mirror of
https://github.com/classilla/tenfourfox.git
synced 2024-09-05 23:54:38 +00:00
290 lines
8.7 KiB
C
290 lines
8.7 KiB
C
/* This Source Code Form is subject to the terms of the Mozilla Public
|
|
* License, v. 2.0. If a copy of the MPL was not distributed with this
|
|
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
|
|
|
|
#include "ecp.h"
|
|
#include "ecl-priv.h"
|
|
#include "mplogic.h"
|
|
#include <stdlib.h>
|
|
|
|
#define MAX_SCRATCH 6
|
|
|
|
/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
|
|
* Modified Jacobian coordinates.
|
|
*
|
|
* Assumes input is already field-encoded using field_enc, and returns
|
|
* output that is still field-encoded.
|
|
*
|
|
*/
|
|
static mp_err
|
|
ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,
|
|
const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,
|
|
mp_int *raz4, mp_int scratch[], const ECGroup *group)
|
|
{
|
|
mp_err res = MP_OKAY;
|
|
mp_int *t0, *t1, *M, *S;
|
|
|
|
t0 = &scratch[0];
|
|
t1 = &scratch[1];
|
|
M = &scratch[2];
|
|
S = &scratch[3];
|
|
|
|
#if MAX_SCRATCH < 4
|
|
#error "Scratch array defined too small "
|
|
#endif
|
|
|
|
/* Check for point at infinity */
|
|
if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
|
|
/* Set r = pt at infinity by setting rz = 0 */
|
|
|
|
MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* M = 3 (px^2) + a*(pz^4) */
|
|
MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));
|
|
MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));
|
|
MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));
|
|
MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));
|
|
|
|
/* rz = 2 * py * pz */
|
|
MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));
|
|
MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));
|
|
|
|
/* t0 = 2y^2 , t1 = 8y^4 */
|
|
MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));
|
|
MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));
|
|
MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));
|
|
MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth));
|
|
|
|
/* S = 4 * px * py^2 = 2 * px * t0 */
|
|
MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));
|
|
MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));
|
|
|
|
|
|
/* rx = M^2 - 2S */
|
|
MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));
|
|
MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
|
|
MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
|
|
|
|
/* ry = M * (S - rx) - t1 */
|
|
MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));
|
|
MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));
|
|
MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));
|
|
|
|
/* ra*z^4 = 2*t1*(apz4) */
|
|
MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));
|
|
MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));
|
|
|
|
|
|
CLEANUP:
|
|
return res;
|
|
}
|
|
|
|
/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
|
|
* (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical.
|
|
* Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
|
|
* already field-encoded using field_enc, and returns output that is still
|
|
* field-encoded. */
|
|
static mp_err
|
|
ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
|
|
const mp_int *paz4, const mp_int *qx,
|
|
const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
|
|
mp_int *raz4, mp_int scratch[], const ECGroup *group)
|
|
{
|
|
mp_err res = MP_OKAY;
|
|
mp_int *A, *B, *C, *D, *C2, *C3;
|
|
|
|
A = &scratch[0];
|
|
B = &scratch[1];
|
|
C = &scratch[2];
|
|
D = &scratch[3];
|
|
C2 = &scratch[4];
|
|
C3 = &scratch[5];
|
|
|
|
#if MAX_SCRATCH < 6
|
|
#error "Scratch array defined too small "
|
|
#endif
|
|
|
|
/* If either P or Q is the point at infinity, then return the other
|
|
* point */
|
|
if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
|
|
MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
|
|
MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
|
|
MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
|
|
MP_CHECKOK(group->meth->
|
|
field_mul(raz4, &group->curvea, raz4, group->meth));
|
|
goto CLEANUP;
|
|
}
|
|
if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
|
|
MP_CHECKOK(mp_copy(px, rx));
|
|
MP_CHECKOK(mp_copy(py, ry));
|
|
MP_CHECKOK(mp_copy(pz, rz));
|
|
MP_CHECKOK(mp_copy(paz4, raz4));
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* A = qx * pz^2, B = qy * pz^3 */
|
|
MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));
|
|
MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));
|
|
MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));
|
|
MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));
|
|
|
|
/* C = A - px, D = B - py */
|
|
MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
|
|
MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));
|
|
|
|
/* C2 = C^2, C3 = C^3 */
|
|
MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
|
|
MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));
|
|
|
|
/* rz = pz * C */
|
|
MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));
|
|
|
|
/* C = px * C^2 */
|
|
MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
|
|
/* A = D^2 */
|
|
MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));
|
|
|
|
/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
|
|
MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
|
|
MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
|
|
MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));
|
|
|
|
/* C3 = py * C^3 */
|
|
MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));
|
|
|
|
/* ry = D * (px * C^2 - rx) - py * C^3 */
|
|
MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
|
|
MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
|
|
MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));
|
|
|
|
/* raz4 = a * rz^4 */
|
|
MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
|
|
MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
|
|
MP_CHECKOK(group->meth->
|
|
field_mul(raz4, &group->curvea, raz4, group->meth));
|
|
CLEANUP:
|
|
return res;
|
|
}
|
|
|
|
/* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
|
|
* curve points P and R can be identical. Uses mixed Modified-Jacobian
|
|
* co-ordinates for doubling and Chudnovsky Jacobian coordinates for
|
|
* additions. Assumes input is already field-encoded using field_enc, and
|
|
* returns output that is still field-encoded. Uses 5-bit window NAF
|
|
* method (algorithm 11) for scalar-point multiplication from Brown,
|
|
* Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic
|
|
* Curves Over Prime Fields. */
|
|
mp_err
|
|
ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,
|
|
mp_int *rx, mp_int *ry, const ECGroup *group)
|
|
{
|
|
mp_err res = MP_OKAY;
|
|
mp_int precomp[16][2], rz, tpx, tpy;
|
|
mp_int raz4;
|
|
mp_int scratch[MAX_SCRATCH];
|
|
signed char *naf = NULL;
|
|
int i, orderBitSize;
|
|
|
|
MP_DIGITS(&rz) = 0;
|
|
MP_DIGITS(&raz4) = 0;
|
|
MP_DIGITS(&tpx) = 0;
|
|
MP_DIGITS(&tpy) = 0;
|
|
for (i = 0; i < 16; i++) {
|
|
MP_DIGITS(&precomp[i][0]) = 0;
|
|
MP_DIGITS(&precomp[i][1]) = 0;
|
|
}
|
|
for (i = 0; i < MAX_SCRATCH; i++) {
|
|
MP_DIGITS(&scratch[i]) = 0;
|
|
}
|
|
|
|
ARGCHK(group != NULL, MP_BADARG);
|
|
ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
|
|
|
|
/* initialize precomputation table */
|
|
MP_CHECKOK(mp_init(&tpx));
|
|
MP_CHECKOK(mp_init(&tpy));;
|
|
MP_CHECKOK(mp_init(&rz));
|
|
MP_CHECKOK(mp_init(&raz4));
|
|
|
|
for (i = 0; i < 16; i++) {
|
|
MP_CHECKOK(mp_init(&precomp[i][0]));
|
|
MP_CHECKOK(mp_init(&precomp[i][1]));
|
|
}
|
|
for (i = 0; i < MAX_SCRATCH; i++) {
|
|
MP_CHECKOK(mp_init(&scratch[i]));
|
|
}
|
|
|
|
/* Set out[8] = P */
|
|
MP_CHECKOK(mp_copy(px, &precomp[8][0]));
|
|
MP_CHECKOK(mp_copy(py, &precomp[8][1]));
|
|
|
|
/* Set (tpx, tpy) = 2P */
|
|
MP_CHECKOK(group->
|
|
point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,
|
|
group));
|
|
|
|
/* Set 3P, 5P, ..., 15P */
|
|
for (i = 8; i < 15; i++) {
|
|
MP_CHECKOK(group->
|
|
point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy,
|
|
&precomp[i + 1][0], &precomp[i + 1][1],
|
|
group));
|
|
}
|
|
|
|
/* Set -15P, -13P, ..., -P */
|
|
for (i = 0; i < 8; i++) {
|
|
MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));
|
|
MP_CHECKOK(group->meth->
|
|
field_neg(&precomp[15 - i][1], &precomp[i][1],
|
|
group->meth));
|
|
}
|
|
|
|
/* R = inf */
|
|
MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
|
|
|
|
orderBitSize = mpl_significant_bits(&group->order);
|
|
|
|
/* Allocate memory for NAF */
|
|
naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));
|
|
if (naf == NULL) {
|
|
res = MP_MEM;
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* Compute 5NAF */
|
|
ec_compute_wNAF(naf, orderBitSize, n, 5);
|
|
|
|
/* wNAF method */
|
|
for (i = orderBitSize; i >= 0; i--) {
|
|
/* R = 2R */
|
|
ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz,
|
|
&raz4, scratch, group);
|
|
if (naf[i] != 0) {
|
|
ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,
|
|
&precomp[(naf[i] + 15) / 2][0],
|
|
&precomp[(naf[i] + 15) / 2][1], rx, ry,
|
|
&rz, &raz4, scratch, group);
|
|
}
|
|
}
|
|
|
|
/* convert result S to affine coordinates */
|
|
MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
|
|
|
|
CLEANUP:
|
|
for (i = 0; i < MAX_SCRATCH; i++) {
|
|
mp_clear(&scratch[i]);
|
|
}
|
|
for (i = 0; i < 16; i++) {
|
|
mp_clear(&precomp[i][0]);
|
|
mp_clear(&precomp[i][1]);
|
|
}
|
|
mp_clear(&tpx);
|
|
mp_clear(&tpy);
|
|
mp_clear(&rz);
|
|
mp_clear(&raz4);
|
|
free(naf);
|
|
return res;
|
|
}
|