(&a, &m, other_modulus_len_bits);
assert_elem_eq(&actual_result, &expected_result);
Ok(())
},
)
}
fn consume_elem<M>(
test_case: &mut test::TestCase,
name: &str,
m: &Modulus<M>,
) -> Elem<M, Unencoded> {
let value = test_case.consume_bytes(name);
Elem::from_be_bytes_padded(untrusted::Input::from(&value), m).unwrap()
}
fn consume_elem_unchecked<M>(
test_case: &mut test::TestCase,
name: &str,
num_limbs: usize,
) -> Elem<M, Unencoded> {
let bytes = test_case.consume_bytes(name);
let mut limbs = BoxedLimbs::zero(num_limbs);
limb::parse_big_endian_and_pad_consttime(untrusted::Input::from(&bytes), &mut limbs)
.unwrap();
Elem {
limbs,
encoding: PhantomData,
}
}
fn consume_modulus<M>(test_case: &mut test::TestCase, name: &str) -> OwnedModulus<M> {
let value = test_case.consume_bytes(name);
OwnedModulus::from_be_bytes(untrusted::Input::from(&value)).unwrap()
}
fn assert_elem_eq<M, E>(a: &Elem<M, E>, b: &Elem<M, E>) {
if elem_verify_equal_consttime(a, b).is_err() {
panic!("{:x?} != {:x?}", &*a.limbs, &*b.limbs);
}
}
fn into_encoded<M>(a: Elem<M, Unencoded>, m: &Modulus<M>) -> Elem<M, R> {
let oneRR = One::newRR(m);
elem_mul(oneRR.as_ref(), a, m)
}
}