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// Copyright 2016 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::{
elem::{binary_op, binary_op_assign},
elem_sqr_mul, elem_sqr_mul_acc, Modulus, *,
};
use crate::c;
use core::marker::PhantomData;
macro_rules! p256_limbs {
[$limb_7:expr, $limb_6:expr, $limb_5:expr, $limb_4:expr,
$limb_3:expr, $limb_2:expr, $limb_1:expr, $limb_0:expr] => {
limbs![0, 0, 0, 0,
$limb_7, $limb_6, $limb_5, $limb_4,
$limb_3, $limb_2, $limb_1, $limb_0]
};
}
pub static COMMON_OPS: CommonOps = CommonOps {
num_limbs: 256 / LIMB_BITS,
q: Modulus {
p: p256_limbs![
0xffffffff, 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0xffffffff, 0xffffffff,
0xffffffff
],
rr: p256_limbs![
0x00000004, 0xfffffffd, 0xffffffff, 0xfffffffe, 0xfffffffb, 0xffffffff, 0x00000000,
0x00000003
],
},
n: Elem {
limbs: p256_limbs![
0xffffffff, 0x00000000, 0xffffffff, 0xffffffff, 0xbce6faad, 0xa7179e84, 0xf3b9cac2,
0xfc632551
],
m: PhantomData,
encoding: PhantomData, // Unencoded
},
a: Elem {
limbs: p256_limbs![
0xfffffffc, 0x00000004, 0x00000000, 0x00000000, 0x00000003, 0xffffffff, 0xffffffff,
0xfffffffc
],
m: PhantomData,
encoding: PhantomData, // R
},
b: Elem {
limbs: p256_limbs![
0xdc30061d, 0x04874834, 0xe5a220ab, 0xf7212ed6, 0xacf005cd, 0x78843090, 0xd89cdf62,
0x29c4bddf
],
m: PhantomData,
encoding: PhantomData, // R
},
elem_add_impl: GFp_nistz256_add,
elem_mul_mont: GFp_nistz256_mul_mont,
elem_sqr_mont: GFp_nistz256_sqr_mont,
point_add_jacobian_impl: GFp_nistz256_point_add,
};
pub static PRIVATE_KEY_OPS: PrivateKeyOps = PrivateKeyOps {
common: &COMMON_OPS,
elem_inv_squared: p256_elem_inv_squared,
point_mul_base_impl: p256_point_mul_base_impl,
point_mul_impl: GFp_nistz256_point_mul,
};
fn p256_elem_inv_squared(a: &Elem<R>) -> Elem<R> {
// Calculate a**-2 (mod q) == a**(q - 3) (mod q)
//
// The exponent (q - 3) is:
//
// 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc
#[inline]
fn sqr_mul(a: &Elem<R>, squarings: usize, b: &Elem<R>) -> Elem<R> {
elem_sqr_mul(&COMMON_OPS, a, squarings, b)
}
#[inline]
fn sqr_mul_acc(a: &mut Elem<R>, squarings: usize, b: &Elem<R>) {
elem_sqr_mul_acc(&COMMON_OPS, a, squarings, b)
}
let b_1 = &a;
let b_11 = sqr_mul(b_1, 1, b_1);
let b_111 = sqr_mul(&b_11, 1, b_1);
let f_11 = sqr_mul(&b_111, 3, &b_111);
let fff = sqr_mul(&f_11, 6, &f_11);
let fff_111 = sqr_mul(&fff, 3, &b_111);
let fffffff_11 = sqr_mul(&fff_111, 15, &fff_111);
let ffffffff = sqr_mul(&fffffff_11, 2, &b_11);
// ffffffff00000001
let mut acc = sqr_mul(&ffffffff, 31 + 1, b_1);
// ffffffff00000001000000000000000000000000ffffffff
sqr_mul_acc(&mut acc, 96 + 32, &ffffffff);
// ffffffff00000001000000000000000000000000ffffffffffffffff
sqr_mul_acc(&mut acc, 32, &ffffffff);
// ffffffff00000001000000000000000000000000fffffffffffffffffffffff_11
sqr_mul_acc(&mut acc, 30, &fffffff_11);
// ffffffff00000001000000000000000000000000fffffffffffffffffffffffc
COMMON_OPS.elem_square(&mut acc);
COMMON_OPS.elem_square(&mut acc);
acc
}
fn p256_point_mul_base_impl(g_scalar: &Scalar) -> Point {
let mut r = Point::new_at_infinity();
unsafe {
GFp_nistz256_point_mul_base(r.xyz.as_mut_ptr(), g_scalar.limbs.as_ptr());
}
r
}
pub static PUBLIC_KEY_OPS: PublicKeyOps = PublicKeyOps {
common: &COMMON_OPS,
};
pub static SCALAR_OPS: ScalarOps = ScalarOps {
common: &COMMON_OPS,
scalar_inv_to_mont_impl: p256_scalar_inv_to_mont,
scalar_mul_mont: GFp_p256_scalar_mul_mont,
};
pub static PUBLIC_SCALAR_OPS: PublicScalarOps = PublicScalarOps {
scalar_ops: &SCALAR_OPS,
public_key_ops: &PUBLIC_KEY_OPS,
private_key_ops: &PRIVATE_KEY_OPS,
q_minus_n: Elem {
limbs: p256_limbs![0, 0, 0, 0, 0x43190553, 0x58e8617b, 0x0c46353d, 0x039cdaae],
m: PhantomData,
encoding: PhantomData, // Unencoded
},
};
pub static PRIVATE_SCALAR_OPS: PrivateScalarOps = PrivateScalarOps {
scalar_ops: &SCALAR_OPS,
oneRR_mod_n: Scalar {
limbs: p256_limbs![
0x66e12d94, 0xf3d95620, 0x2845b239, 0x2b6bec59, 0x4699799c, 0x49bd6fa6, 0x83244c95,
0xbe79eea2
],
m: PhantomData,
encoding: PhantomData, // R
},
};
fn p256_scalar_inv_to_mont(a: &Scalar<Unencoded>) -> Scalar<R> {
// Calculate the modular inverse of scalar |a| using Fermat's Little
// Theorem:
//
// a**-1 (mod n) == a**(n - 2) (mod n)
//
// The exponent (n - 2) is:
//
// 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc63254f
#[inline]
fn mul(a: &Scalar<R>, b: &Scalar<R>) -> Scalar<R> { binary_op(GFp_p256_scalar_mul_mont, a, b) }
#[inline]
fn sqr(a: &Scalar<R>) -> Scalar<R> { unary_op(GFp_p256_scalar_sqr_mont, a) }
// Returns (`a` squared `squarings` times) * `b`.
fn sqr_mul(a: &Scalar<R>, squarings: c::int, b: &Scalar<R>) -> Scalar<R> {
debug_assert!(squarings >= 1);
let mut tmp = Scalar::zero();
unsafe { GFp_p256_scalar_sqr_rep_mont(tmp.limbs.as_mut_ptr(), a.limbs.as_ptr(), squarings) }
mul(&tmp, b)
}
// Sets `acc` = (`acc` squared `squarings` times) * `b`.
fn sqr_mul_acc(acc: &mut Scalar<R>, squarings: c::int, b: &Scalar<R>) {
debug_assert!(squarings >= 1);
unsafe {
GFp_p256_scalar_sqr_rep_mont(acc.limbs.as_mut_ptr(), acc.limbs.as_ptr(), squarings)
}
binary_op_assign(GFp_p256_scalar_mul_mont, acc, b);
}
fn to_mont(a: &Scalar) -> Scalar<R> {
static N_RR: Scalar<Unencoded> = Scalar {
limbs: p256_limbs![
0x66e12d94, 0xf3d95620, 0x2845b239, 0x2b6bec59, 0x4699799c, 0x49bd6fa6, 0x83244c95,
0xbe79eea2
],
m: PhantomData,
encoding: PhantomData,
};
binary_op(GFp_p256_scalar_mul_mont, a, &N_RR)
}
// Indexes into `d`.
const B_1: usize = 0;
const B_10: usize = 1;
const B_11: usize = 2;
const B_101: usize = 3;
const B_111: usize = 4;
const B_1111: usize = 5;
const B_10101: usize = 6;
const B_101111: usize = 7;
const DIGIT_COUNT: usize = 8;
let mut d = [Scalar::zero(); DIGIT_COUNT];
d[B_1] = to_mont(a);
d[B_10] = sqr(&d[B_1]);
d[B_11] = mul(&d[B_10], &d[B_1]);
d[B_101] = mul(&d[B_10], &d[B_11]);
d[B_111] = mul(&d[B_101], &d[B_10]);
let b_1010 = sqr(&d[B_101]);
d[B_1111] = mul(&b_1010, &d[B_101]);
d[B_10101] = sqr_mul(&b_1010, 0 + 1, &d[B_1]);
let b_101010 = sqr(&d[B_10101]);
d[B_101111] = mul(&b_101010, &d[B_101]);
let b_111111 = mul(&b_101010, &d[B_10101]);
let ff = sqr_mul(&b_111111, 0 + 2, &d[B_11]);
let ffff = sqr_mul(&ff, 0 + 8, &ff);
let ffffffff = sqr_mul(&ffff, 0 + 16, &ffff);
// ffffffff00000000ffffffff
let mut acc = sqr_mul(&ffffffff, 32 + 32, &ffffffff);
// ffffffff00000000ffffffffffffffff
sqr_mul_acc(&mut acc, 0 + 32, &ffffffff);
// The rest of the exponent, in binary, is:
//
// 1011110011100110111110101010110110100111000101111001111010000100
// 1111001110111001110010101100001011111100011000110010010101001111
static REMAINING_WINDOWS: [(u8, u8); 26] = [
(6, B_101111 as u8),
(2 + 3, B_111 as u8),
(2 + 2, B_11 as u8),
(1 + 4, B_1111 as u8),
(5, B_10101 as u8),
(1 + 3, B_101 as u8),
(3, B_101 as u8),
(3, B_101 as u8),
(2 + 3, B_111 as u8),
(3 + 6, B_101111 as u8),
(2 + 4, B_1111 as u8),
(1 + 1, B_1 as u8),
(4 + 1, B_1 as u8),
(2 + 4, B_1111 as u8),
(2 + 3, B_111 as u8),
(1 + 3, B_111 as u8),
(2 + 3, B_111 as u8),
(2 + 3, B_101 as u8),
(1 + 2, B_11 as u8),
(4 + 6, B_101111 as u8),
(2, B_11 as u8),
(3 + 2, B_11 as u8),
(3 + 2, B_11 as u8),
(2 + 1, B_1 as u8),
(2 + 5, B_10101 as u8),
(2 + 4, B_1111 as u8),
];
for &(squarings, digit) in &REMAINING_WINDOWS {
sqr_mul_acc(&mut acc, squarings as c::int, &d[digit as usize]);
}
acc
}
extern "C" {
fn GFp_nistz256_add(
r: *mut Limb, // [COMMON_OPS.num_limbs]
a: *const Limb, // [COMMON_OPS.num_limbs]
b: *const Limb, // [COMMON_OPS.num_limbs]
);
fn GFp_nistz256_mul_mont(
r: *mut Limb, // [COMMON_OPS.num_limbs]
a: *const Limb, // [COMMON_OPS.num_limbs]
b: *const Limb, // [COMMON_OPS.num_limbs]
);
fn GFp_nistz256_sqr_mont(
r: *mut Limb, // [COMMON_OPS.num_limbs]
a: *const Limb, // [COMMON_OPS.num_limbs]
);
fn GFp_nistz256_point_add(
r: *mut Limb, // [3][COMMON_OPS.num_limbs]
a: *const Limb, // [3][COMMON_OPS.num_limbs]
b: *const Limb, // [3][COMMON_OPS.num_limbs]
);
fn GFp_nistz256_point_mul(
r: *mut Limb, // [3][COMMON_OPS.num_limbs]
p_scalar: *const Limb, // [COMMON_OPS.num_limbs]
p_x: *const Limb, // [COMMON_OPS.num_limbs]
p_y: *const Limb, // [COMMON_OPS.num_limbs]
);
fn GFp_nistz256_point_mul_base(
r: *mut Limb, // [3][COMMON_OPS.num_limbs]
g_scalar: *const Limb, // [COMMON_OPS.num_limbs]
);
fn GFp_p256_scalar_mul_mont(
r: *mut Limb, // [COMMON_OPS.num_limbs]
a: *const Limb, // [COMMON_OPS.num_limbs]
b: *const Limb, // [COMMON_OPS.num_limbs]
);
fn GFp_p256_scalar_sqr_mont(
r: *mut Limb, // [COMMON_OPS.num_limbs]
a: *const Limb, // [COMMON_OPS.num_limbs]
);
fn GFp_p256_scalar_sqr_rep_mont(
r: *mut Limb, // [COMMON_OPS.num_limbs]
a: *const Limb, // [COMMON_OPS.num_limbs]
rep: c::int,
);
}
#[cfg(feature = "internal_benches")]
mod internal_benches {
use super::{super::internal_benches::*, *};
bench_curve!(&[
Scalar {
limbs: LIMBS_1,
m: PhantomData,
encoding: PhantomData,
},
Scalar {
limbs: LIMBS_ALTERNATING_10,
m: PhantomData,
encoding: PhantomData,
},
Scalar {
// n - 1
limbs: p256_limbs![
0xffffffff,
0x00000000,
0xffffffff,
0xffffffff,
0xbce6faad,
0xa7179e84,
0xf3b9cac2,
0xfc632551 - 1
],
m: PhantomData,
encoding: PhantomData,
},
]);
}