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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 core::marker::PhantomData;
macro_rules! p384_limbs {
[$limb_b:expr, $limb_a:expr, $limb_9:expr, $limb_8:expr,
$limb_7:expr, $limb_6:expr, $limb_5:expr, $limb_4:expr,
$limb_3:expr, $limb_2:expr, $limb_1:expr, $limb_0:expr] => {
limbs![$limb_b, $limb_a, $limb_9, $limb_8,
$limb_7, $limb_6, $limb_5, $limb_4,
$limb_3, $limb_2, $limb_1, $limb_0]
};
}
pub static COMMON_OPS: CommonOps = CommonOps {
num_limbs: 384 / LIMB_BITS,
q: Modulus {
p: p384_limbs![
0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
0xfffffffe, 0xffffffff, 0x00000000, 0x00000000, 0xffffffff
],
rr: limbs![0, 0, 0, 1, 2, 0, 0xfffffffe, 0, 2, 0, 0xfffffffe, 1],
},
n: Elem {
limbs: p384_limbs![
0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xc7634d81,
0xf4372ddf, 0x581a0db2, 0x48b0a77a, 0xecec196a, 0xccc52973
],
m: PhantomData,
encoding: PhantomData, // Unencoded
},
a: Elem {
limbs: p384_limbs![
0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
0xfffffffb, 0xfffffffc, 0x00000000, 0x00000003, 0xfffffffc
],
m: PhantomData,
encoding: PhantomData, // Unreduced
},
b: Elem {
limbs: p384_limbs![
0xcd08114b, 0x604fbff9, 0xb62b21f4, 0x1f022094, 0xe3374bee, 0x94938ae2, 0x77f2209b,
0x1920022e, 0xf729add8, 0x7a4c32ec, 0x08118871, 0x9d412dcc
],
m: PhantomData,
encoding: PhantomData, // Unreduced
},
elem_add_impl: GFp_p384_elem_add,
elem_mul_mont: GFp_p384_elem_mul_mont,
elem_sqr_mont: GFp_p384_elem_sqr_mont,
point_add_jacobian_impl: GFp_nistz384_point_add,
};
pub static PRIVATE_KEY_OPS: PrivateKeyOps = PrivateKeyOps {
common: &COMMON_OPS,
elem_inv_squared: p384_elem_inv_squared,
point_mul_base_impl: p384_point_mul_base_impl,
point_mul_impl: GFp_nistz384_point_mul,
};
fn p384_elem_inv_squared(a: &Elem<R>) -> Elem<R> {
// Calculate a**-2 (mod q) == a**(q - 3) (mod q)
//
// The exponent (q - 3) is:
//
// 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe\
// ffffffff0000000000000000fffffffc
#[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 fffffffffffffff = sqr_mul(&fffffff_11, 30, &fffffff_11);
let ffffffffffffffffffffffffffffff = sqr_mul(&fffffffffffffff, 60, &fffffffffffffff);
// ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
let mut acc = sqr_mul(
&ffffffffffffffffffffffffffffff,
120,
&ffffffffffffffffffffffffffffff,
);
// fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff_111
sqr_mul_acc(&mut acc, 15, &fff_111);
// fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff
sqr_mul_acc(&mut acc, 1 + 30, &fffffff_11);
sqr_mul_acc(&mut acc, 2, &b_11);
// fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff
// 0000000000000000fffffff_11
sqr_mul_acc(&mut acc, 64 + 30, &fffffff_11);
// fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff
// 0000000000000000fffffffc
COMMON_OPS.elem_square(&mut acc);
COMMON_OPS.elem_square(&mut acc);
acc
}
fn p384_point_mul_base_impl(a: &Scalar) -> Point {
// XXX: Not efficient. TODO: Precompute multiples of the generator.
static P384_GENERATOR: (Elem<R>, Elem<R>) = (
Elem {
limbs: p384_limbs![
0x4d3aadc2, 0x299e1513, 0x812ff723, 0x614ede2b, 0x64548684, 0x59a30eff, 0x879c3afc,
0x541b4d6e, 0x20e378e2, 0xa0d6ce38, 0x3dd07566, 0x49c0b528
],
m: PhantomData,
encoding: PhantomData,
},
Elem {
limbs: p384_limbs![
0x2b78abc2, 0x5a15c5e9, 0xdd800226, 0x3969a840, 0xc6c35219, 0x68f4ffd9, 0x8bade756,
0x2e83b050, 0xa1bfa8bf, 0x7bb4a9ac, 0x23043dad, 0x4b03a4fe
],
m: PhantomData,
encoding: PhantomData,
},
);
PRIVATE_KEY_OPS.point_mul(a, &P384_GENERATOR)
}
pub static PUBLIC_KEY_OPS: PublicKeyOps = PublicKeyOps {
common: &COMMON_OPS,
};
pub static SCALAR_OPS: ScalarOps = ScalarOps {
common: &COMMON_OPS,
scalar_inv_to_mont_impl: p384_scalar_inv_to_mont,
scalar_mul_mont: GFp_p384_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: p384_limbs![
0, 0, 0, 0, 0, 0, 0x389cb27e, 0x0bc8d21f, 0xa7e5f24c, 0xb74f5885, 0x1313e696,
0x333ad68c
],
m: PhantomData,
encoding: PhantomData, // Unencoded
},
};
pub static PRIVATE_SCALAR_OPS: PrivateScalarOps = PrivateScalarOps {
scalar_ops: &SCALAR_OPS,
oneRR_mod_n: Scalar {
limbs: N_RR_LIMBS,
m: PhantomData,
encoding: PhantomData, // R
},
};
fn p384_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:
//
// 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf\
// 581a0db248b0a77aecec196accc52971.
fn mul(a: &Scalar<R>, b: &Scalar<R>) -> Scalar<R> { binary_op(GFp_p384_scalar_mul_mont, a, b) }
fn sqr(a: &Scalar<R>) -> Scalar<R> { binary_op(GFp_p384_scalar_mul_mont, a, a) }
fn sqr_mut(a: &mut Scalar<R>) { unary_op_from_binary_op_assign(GFp_p384_scalar_mul_mont, a); }
// Returns (`a` squared `squarings` times) * `b`.
fn sqr_mul(a: &Scalar<R>, squarings: usize, b: &Scalar<R>) -> Scalar<R> {
debug_assert!(squarings >= 1);
let mut tmp = sqr(a);
for _ in 1..squarings {
sqr_mut(&mut tmp);
}
mul(&tmp, b)
}
// Sets `acc` = (`acc` squared `squarings` times) * `b`.
fn sqr_mul_acc(acc: &mut Scalar<R>, squarings: usize, b: &Scalar<R>) {
debug_assert!(squarings >= 1);
for _ in 0..squarings {
sqr_mut(acc);
}
binary_op_assign(GFp_p384_scalar_mul_mont, acc, b)
}
fn to_mont(a: &Scalar<Unencoded>) -> Scalar<R> {
static N_RR: Scalar<Unencoded> = Scalar {
limbs: N_RR_LIMBS,
m: PhantomData,
encoding: PhantomData,
};
binary_op(GFp_p384_scalar_mul_mont, a, &N_RR)
}
// Indexes into `d`.
const B_1: usize = 0;
const B_11: usize = 1;
const B_101: usize = 2;
const B_111: usize = 3;
const B_1001: usize = 4;
const B_1011: usize = 5;
const B_1101: usize = 6;
const B_1111: usize = 7;
const DIGIT_COUNT: usize = 8;
let mut d = [Scalar::zero(); DIGIT_COUNT];
d[B_1] = to_mont(a);
let b_10 = sqr(&d[B_1]);
for i in B_11..DIGIT_COUNT {
d[i] = mul(&d[i - 1], &b_10);
}
let ff = sqr_mul(&d[B_1111], 0 + 4, &d[B_1111]);
let ffff = sqr_mul(&ff, 0 + 8, &ff);
let ffffffff = sqr_mul(&ffff, 0 + 16, &ffff);
let ffffffffffffffff = sqr_mul(&ffffffff, 0 + 32, &ffffffff);
let ffffffffffffffffffffffff = sqr_mul(&ffffffffffffffff, 0 + 32, &ffffffff);
// ffffffffffffffffffffffffffffffffffffffffffffffff
let mut acc = sqr_mul(&ffffffffffffffffffffffff, 0 + 96, &ffffffffffffffffffffffff);
// The rest of the exponent, in binary, is:
//
// 1100011101100011010011011000000111110100001101110010110111011111
// 0101100000011010000011011011001001001000101100001010011101111010
// 1110110011101100000110010110101011001100110001010010100101110001
static REMAINING_WINDOWS: [(u8, u8); 39] = [
(2, B_11 as u8),
(3 + 3, B_111 as u8),
(1 + 2, B_11 as u8),
(3 + 2, B_11 as u8),
(1 + 4, B_1001 as u8),
(4, B_1011 as u8),
(6 + 4, B_1111 as u8),
(3, B_101 as u8),
(4 + 1, B_1 as u8),
(4, B_1011 as u8),
(4, B_1001 as u8),
(1 + 4, B_1101 as u8),
(4, B_1101 as u8),
(4, B_1111 as u8),
(1 + 4, B_1011 as u8),
(6 + 4, B_1101 as u8),
(5 + 4, B_1101 as u8),
(4, B_1011 as u8),
(2 + 4, B_1001 as u8),
(2 + 1, B_1 as u8),
(3 + 4, B_1011 as u8),
(4 + 3, B_101 as u8),
(2 + 3, B_111 as u8),
(1 + 4, B_1111 as u8),
(1 + 4, B_1011 as u8),
(4, B_1011 as u8),
(2 + 3, B_111 as u8),
(1 + 2, B_11 as u8),
(5 + 2, B_11 as u8),
(2 + 4, B_1011 as u8),
(1 + 3, B_101 as u8),
(1 + 2, B_11 as u8),
(2 + 2, B_11 as u8),
(2 + 2, B_11 as u8),
(3 + 3, B_101 as u8),
(2 + 3, B_101 as u8),
(2 + 3, B_101 as u8),
(2, B_11 as u8),
(3 + 1, B_1 as u8),
];
for &(squarings, digit) in &REMAINING_WINDOWS[..] {
sqr_mul_acc(&mut acc, squarings as usize, &d[digit as usize]);
}
acc
}
unsafe extern "C" fn GFp_p384_elem_sqr_mont(
r: *mut Limb, // [COMMON_OPS.num_limbs]
a: *const Limb, // [COMMON_OPS.num_limbs]
) {
// XXX: Inefficient. TODO: Make a dedicated squaring routine.
GFp_p384_elem_mul_mont(r, a, a);
}
const N_RR_LIMBS: [Limb; MAX_LIMBS] = p384_limbs![
0x0c84ee01, 0x2b39bf21, 0x3fb05b7a, 0x28266895, 0xd40d4917, 0x4aab1cc5, 0xbc3e483a, 0xfcb82947,
0xff3d81e5, 0xdf1aa419, 0x2d319b24, 0x19b409a9
];
extern "C" {
fn GFp_p384_elem_add(
r: *mut Limb, // [COMMON_OPS.num_limbs]
a: *const Limb, // [COMMON_OPS.num_limbs]
b: *const Limb, // [COMMON_OPS.num_limbs]
);
fn GFp_p384_elem_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_nistz384_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_nistz384_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_p384_scalar_mul_mont(
r: *mut Limb, // [COMMON_OPS.num_limbs]
a: *const Limb, // [COMMON_OPS.num_limbs]
b: *const Limb, // [COMMON_OPS.num_limbs]
);
}
#[cfg(feature = "internal_benches")]
mod internal_benches {
use super::{super::internal_benches::*, *};
bench_curve!(&[
Scalar { limbs: LIMBS_1 },
Scalar {
limbs: LIMBS_ALTERNATING_10,
},
Scalar {
// n - 1
limbs: p384_limbs![
0xffffffff,
0xffffffff,
0xffffffff,
0xffffffff,
0xffffffff,
0xffffffff,
0xc7634d81,
0xf4372ddf,
0x581a0db2,
0x48b0a77a,
0xecec196a,
0xccc52973 - 1
],
},
]);
}