258 lines
8.0 KiB
C++
258 lines
8.0 KiB
C++
/* Copyright (c) 2014, Intel Corporation.
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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 AUTHOR DISCLAIMS 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 AUTHOR 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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/* Developers and authors:
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* Shay Gueron (1, 2), and Vlad Krasnov (1)
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* (1) Intel Corporation, Israel Development Center
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* (2) University of Haifa
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* Reference:
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* Shay Gueron and Vlad Krasnov
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* "Fast Prime Field Elliptic Curve Cryptography with 256 Bit Primes"
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* http://eprint.iacr.org/2013/816 */
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#include "ecp_nistz.h"
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#if defined(__GNUC__)
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#pragma GCC diagnostic push
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#pragma GCC diagnostic ignored "-Wsign-conversion"
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#endif
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/* Point double: r = 2*a */
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void GFp_nistz384_point_double(P384_POINT *r, const P384_POINT *a) {
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BN_ULONG S[P384_LIMBS];
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BN_ULONG M[P384_LIMBS];
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BN_ULONG Zsqr[P384_LIMBS];
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BN_ULONG tmp0[P384_LIMBS];
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const BN_ULONG *in_x = a->X;
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const BN_ULONG *in_y = a->Y;
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const BN_ULONG *in_z = a->Z;
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BN_ULONG *res_x = r->X;
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BN_ULONG *res_y = r->Y;
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BN_ULONG *res_z = r->Z;
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elem_mul_by_2(S, in_y);
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elem_sqr_mont(Zsqr, in_z);
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elem_sqr_mont(S, S);
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elem_mul_mont(res_z, in_z, in_y);
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elem_mul_by_2(res_z, res_z);
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elem_add(M, in_x, Zsqr);
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elem_sub(Zsqr, in_x, Zsqr);
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elem_sqr_mont(res_y, S);
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elem_div_by_2(res_y, res_y);
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elem_mul_mont(M, M, Zsqr);
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elem_mul_by_3(M, M);
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elem_mul_mont(S, S, in_x);
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elem_mul_by_2(tmp0, S);
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elem_sqr_mont(res_x, M);
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elem_sub(res_x, res_x, tmp0);
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elem_sub(S, S, res_x);
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elem_mul_mont(S, S, M);
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elem_sub(res_y, S, res_y);
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}
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/* Point addition: r = a+b */
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void GFp_nistz384_point_add(P384_POINT *r, const P384_POINT *a,
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const P384_POINT *b) {
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BN_ULONG U2[P384_LIMBS], S2[P384_LIMBS];
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BN_ULONG U1[P384_LIMBS], S1[P384_LIMBS];
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BN_ULONG Z1sqr[P384_LIMBS];
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BN_ULONG Z2sqr[P384_LIMBS];
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BN_ULONG H[P384_LIMBS], R[P384_LIMBS];
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BN_ULONG Hsqr[P384_LIMBS];
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BN_ULONG Rsqr[P384_LIMBS];
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BN_ULONG Hcub[P384_LIMBS];
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BN_ULONG res_x[P384_LIMBS];
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BN_ULONG res_y[P384_LIMBS];
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BN_ULONG res_z[P384_LIMBS];
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const BN_ULONG *in1_x = a->X;
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const BN_ULONG *in1_y = a->Y;
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const BN_ULONG *in1_z = a->Z;
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const BN_ULONG *in2_x = b->X;
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const BN_ULONG *in2_y = b->Y;
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const BN_ULONG *in2_z = b->Z;
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BN_ULONG in1infty = is_zero(a->Z);
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BN_ULONG in2infty = is_zero(b->Z);
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elem_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
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elem_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
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elem_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
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elem_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
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elem_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
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elem_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
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elem_sub(R, S2, S1); /* R = S2 - S1 */
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elem_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
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elem_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
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elem_sub(H, U2, U1); /* H = U2 - U1 */
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BN_ULONG is_exceptional = is_equal(U1, U2) & ~in1infty & ~in2infty;
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if (is_exceptional) {
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if (is_equal(S1, S2)) {
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GFp_nistz384_point_double(r, a);
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} else {
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limbs_zero(r->X, P384_LIMBS);
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limbs_zero(r->Y, P384_LIMBS);
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limbs_zero(r->Z, P384_LIMBS);
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}
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return;
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}
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elem_sqr_mont(Rsqr, R); /* R^2 */
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elem_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
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elem_sqr_mont(Hsqr, H); /* H^2 */
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elem_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
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elem_mul_mont(Hcub, Hsqr, H); /* H^3 */
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elem_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
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elem_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
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elem_sub(res_x, Rsqr, Hsqr);
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elem_sub(res_x, res_x, Hcub);
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elem_sub(res_y, U2, res_x);
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elem_mul_mont(S2, S1, Hcub);
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elem_mul_mont(res_y, R, res_y);
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elem_sub(res_y, res_y, S2);
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copy_conditional(res_x, in2_x, in1infty);
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copy_conditional(res_y, in2_y, in1infty);
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copy_conditional(res_z, in2_z, in1infty);
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copy_conditional(res_x, in1_x, in2infty);
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copy_conditional(res_y, in1_y, in2infty);
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copy_conditional(res_z, in1_z, in2infty);
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limbs_copy(r->X, res_x, P384_LIMBS);
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limbs_copy(r->Y, res_y, P384_LIMBS);
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limbs_copy(r->Z, res_z, P384_LIMBS);
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}
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static void add_precomputed_w5(P384_POINT *r, crypto_word wvalue,
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const P384_POINT table[16]) {
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crypto_word recoded_is_negative;
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crypto_word recoded;
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booth_recode(&recoded_is_negative, &recoded, wvalue, 5);
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alignas(64) P384_POINT h;
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gfp_p384_point_select_w5(&h, table, recoded);
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alignas(64) BN_ULONG tmp[P384_LIMBS];
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GFp_p384_elem_neg(tmp, h.Y);
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copy_conditional(h.Y, tmp, recoded_is_negative);
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GFp_nistz384_point_add(r, r, &h);
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}
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/* r = p * p_scalar */
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void GFp_nistz384_point_mul(P384_POINT *r, const BN_ULONG p_scalar[P384_LIMBS],
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const BN_ULONG p_x[P384_LIMBS],
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const BN_ULONG p_y[P384_LIMBS]) {
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static const size_t kWindowSize = 5;
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static const crypto_word kMask = (1 << (5 /* kWindowSize */ + 1)) - 1;
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uint8_t p_str[(P384_LIMBS * sizeof(Limb)) + 1];
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gfp_little_endian_bytes_from_scalar(p_str, sizeof(p_str) / sizeof(p_str[0]),
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p_scalar, P384_LIMBS);
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/* A |P384_POINT| is (3 * 48) = 144 bytes, and the 64-byte alignment should
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* add no more than 63 bytes of overhead. Thus, |table| should require
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* ~2367 ((144 * 16) + 63) bytes of stack space. */
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alignas(64) P384_POINT table[16];
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/* table[0] is implicitly (0,0,0) (the point at infinity), therefore it is
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* not stored. All other values are actually stored with an offset of -1 in
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* table. */
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P384_POINT *row = table;
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limbs_copy(row[1 - 1].X, p_x, P384_LIMBS);
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limbs_copy(row[1 - 1].Y, p_y, P384_LIMBS);
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limbs_copy(row[1 - 1].Z, ONE, P384_LIMBS);
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GFp_nistz384_point_double(&row[2 - 1], &row[1 - 1]);
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GFp_nistz384_point_add(&row[3 - 1], &row[2 - 1], &row[1 - 1]);
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GFp_nistz384_point_double(&row[4 - 1], &row[2 - 1]);
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GFp_nistz384_point_double(&row[6 - 1], &row[3 - 1]);
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GFp_nistz384_point_double(&row[8 - 1], &row[4 - 1]);
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GFp_nistz384_point_double(&row[12 - 1], &row[6 - 1]);
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GFp_nistz384_point_add(&row[5 - 1], &row[4 - 1], &row[1 - 1]);
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GFp_nistz384_point_add(&row[7 - 1], &row[6 - 1], &row[1 - 1]);
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GFp_nistz384_point_add(&row[9 - 1], &row[8 - 1], &row[1 - 1]);
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GFp_nistz384_point_add(&row[13 - 1], &row[12 - 1], &row[1 - 1]);
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GFp_nistz384_point_double(&row[14 - 1], &row[7 - 1]);
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GFp_nistz384_point_double(&row[10 - 1], &row[5 - 1]);
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GFp_nistz384_point_add(&row[15 - 1], &row[14 - 1], &row[1 - 1]);
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GFp_nistz384_point_add(&row[11 - 1], &row[10 - 1], &row[1 - 1]);
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GFp_nistz384_point_double(&row[16 - 1], &row[8 - 1]);
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static const size_t START_INDEX = 384 - 4;
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size_t index = START_INDEX;
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BN_ULONG recoded_is_negative;
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crypto_word recoded;
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crypto_word wvalue = p_str[(index - 1) / 8];
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wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
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booth_recode(&recoded_is_negative, &recoded, wvalue, 5);
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dev_assert_secret(!recoded_is_negative);
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gfp_p384_point_select_w5(r, table, recoded);
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while (index >= kWindowSize) {
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if (index != START_INDEX) {
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size_t off = (index - 1) / 8;
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wvalue = p_str[off] | p_str[off + 1] << 8;
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wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
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add_precomputed_w5(r, wvalue, table);
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}
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index -= kWindowSize;
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GFp_nistz384_point_double(r, r);
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GFp_nistz384_point_double(r, r);
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GFp_nistz384_point_double(r, r);
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GFp_nistz384_point_double(r, r);
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GFp_nistz384_point_double(r, r);
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}
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/* Final window */
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wvalue = p_str[0];
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wvalue = (wvalue << 1) & kMask;
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add_precomputed_w5(r, wvalue, table);
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}
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#if defined(__GNUC__)
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#pragma GCC diagnostic pop
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#endif
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