263 lines
8.5 KiB
C
263 lines
8.5 KiB
C
/* Copyright 2016 Brian Smith.
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*
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* Permission to use, copy, modify, and/or distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHORS DISCLAIM ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY
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* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
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* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
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* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
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#include "../limbs/limbs.h"
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#include <string.h>
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#include "ecp_nistz384.h"
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#include "../bn/internal.h"
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#include "../internal.h"
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#include "../limbs/limbs.inl"
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/* XXX: Here we assume that the conversion from |Carry| to |Limb| is
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* constant-time, but we haven't verified that assumption. TODO: Fix it so
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* we don't need to make that assumption. */
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typedef Limb Elem[P384_LIMBS];
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typedef Limb ScalarMont[P384_LIMBS];
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typedef Limb Scalar[P384_LIMBS];
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/* Prototypes to avoid -Wmissing-prototypes warnings. */
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void GFp_p384_elem_add(Elem r, const Elem a, const Elem b);
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void GFp_p384_elem_sub(Elem r, const Elem a, const Elem b);
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void GFp_p384_elem_div_by_2(Elem r, const Elem a);
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void GFp_p384_elem_mul_mont(Elem r, const Elem a, const Elem b);
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void GFp_p384_elem_neg(Elem r, const Elem a);
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void GFp_p384_scalar_inv_to_mont(ScalarMont r, const Scalar a);
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void GFp_p384_scalar_mul_mont(ScalarMont r, const ScalarMont a,
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const ScalarMont b);
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static const BN_ULONG Q[P384_LIMBS] = {
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TOBN(0x00000000, 0xffffffff),
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TOBN(0xffffffff, 0x00000000),
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TOBN(0xffffffff, 0xfffffffe),
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TOBN(0xffffffff, 0xffffffff),
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TOBN(0xffffffff, 0xffffffff),
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TOBN(0xffffffff, 0xffffffff),
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};
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static const BN_ULONG N[P384_LIMBS] = {
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TOBN(0xecec196a, 0xccc52973),
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TOBN(0x581a0db2, 0x48b0a77a),
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TOBN(0xc7634d81, 0xf4372ddf),
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TOBN(0xffffffff, 0xffffffff),
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TOBN(0xffffffff, 0xffffffff),
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TOBN(0xffffffff, 0xffffffff),
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};
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OPENSSL_COMPILE_ASSERT(sizeof(size_t) == sizeof(Limb),
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size_t_and_gfp_limb_are_different_sizes);
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OPENSSL_COMPILE_ASSERT(sizeof(size_t) == sizeof(BN_ULONG),
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size_t_and_bn_ulong_are_different_sizes);
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static const BN_ULONG ONE[P384_LIMBS] = {
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TOBN(0xffffffff, 1), TOBN(0, 0xffffffff), TOBN(0, 1), TOBN(0, 0), TOBN(0, 0),
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TOBN(0, 0),
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};
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/* XXX: MSVC for x86 warns when it fails to inline these functions it should
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* probably inline. */
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#if defined(_MSC_VER) && defined(OPENSSL_X86)
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#define INLINE_IF_POSSIBLE __forceinline
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#else
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#define INLINE_IF_POSSIBLE inline
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#endif
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static INLINE_IF_POSSIBLE Limb is_equal(const Elem a, const Elem b) {
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return LIMBS_equal(a, b, P384_LIMBS);
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}
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static INLINE_IF_POSSIBLE void copy_conditional(Elem r, const Elem a,
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const Limb condition) {
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for (size_t i = 0; i < P384_LIMBS; ++i) {
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r[i] = constant_time_select_size_t(condition, a[i], r[i]);
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}
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}
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static void elem_add(Elem r, const Elem a, const Elem b) {
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LIMBS_add_mod(r, a, b, Q, P384_LIMBS);
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}
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static void elem_sub(Elem r, const Elem a, const Elem b) {
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LIMBS_sub_mod(r, a, b, Q, P384_LIMBS);
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}
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static void elem_div_by_2(Elem r, const Elem a) {
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/* Consider the case where `a` is even. Then we can shift `a` right one bit
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* and the result will still be valid because we didn't lose any bits and so
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* `(a >> 1) * 2 == a (mod q)`, which is the invariant we must satisfy.
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*
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* The remainder of this comment is considering the case where `a` is odd.
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*
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* Since `a` is odd, it isn't the case that `(a >> 1) * 2 == a (mod q)`
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* because the lowest bit is lost during the shift. For example, consider:
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*
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* ```python
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* q = 2**384 - 2**128 - 2**96 + 2**32 - 1
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* a = 2**383
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* two_a = a * 2 % q
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* assert two_a == 0x100000000ffffffffffffffff00000001
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* ```
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*
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* Notice there how `(2 * a) % q` wrapped around to a smaller odd value. When
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* we divide `two_a` by two (mod q), we need to get the value `2**383`, which
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* we obviously can't get with just a right shift.
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*
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* `q` is odd, and `a` is odd, so `a + q` is even. We could calculate
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* `(a + q) >> 1` and then reduce it mod `q`. However, then we would have to
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* keep track of an extra most significant bit. We can avoid that by instead
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* calculating `(a >> 1) + ((q + 1) >> 1)`. The `1` in `q + 1` is the least
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* significant bit of `a`. `q + 1` is even, which means it can be shifted
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* without losing any bits. Since `q` is odd, `q - 1` is even, so the largest
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* odd field element is `q - 2`. Thus we know that `a <= q - 2`. We know
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* `(q + 1) >> 1` is `(q + 1) / 2` since (`q + 1`) is even. The value of
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* `a >> 1` is `(a - 1)/2` since the shift will drop the least significant
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* bit of `a`, which is 1. Thus:
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*
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* sum = ((q + 1) >> 1) + (a >> 1)
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* sum = (q + 1)/2 + (a >> 1) (substituting (q + 1)/2)
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* <= (q + 1)/2 + (q - 2 - 1)/2 (substituting a <= q - 2)
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* <= (q + 1)/2 + (q - 3)/2 (simplifying)
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* <= (q + 1 + q - 3)/2 (factoring out the common divisor)
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* <= (2q - 2)/2 (simplifying)
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* <= q - 1 (simplifying)
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*
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* Thus, no reduction of the sum mod `q` is necessary. */
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Limb is_odd = constant_time_is_nonzero_size_t(a[0] & 1);
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/* r = a >> 1. */
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Limb carry = a[P384_LIMBS - 1] & 1;
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r[P384_LIMBS - 1] = a[P384_LIMBS - 1] >> 1;
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for (size_t i = 1; i < P384_LIMBS; ++i) {
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Limb new_carry = a[P384_LIMBS - i - 1];
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r[P384_LIMBS - i - 1] =
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(a[P384_LIMBS - i - 1] >> 1) | (carry << (LIMB_BITS - 1));
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carry = new_carry;
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}
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static const Elem Q_PLUS_1_SHR_1 = {
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TOBN(0x00000000, 0x80000000), TOBN(0x7fffffff, 0x80000000),
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TOBN(0xffffffff, 0xffffffff), TOBN(0xffffffff, 0xffffffff),
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TOBN(0xffffffff, 0xffffffff), TOBN(0x7fffffff, 0xffffffff),
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};
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Elem adjusted;
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BN_ULONG carry2 = limbs_add(adjusted, r, Q_PLUS_1_SHR_1, P384_LIMBS);
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#if defined(NDEBUG)
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(void)carry2;
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#endif
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assert(carry2 == 0);
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copy_conditional(r, adjusted, is_odd);
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}
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static inline void elem_mul_mont(Elem r, const Elem a, const Elem b) {
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static const BN_ULONG Q_N0[] = {
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BN_MONT_CTX_N0(0x1, 0x1)
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};
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/* XXX: Not (clearly) constant-time; inefficient.*/
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GFp_bn_mul_mont(r, a, b, Q, Q_N0, P384_LIMBS);
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}
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static inline void elem_mul_by_2(Elem r, const Elem a) {
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LIMBS_shl_mod(r, a, Q, P384_LIMBS);
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}
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static INLINE_IF_POSSIBLE void elem_mul_by_3(Elem r, const Elem a) {
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/* XXX: inefficient. TODO: Replace with an integrated shift + add. */
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Elem doubled;
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elem_add(doubled, a, a);
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elem_add(r, doubled, a);
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}
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static inline void elem_sqr_mont(Elem r, const Elem a) {
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/* XXX: Inefficient. TODO: Add a dedicated squaring routine. */
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elem_mul_mont(r, a, a);
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}
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void GFp_p384_elem_add(Elem r, const Elem a, const Elem b) {
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elem_add(r, a, b);
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}
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void GFp_p384_elem_sub(Elem r, const Elem a, const Elem b) {
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elem_sub(r, a, b);
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}
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void GFp_p384_elem_div_by_2(Elem r, const Elem a) {
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elem_div_by_2(r, a);
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}
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void GFp_p384_elem_mul_mont(Elem r, const Elem a, const Elem b) {
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elem_mul_mont(r, a, b);
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}
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void GFp_p384_elem_neg(Elem r, const Elem a) {
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Limb is_zero = LIMBS_are_zero(a, P384_LIMBS);
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Carry borrow = limbs_sub(r, Q, a, P384_LIMBS);
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#if defined(NDEBUG)
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(void)borrow;
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#endif
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assert(borrow == 0);
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for (size_t i = 0; i < P384_LIMBS; ++i) {
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r[i] = constant_time_select_size_t(is_zero, 0, r[i]);
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}
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}
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void GFp_p384_scalar_mul_mont(ScalarMont r, const ScalarMont a,
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const ScalarMont b) {
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static const BN_ULONG N_N0[] = {
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BN_MONT_CTX_N0(0x6ed46089, 0xe88fdc45)
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};
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/* XXX: Inefficient. TODO: Add dedicated multiplication routine. */
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GFp_bn_mul_mont(r, a, b, N, N_N0, P384_LIMBS);
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}
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/* TODO(perf): Optimize this. */
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static void gfp_p384_point_select_w5(P384_POINT *out,
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const P384_POINT table[16], size_t index) {
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Elem x; memset(x, 0, sizeof(x));
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Elem y; memset(y, 0, sizeof(y));
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Elem z; memset(z, 0, sizeof(z));
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for (size_t i = 0; i < 16; ++i) {
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Limb mask = constant_time_eq_size_t(index, i + 1);
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for (size_t j = 0; j < P384_LIMBS; ++j) {
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x[j] |= table[i].X[j] & mask;
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y[j] |= table[i].Y[j] & mask;
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z[j] |= table[i].Z[j] & mask;
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}
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}
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memcpy(out->X, x, sizeof(x));
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memcpy(out->Y, y, sizeof(y));
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memcpy(out->Z, z, sizeof(z));
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}
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#include "ecp_nistz384.inl"
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