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965 lines
25 KiB
965 lines
25 KiB
/**
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* Copyright (c) 2013-2014 Tomas Dzetkulic
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* Copyright (c) 2013-2014 Pavol Rusnak
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*
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* Permission is hereby granted, free of charge, to any person obtaining
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* a copy of this software and associated documentation files (the "Software"),
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* to deal in the Software without restriction, including without limitation
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* the rights to use, copy, modify, merge, publish, distribute, sublicense,
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* and/or sell copies of the Software, and to permit persons to whom the
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* Software is furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included
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* in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES
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* OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
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* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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* OTHER DEALINGS IN THE SOFTWARE.
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*/
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#include <stdint.h>
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#include <stdlib.h>
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#include <string.h>
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#include <assert.h>
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#include "bignum.h"
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#include "rand.h"
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#include "sha2.h"
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#include "ripemd160.h"
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#include "hmac.h"
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#include "ecdsa.h"
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#include "base58.h"
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// Set cp2 = cp1
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void point_copy(const curve_point *cp1, curve_point *cp2)
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{
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*cp2 = *cp1;
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}
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// cp2 = cp1 + cp2
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void point_add(const curve_point *cp1, curve_point *cp2)
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{
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int i;
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uint32_t temp;
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bignum256 lambda, inv, xr, yr;
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if (point_is_infinity(cp1)) {
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return;
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}
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if (point_is_infinity(cp2)) {
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point_copy(cp1, cp2);
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return;
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}
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if (point_is_equal(cp1, cp2)) {
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point_double(cp2);
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return;
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}
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if (point_is_negative_of(cp1, cp2)) {
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point_set_infinity(cp2);
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return;
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}
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bn_subtractmod(&(cp2->x), &(cp1->x), &inv, &prime256k1);
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bn_inverse(&inv, &prime256k1);
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bn_subtractmod(&(cp2->y), &(cp1->y), &lambda, &prime256k1);
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bn_multiply(&inv, &lambda, &prime256k1);
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// xr = lambda^2 - x1 - x2
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xr = lambda;
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bn_multiply(&xr, &xr, &prime256k1);
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temp = 1;
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for (i = 0; i < 9; i++) {
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temp += 0x3FFFFFFF + xr.val[i] + 2u * prime256k1.val[i] - cp1->x.val[i] - cp2->x.val[i];
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xr.val[i] = temp & 0x3FFFFFFF;
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temp >>= 30;
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}
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bn_fast_mod(&xr, &prime256k1);
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bn_mod(&xr, &prime256k1);
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// yr = lambda (x1 - xr) - y1
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bn_subtractmod(&(cp1->x), &xr, &yr, &prime256k1);
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bn_multiply(&lambda, &yr, &prime256k1);
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bn_subtractmod(&yr, &(cp1->y), &yr, &prime256k1);
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bn_fast_mod(&yr, &prime256k1);
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bn_mod(&yr, &prime256k1);
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cp2->x = xr;
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cp2->y = yr;
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}
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// cp = cp + cp
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void point_double(curve_point *cp)
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{
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int i;
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uint32_t temp;
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bignum256 lambda, xr, yr;
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if (point_is_infinity(cp)) {
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return;
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}
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if (bn_is_zero(&(cp->y))) {
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point_set_infinity(cp);
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return;
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}
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// lambda = 3/2 x^2 / y
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lambda = cp->y;
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bn_inverse(&lambda, &prime256k1);
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bn_multiply(&cp->x, &lambda, &prime256k1);
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bn_multiply(&cp->x, &lambda, &prime256k1);
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bn_mult_3_2(&lambda, &prime256k1);
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// xr = lambda^2 - 2*x
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xr = lambda;
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bn_multiply(&xr, &xr, &prime256k1);
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temp = 1;
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for (i = 0; i < 9; i++) {
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temp += 0x3FFFFFFF + xr.val[i] + 2u * (prime256k1.val[i] - cp->x.val[i]);
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xr.val[i] = temp & 0x3FFFFFFF;
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temp >>= 30;
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}
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bn_fast_mod(&xr, &prime256k1);
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bn_mod(&xr, &prime256k1);
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// yr = lambda (x - xr) - y
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bn_subtractmod(&(cp->x), &xr, &yr, &prime256k1);
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bn_multiply(&lambda, &yr, &prime256k1);
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bn_subtractmod(&yr, &(cp->y), &yr, &prime256k1);
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bn_fast_mod(&yr, &prime256k1);
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bn_mod(&yr, &prime256k1);
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cp->x = xr;
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cp->y = yr;
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}
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// set point to internal representation of point at infinity
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void point_set_infinity(curve_point *p)
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{
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bn_zero(&(p->x));
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bn_zero(&(p->y));
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}
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// return true iff p represent point at infinity
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// both coords are zero in internal representation
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int point_is_infinity(const curve_point *p)
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{
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return bn_is_zero(&(p->x)) && bn_is_zero(&(p->y));
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}
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// return true iff both points are equal
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int point_is_equal(const curve_point *p, const curve_point *q)
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{
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return bn_is_equal(&(p->x), &(q->x)) && bn_is_equal(&(p->y), &(q->y));
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}
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// returns true iff p == -q
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// expects p and q be valid points on curve other than point at infinity
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int point_is_negative_of(const curve_point *p, const curve_point *q)
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{
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// if P == (x, y), then -P would be (x, -y) on this curve
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if (!bn_is_equal(&(p->x), &(q->x))) {
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return 0;
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}
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// we shouldn't hit this for a valid point
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if (bn_is_zero(&(p->y))) {
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return 0;
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}
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return !bn_is_equal(&(p->y), &(q->y));
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}
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// Negate a (modulo prime) if cond is 0xffffffff, keep it if cond is 0.
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// The timing of this function does not depend on cond.
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static void conditional_negate(uint32_t cond, bignum256 *a, const bignum256 *prime)
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{
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int j;
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uint32_t tmp = 1;
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for (j = 0; j < 8; j++) {
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tmp += 0x3fffffff + prime->val[j] - a->val[j];
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a->val[j] = ((tmp & 0x3fffffff) & cond) | (a->val[j] & ~cond);
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tmp >>= 30;
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}
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tmp += 0x3fffffff + prime->val[j] - a->val[j];
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a->val[j] = ((tmp & 0x3fffffff) & cond) | (a->val[j] & ~cond);
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}
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typedef struct jacobian_curve_point {
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bignum256 x, y, z;
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} jacobian_curve_point;
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static void curve_to_jacobian(const curve_point *p, jacobian_curve_point *jp) {
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int i;
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// randomize z coordinate
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for (i = 0; i < 8; i++) {
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jp->z.val[i] = random32() & 0x3FFFFFFF;
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}
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jp->z.val[8] = (random32() & 0x7fff) + 1;
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jp->x = jp->z;
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bn_multiply(&jp->z, &jp->x, &prime256k1);
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// x = z^2
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jp->y = jp->x;
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bn_multiply(&jp->z, &jp->y, &prime256k1);
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// y = z^3
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bn_multiply(&p->x, &jp->x, &prime256k1);
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bn_multiply(&p->y, &jp->y, &prime256k1);
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bn_mod(&jp->x, &prime256k1);
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bn_mod(&jp->y, &prime256k1);
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}
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static void jacobian_to_curve(const jacobian_curve_point *jp, curve_point *p) {
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p->y = jp->z;
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bn_mod(&p->y, &prime256k1);
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bn_inverse(&p->y, &prime256k1);
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// p->y = z^-1
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p->x = p->y;
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bn_multiply(&p->x, &p->x, &prime256k1);
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// p->x = z^-2
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bn_multiply(&p->x, &p->y, &prime256k1);
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// p->y = z^-3
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bn_multiply(&jp->x, &p->x, &prime256k1);
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// p->x = jp->x * z^-2
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bn_multiply(&jp->y, &p->y, &prime256k1);
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// p->y = jp->y * z^-3
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bn_mod(&p->x, &prime256k1);
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bn_mod(&p->y, &prime256k1);
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}
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static void point_jacobian_add(const curve_point *p1, jacobian_curve_point *p2) {
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bignum256 r, h;
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bignum256 rsq, hcb, hcby2, hsqx2;
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int j;
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uint64_t tmp1;
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/* usual algorithm:
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*
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* lambda = (y1 - y2/z2^3) / (x1 - x2/z2^2)
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* x3/z3^2 = lambda^2 - x1 - x2/z2^2
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* y3/z3^3 = lambda * (x2/z2^2 - x3/z3^2) - y2/z2^3
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*
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* to get rid of fraction we set
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* r = (y1 * z2^3 - y2) (the numerator of lambda * z2^3)
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* h = (x1 * z2^2 - x2) (the denominator of lambda * z2^2)
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* Hence,
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* lambda = r / (h*z2)
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*
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* With z3 = h*z2 (the denominator of lambda)
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* we get x3 = lambda^2*z3^2 - x1*z3^2 - x2/z2^2*z3^2
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* = r^2 - x1*h^2*z2^2 - x2*h^2
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* = r^2 - h^2*(x1*z2^2 + x2)
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* = r^2 - h^2*(h + 2*x2)
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* = r^2 - h^3 - 2*h^2*x2
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* and y3 = (lambda * (x2/z2^2 - x3/z3^2) - y2/z2^3) * z3^3
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* = r * (h^2*x2 - x3) - h^3*y2
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*/
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/* h = x1*z2^2 - x2
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* r = y1*z2^3 - y2
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* x3 = r^2 - h^3 - 2*h^2*x2
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* y3 = r*(h^2*x2 - x3) - h^3*y2
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* z3 = h*z2
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*/
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// h = x1 * z2^2 - x2;
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// r = y1 * z2^3 - y2;
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h = p2->z;
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bn_multiply(&h, &h, &prime256k1); // h = z2^2
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r = p2->z;
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bn_multiply(&h, &r, &prime256k1); // r = z2^3
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bn_multiply(&p1->x, &h, &prime256k1);
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bn_subtractmod(&h, &p2->x, &h, &prime256k1);
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// h = x1 * z2^2 - x2;
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bn_multiply(&p1->y, &r, &prime256k1);
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bn_subtractmod(&r, &p2->y, &r, &prime256k1);
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// r = y1 * z2^3 - y2;
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// hsqx2 = h^2
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hsqx2 = h;
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bn_multiply(&hsqx2, &hsqx2, &prime256k1);
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// hcb = h^3
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hcb = h;
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bn_multiply(&hsqx2, &hcb, &prime256k1);
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// hsqx2 = h^2 * x2
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bn_multiply(&p2->x, &hsqx2, &prime256k1);
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// hcby2 = h^3 * y2
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hcby2 = hcb;
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bn_multiply(&p2->y, &hcby2, &prime256k1);
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// rsq = r^2
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rsq = r;
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bn_multiply(&rsq, &rsq, &prime256k1);
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// z3 = h*z2
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bn_multiply(&h, &p2->z, &prime256k1);
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bn_mod(&p2->z, &prime256k1);
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// x3 = r^2 - h^3 - 2h^2x2
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tmp1 = 0;
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for (j = 0; j < 9; j++) {
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tmp1 += (uint64_t) rsq.val[j] + 4*prime256k1.val[j] - hcb.val[j] - 2*hsqx2.val[j];
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assert(tmp1 < 5 * 0x40000000ull);
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p2->x.val[j] = tmp1 & 0x3fffffff;
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tmp1 >>= 30;
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}
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bn_fast_mod(&p2->x, &prime256k1);
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bn_mod(&p2->x, &prime256k1);
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// y3 = r*(h^2x2 - x3) - y2*h^3
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bn_subtractmod(&hsqx2, &p2->x, &p2->y, &prime256k1);
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bn_multiply(&r, &p2->y, &prime256k1);
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bn_subtractmod(&p2->y, &hcby2, &p2->y, &prime256k1);
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bn_fast_mod(&p2->y, &prime256k1);
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bn_mod(&p2->y, &prime256k1);
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}
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static void point_jacobian_double(jacobian_curve_point *p) {
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bignum256 m, msq, ysq, xysq;
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int j;
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uint32_t tmp1;
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/* usual algorithm:
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*
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* lambda = (3(x/z^2)^2 / 2y/z^3) = 3x^2/2yz
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* x3/z3^2 = lambda^2 - 2x/z^2
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* y3/z3^3 = lambda * (x/z^2 - x3/z3^2) - y/z^3
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*
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* to get rid of fraction we set
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* m = 3/2 x^2
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* Hence,
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* lambda = m / yz
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*
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* With z3 = yz (the denominator of lambda)
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* we get x3 = lambda^2*z3^2 - 2*x/z^2*z3^2
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* = m^2 - 2*xy^2
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* and y3 = (lambda * (x/z^2 - x3/z3^2) - y/z^3) * z3^3
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* = m * (xy^2 - x3) - y^4
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*/
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/* m = 3/2*x*x
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* x3 = m^2 - 2*xy^2
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* y3 = m*(xy^2 - x3) - 8y^4
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* z3 = y*z
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*/
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m = p->x;
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bn_multiply(&m, &m, &prime256k1);
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bn_mult_3_2(&m, &prime256k1);
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// msq = m^2
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msq = m;
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bn_multiply(&msq, &msq, &prime256k1);
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// ysq = y^2
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ysq = p->y;
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bn_multiply(&ysq, &ysq, &prime256k1);
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// xysq = xy^2
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xysq = p->x;
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bn_multiply(&ysq, &xysq, &prime256k1);
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// z3 = yz
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bn_multiply(&p->y, &p->z, &prime256k1);
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bn_mod(&p->z, &prime256k1);
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// x3 = m^2 - 2*xy^2
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tmp1 = 0;
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for (j = 0; j < 9; j++) {
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tmp1 += msq.val[j] + 3*prime256k1.val[j] - 2*xysq.val[j];
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p->x.val[j] = tmp1 & 0x3fffffff;
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tmp1 >>= 30;
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}
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bn_fast_mod(&p->x, &prime256k1);
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bn_mod(&p->x, &prime256k1);
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// y3 = m*(xy^2 - x3) - y^4
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bn_subtractmod(&xysq, &p->x, &p->y, &prime256k1);
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bn_multiply(&m, &p->y, &prime256k1);
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bn_multiply(&ysq, &ysq, &prime256k1);
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bn_subtractmod(&p->y, &ysq, &p->y, &prime256k1);
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bn_fast_mod(&p->y, &prime256k1);
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bn_mod(&p->y, &prime256k1);
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}
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// res = k * p
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void point_multiply(const bignum256 *k, const curve_point *p, curve_point *res)
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{
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// this algorithm is loosely based on
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// Katsuyuki Okeya and Tsuyoshi Takagi, The Width-w NAF Method Provides
|
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// Small Memory and Fast Elliptic Scalar Multiplications Secure against
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// Side Channel Attacks.
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assert (bn_is_less(k, &order256k1));
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int i, j;
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int pos, shift;
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bignum256 a;
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uint32_t is_even = (k->val[0] & 1) - 1;
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uint32_t bits, sign, nsign;
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jacobian_curve_point jres;
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curve_point pmult[8];
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// is_even = 0xffffffff if k is even, 0 otherwise.
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// add 2^256.
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// make number odd: subtract order256k1 if even
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uint32_t tmp = 1;
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uint32_t is_non_zero = 0;
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for (j = 0; j < 8; j++) {
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is_non_zero |= k->val[j];
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tmp += 0x3fffffff + k->val[j] - (order256k1.val[j] & is_even);
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a.val[j] = tmp & 0x3fffffff;
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tmp >>= 30;
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}
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is_non_zero |= k->val[j];
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a.val[j] = tmp + 0xffff + k->val[j] - (order256k1.val[j] & is_even);
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assert((a.val[0] & 1) != 0);
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// special case 0*p: just return zero. We don't care about constant time.
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if (!is_non_zero) {
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point_set_infinity(res);
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return;
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}
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// Now a = k + 2^256 (mod order256k1) and a is odd.
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//
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// The idea is to bring the new a into the form.
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// sum_{i=0..64} a[i] 16^i, where |a[i]| < 16 and a[i] is odd.
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// a[0] is odd, since a is odd. If a[i] would be even, we can
|
|
// add 1 to it and subtract 16 from a[i-1]. Afterwards,
|
|
// a[64] = 1, which is the 2^256 that we added before.
|
|
//
|
|
// Since k = a - 2^256 (mod order256k1), we can compute
|
|
// k*p = sum_{i=0..63} a[i] 16^i * p
|
|
//
|
|
// We compute |a[i]| * p in advance for all possible
|
|
// values of |a[i]| * p. pmult[i] = (2*i+1) * p
|
|
// We compute p, 3*p, ..., 15*p and store it in the table pmult.
|
|
// store p^2 temporarily in pmult[7]
|
|
pmult[7] = *p;
|
|
point_double(&pmult[7]);
|
|
// compute 3*p, etc by repeatedly adding p^2.
|
|
pmult[0] = *p;
|
|
for (i = 1; i < 8; i++) {
|
|
pmult[i] = pmult[7];
|
|
point_add(&pmult[i-1], &pmult[i]);
|
|
}
|
|
|
|
// now compute res = sum_{i=0..63} a[i] * 16^i * p step by step,
|
|
// starting with i = 63.
|
|
// initialize jres = |a[63]| * p.
|
|
// Note that a[i] = a>>(4*i) & 0xf if (a&0x10) != 0
|
|
// and - (16 - (a>>(4*i) & 0xf)) otherwise. We can compute this as
|
|
// ((a ^ (((a >> 4) & 1) - 1)) & 0xf) >> 1
|
|
// since a is odd.
|
|
bits = a.val[8] >> 12;
|
|
sign = (bits >> 4) - 1;
|
|
bits ^= sign;
|
|
bits &= 15;
|
|
curve_to_jacobian(&pmult[bits>>1], &jres);
|
|
for (i = 62; i >= 0; i--) {
|
|
// sign = sign(a[i+1]) (0xffffffff for negative, 0 for positive)
|
|
// invariant jres = (-1)^sign sum_{j=i+1..63} (a[j] * 16^{j-i-1} * p)
|
|
|
|
point_jacobian_double(&jres);
|
|
point_jacobian_double(&jres);
|
|
point_jacobian_double(&jres);
|
|
point_jacobian_double(&jres);
|
|
|
|
// get lowest 5 bits of a >> (i*4).
|
|
pos = i*4/30; shift = i*4 % 30;
|
|
bits = (a.val[pos+1]<<(30-shift) | a.val[pos] >> shift) & 31;
|
|
nsign = (bits >> 4) - 1;
|
|
bits ^= nsign;
|
|
bits &= 15;
|
|
|
|
// negate last result to make signs of this round and the
|
|
// last round equal.
|
|
conditional_negate(sign ^ nsign, &jres.z, &prime256k1);
|
|
|
|
// add odd factor
|
|
point_jacobian_add(&pmult[bits >> 1], &jres);
|
|
sign = nsign;
|
|
}
|
|
conditional_negate(sign, &jres.z, &prime256k1);
|
|
jacobian_to_curve(&jres, res);
|
|
}
|
|
|
|
#if USE_PRECOMPUTED_CP
|
|
|
|
// res = k * G
|
|
// k must be a normalized number with 0 <= k < order256k1
|
|
void scalar_multiply(const bignum256 *k, curve_point *res)
|
|
{
|
|
assert (bn_is_less(k, &order256k1));
|
|
|
|
int i, j;
|
|
bignum256 a;
|
|
uint32_t is_even = (k->val[0] & 1) - 1;
|
|
uint32_t lowbits;
|
|
jacobian_curve_point jres;
|
|
|
|
// is_even = 0xffffffff if k is even, 0 otherwise.
|
|
|
|
// add 2^256.
|
|
// make number odd: subtract order256k1 if even
|
|
uint32_t tmp = 1;
|
|
uint32_t is_non_zero = 0;
|
|
for (j = 0; j < 8; j++) {
|
|
is_non_zero |= k->val[j];
|
|
tmp += 0x3fffffff + k->val[j] - (order256k1.val[j] & is_even);
|
|
a.val[j] = tmp & 0x3fffffff;
|
|
tmp >>= 30;
|
|
}
|
|
is_non_zero |= k->val[j];
|
|
a.val[j] = tmp + 0xffff + k->val[j] - (order256k1.val[j] & is_even);
|
|
assert((a.val[0] & 1) != 0);
|
|
|
|
// special case 0*G: just return zero. We don't care about constant time.
|
|
if (!is_non_zero) {
|
|
point_set_infinity(res);
|
|
return;
|
|
}
|
|
|
|
// Now a = k + 2^256 (mod order256k1) and a is odd.
|
|
//
|
|
// The idea is to bring the new a into the form.
|
|
// sum_{i=0..64} a[i] 16^i, where |a[i]| < 16 and a[i] is odd.
|
|
// a[0] is odd, since a is odd. If a[i] would be even, we can
|
|
// add 1 to it and subtract 16 from a[i-1]. Afterwards,
|
|
// a[64] = 1, which is the 2^256 that we added before.
|
|
//
|
|
// Since k = a - 2^256 (mod order256k1), we can compute
|
|
// k*G = sum_{i=0..63} a[i] 16^i * G
|
|
//
|
|
// We have a big table secp256k1_cp that stores all possible
|
|
// values of |a[i]| 16^i * G.
|
|
// secp256k1_cp[i][j] = (2*j+1) * 16^i * G
|
|
|
|
// now compute res = sum_{i=0..63} a[i] * 16^i * G step by step.
|
|
// initial res = |a[0]| * G. Note that a[0] = a & 0xf if (a&0x10) != 0
|
|
// and - (16 - (a & 0xf)) otherwise. We can compute this as
|
|
// ((a ^ (((a >> 4) & 1) - 1)) & 0xf) >> 1
|
|
// since a is odd.
|
|
lowbits = a.val[0] & ((1 << 5) - 1);
|
|
lowbits ^= (lowbits >> 4) - 1;
|
|
lowbits &= 15;
|
|
curve_to_jacobian(&secp256k1_cp[0][lowbits >> 1], &jres);
|
|
for (i = 1; i < 64; i ++) {
|
|
// invariant res = sign(a[i-1]) sum_{j=0..i-1} (a[j] * 16^j * G)
|
|
|
|
// shift a by 4 places.
|
|
for (j = 0; j < 8; j++) {
|
|
a.val[j] = (a.val[j] >> 4) | ((a.val[j + 1] & 0xf) << 26);
|
|
}
|
|
a.val[j] >>= 4;
|
|
// a = old(a)>>(4*i)
|
|
// a is even iff sign(a[i-1]) = -1
|
|
|
|
lowbits = a.val[0] & ((1 << 5) - 1);
|
|
lowbits ^= (lowbits >> 4) - 1;
|
|
lowbits &= 15;
|
|
// negate last result to make signs of this round and the
|
|
// last round equal.
|
|
conditional_negate((lowbits & 1) - 1, &jres.y, &prime256k1);
|
|
|
|
// add odd factor
|
|
point_jacobian_add(&secp256k1_cp[i][lowbits >> 1], &jres);
|
|
}
|
|
conditional_negate(((a.val[0] >> 4) & 1) - 1, &jres.y, &prime256k1);
|
|
jacobian_to_curve(&jres, res);
|
|
}
|
|
|
|
#else
|
|
|
|
void scalar_multiply(const bignum256 *k, curve_point *res)
|
|
{
|
|
point_multiply(k, &G256k1, res);
|
|
}
|
|
|
|
#endif
|
|
|
|
// generate random K for signing
|
|
int generate_k_random(bignum256 *k) {
|
|
int i, j;
|
|
for (j = 0; j < 10000; j++) {
|
|
for (i = 0; i < 8; i++) {
|
|
k->val[i] = random32() & 0x3FFFFFFF;
|
|
}
|
|
k->val[8] = random32() & 0xFFFF;
|
|
// if k is too big or too small, we don't like it
|
|
if ( !bn_is_zero(k) && bn_is_less(k, &order256k1) ) {
|
|
return 0; // good number - no error
|
|
}
|
|
}
|
|
// we generated 10000 numbers, none of them is good -> fail
|
|
return 1;
|
|
}
|
|
|
|
// generate K in a deterministic way, according to RFC6979
|
|
// http://tools.ietf.org/html/rfc6979
|
|
int generate_k_rfc6979(bignum256 *secret, const uint8_t *priv_key, const uint8_t *hash)
|
|
{
|
|
int i;
|
|
uint8_t v[32], k[32], bx[2*32], buf[32 + 1 + sizeof(bx)];
|
|
bignum256 z1;
|
|
|
|
memcpy(bx, priv_key, 32);
|
|
bn_read_be(hash, &z1);
|
|
bn_mod(&z1, &order256k1);
|
|
bn_write_be(&z1, bx + 32);
|
|
|
|
memset(v, 1, sizeof(v));
|
|
memset(k, 0, sizeof(k));
|
|
|
|
memcpy(buf, v, sizeof(v));
|
|
buf[sizeof(v)] = 0x00;
|
|
memcpy(buf + sizeof(v) + 1, bx, 64);
|
|
hmac_sha256(k, sizeof(k), buf, sizeof(buf), k);
|
|
hmac_sha256(k, sizeof(k), v, sizeof(v), v);
|
|
|
|
memcpy(buf, v, sizeof(v));
|
|
buf[sizeof(v)] = 0x01;
|
|
memcpy(buf + sizeof(v) + 1, bx, 64);
|
|
hmac_sha256(k, sizeof(k), buf, sizeof(buf), k);
|
|
hmac_sha256(k, sizeof(k), v, sizeof(v), v);
|
|
|
|
for (i = 0; i < 10000; i++) {
|
|
hmac_sha256(k, sizeof(k), v, sizeof(v), v);
|
|
bn_read_be(v, secret);
|
|
if ( !bn_is_zero(secret) && bn_is_less(secret, &order256k1) ) {
|
|
return 0; // good number -> no error
|
|
}
|
|
memcpy(buf, v, sizeof(v));
|
|
buf[sizeof(v)] = 0x00;
|
|
hmac_sha256(k, sizeof(k), buf, sizeof(v) + 1, k);
|
|
hmac_sha256(k, sizeof(k), v, sizeof(v), v);
|
|
}
|
|
// we generated 10000 numbers, none of them is good -> fail
|
|
return 1;
|
|
}
|
|
|
|
// msg is a data to be signed
|
|
// msg_len is the message length
|
|
int ecdsa_sign(const uint8_t *priv_key, const uint8_t *msg, uint32_t msg_len, uint8_t *sig, uint8_t *pby)
|
|
{
|
|
uint8_t hash[32];
|
|
sha256_Raw(msg, msg_len, hash);
|
|
return ecdsa_sign_digest(priv_key, hash, sig, pby);
|
|
}
|
|
|
|
// msg is a data to be signed
|
|
// msg_len is the message length
|
|
int ecdsa_sign_double(const uint8_t *priv_key, const uint8_t *msg, uint32_t msg_len, uint8_t *sig, uint8_t *pby)
|
|
{
|
|
uint8_t hash[32];
|
|
sha256_Raw(msg, msg_len, hash);
|
|
sha256_Raw(hash, 32, hash);
|
|
return ecdsa_sign_digest(priv_key, hash, sig, pby);
|
|
}
|
|
|
|
// uses secp256k1 curve
|
|
// priv_key is a 32 byte big endian stored number
|
|
// sig is 64 bytes long array for the signature
|
|
// digest is 32 bytes of digest
|
|
int ecdsa_sign_digest(const uint8_t *priv_key, const uint8_t *digest, uint8_t *sig, uint8_t *pby)
|
|
{
|
|
uint32_t i;
|
|
curve_point R;
|
|
bignum256 k, z;
|
|
bignum256 *da = &R.y;
|
|
|
|
bn_read_be(digest, &z);
|
|
|
|
#if USE_RFC6979
|
|
// generate K deterministically
|
|
if (generate_k_rfc6979(&k, priv_key, digest) != 0) {
|
|
return 1;
|
|
}
|
|
#else
|
|
// generate random number k
|
|
if (generate_k_random(&k) != 0) {
|
|
return 1;
|
|
}
|
|
#endif
|
|
|
|
// compute k*G
|
|
scalar_multiply(&k, &R);
|
|
if (pby) {
|
|
*pby = R.y.val[0] & 1;
|
|
}
|
|
// r = (rx mod n)
|
|
bn_mod(&R.x, &order256k1);
|
|
// if r is zero, we fail
|
|
if (bn_is_zero(&R.x)) return 2;
|
|
bn_inverse(&k, &order256k1);
|
|
bn_read_be(priv_key, da);
|
|
bn_multiply(&R.x, da, &order256k1);
|
|
for (i = 0; i < 8; i++) {
|
|
da->val[i] += z.val[i];
|
|
da->val[i + 1] += (da->val[i] >> 30);
|
|
da->val[i] &= 0x3FFFFFFF;
|
|
}
|
|
da->val[8] += z.val[8];
|
|
bn_multiply(da, &k, &order256k1);
|
|
bn_mod(&k, &order256k1);
|
|
// if k is zero, we fail
|
|
if (bn_is_zero(&k)) return 3;
|
|
|
|
// if S > order/2 => S = -S
|
|
if (bn_is_less(&order256k1_half, &k)) {
|
|
bn_subtract(&order256k1, &k, &k);
|
|
if (pby) {
|
|
*pby = !*pby;
|
|
}
|
|
}
|
|
|
|
// we are done, R.x and k is the result signature
|
|
bn_write_be(&R.x, sig);
|
|
bn_write_be(&k, sig + 32);
|
|
|
|
return 0;
|
|
}
|
|
|
|
void ecdsa_get_public_key33(const uint8_t *priv_key, uint8_t *pub_key)
|
|
{
|
|
curve_point R;
|
|
bignum256 k;
|
|
|
|
bn_read_be(priv_key, &k);
|
|
// compute k*G
|
|
scalar_multiply(&k, &R);
|
|
pub_key[0] = 0x02 | (R.y.val[0] & 0x01);
|
|
bn_write_be(&R.x, pub_key + 1);
|
|
}
|
|
|
|
void ecdsa_get_public_key65(const uint8_t *priv_key, uint8_t *pub_key)
|
|
{
|
|
curve_point R;
|
|
bignum256 k;
|
|
|
|
bn_read_be(priv_key, &k);
|
|
// compute k*G
|
|
scalar_multiply(&k, &R);
|
|
pub_key[0] = 0x04;
|
|
bn_write_be(&R.x, pub_key + 1);
|
|
bn_write_be(&R.y, pub_key + 33);
|
|
}
|
|
|
|
void ecdsa_get_pubkeyhash(const uint8_t *pub_key, uint8_t *pubkeyhash)
|
|
{
|
|
uint8_t h[32];
|
|
if (pub_key[0] == 0x04) { // uncompressed format
|
|
sha256_Raw(pub_key, 65, h);
|
|
} else if (pub_key[0] == 0x00) { // point at infinity
|
|
sha256_Raw(pub_key, 1, h);
|
|
} else {
|
|
sha256_Raw(pub_key, 33, h); // expecting compressed format
|
|
}
|
|
ripemd160(h, 32, pubkeyhash);
|
|
}
|
|
|
|
void ecdsa_get_address_raw(const uint8_t *pub_key, uint8_t version, uint8_t *addr_raw)
|
|
{
|
|
addr_raw[0] = version;
|
|
ecdsa_get_pubkeyhash(pub_key, addr_raw + 1);
|
|
}
|
|
|
|
void ecdsa_get_address(const uint8_t *pub_key, uint8_t version, char *addr, int addrsize)
|
|
{
|
|
uint8_t raw[21];
|
|
ecdsa_get_address_raw(pub_key, version, raw);
|
|
base58_encode_check(raw, 21, addr, addrsize);
|
|
}
|
|
|
|
void ecdsa_get_wif(const uint8_t *priv_key, uint8_t version, char *wif, int wifsize)
|
|
{
|
|
uint8_t data[34];
|
|
data[0] = version;
|
|
memcpy(data + 1, priv_key, 32);
|
|
data[33] = 0x01;
|
|
base58_encode_check(data, 34, wif, wifsize);
|
|
}
|
|
|
|
int ecdsa_address_decode(const char *addr, uint8_t *out)
|
|
{
|
|
if (!addr) return 0;
|
|
return base58_decode_check(addr, out, 21) == 21;
|
|
}
|
|
|
|
void uncompress_coords(uint8_t odd, const bignum256 *x, bignum256 *y)
|
|
{
|
|
// y^2 = x^3 + 0*x + 7
|
|
memcpy(y, x, sizeof(bignum256)); // y is x
|
|
bn_multiply(x, y, &prime256k1); // y is x^2
|
|
bn_multiply(x, y, &prime256k1); // y is x^3
|
|
bn_addmodi(y, 7, &prime256k1); // y is x^3 + 7
|
|
bn_sqrt(y, &prime256k1); // y = sqrt(y)
|
|
if ((odd & 0x01) != (y->val[0] & 1)) {
|
|
bn_subtract(&prime256k1, y, y); // y = -y
|
|
}
|
|
}
|
|
|
|
int ecdsa_read_pubkey(const uint8_t *pub_key, curve_point *pub)
|
|
{
|
|
if (pub_key[0] == 0x04) {
|
|
bn_read_be(pub_key + 1, &(pub->x));
|
|
bn_read_be(pub_key + 33, &(pub->y));
|
|
return ecdsa_validate_pubkey(pub);
|
|
}
|
|
if (pub_key[0] == 0x02 || pub_key[0] == 0x03) { // compute missing y coords
|
|
bn_read_be(pub_key + 1, &(pub->x));
|
|
uncompress_coords(pub_key[0], &(pub->x), &(pub->y));
|
|
return ecdsa_validate_pubkey(pub);
|
|
}
|
|
// error
|
|
return 0;
|
|
}
|
|
|
|
// Verifies that:
|
|
// - pub is not the point at infinity.
|
|
// - pub->x and pub->y are in range [0,p-1].
|
|
// - pub is on the curve.
|
|
|
|
int ecdsa_validate_pubkey(const curve_point *pub)
|
|
{
|
|
bignum256 y_2, x_3_b;
|
|
|
|
if (point_is_infinity(pub)) {
|
|
return 0;
|
|
}
|
|
|
|
if (!bn_is_less(&(pub->x), &prime256k1) || !bn_is_less(&(pub->y), &prime256k1)) {
|
|
return 0;
|
|
}
|
|
|
|
memcpy(&y_2, &(pub->y), sizeof(bignum256));
|
|
memcpy(&x_3_b, &(pub->x), sizeof(bignum256));
|
|
|
|
// y^2
|
|
bn_multiply(&(pub->y), &y_2, &prime256k1);
|
|
bn_mod(&y_2, &prime256k1);
|
|
|
|
// x^3 + b
|
|
bn_multiply(&(pub->x), &x_3_b, &prime256k1);
|
|
bn_multiply(&(pub->x), &x_3_b, &prime256k1);
|
|
bn_addmodi(&x_3_b, 7, &prime256k1);
|
|
|
|
if (!bn_is_equal(&x_3_b, &y_2)) {
|
|
return 0;
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
// uses secp256k1 curve
|
|
// pub_key - 65 bytes uncompressed key
|
|
// signature - 64 bytes signature
|
|
// msg is a data that was signed
|
|
// msg_len is the message length
|
|
|
|
int ecdsa_verify(const uint8_t *pub_key, const uint8_t *sig, const uint8_t *msg, uint32_t msg_len)
|
|
{
|
|
uint8_t hash[32];
|
|
sha256_Raw(msg, msg_len, hash);
|
|
return ecdsa_verify_digest(pub_key, sig, hash);
|
|
}
|
|
|
|
int ecdsa_verify_double(const uint8_t *pub_key, const uint8_t *sig, const uint8_t *msg, uint32_t msg_len)
|
|
{
|
|
uint8_t hash[32];
|
|
sha256_Raw(msg, msg_len, hash);
|
|
sha256_Raw(hash, 32, hash);
|
|
return ecdsa_verify_digest(pub_key, sig, hash);
|
|
}
|
|
|
|
// returns 0 if verification succeeded
|
|
int ecdsa_verify_digest(const uint8_t *pub_key, const uint8_t *sig, const uint8_t *digest)
|
|
{
|
|
curve_point pub, res;
|
|
bignum256 r, s, z;
|
|
|
|
if (!ecdsa_read_pubkey(pub_key, &pub)) {
|
|
return 1;
|
|
}
|
|
|
|
bn_read_be(sig, &r);
|
|
bn_read_be(sig + 32, &s);
|
|
|
|
bn_read_be(digest, &z);
|
|
|
|
if (bn_is_zero(&r) || bn_is_zero(&s) ||
|
|
(!bn_is_less(&r, &order256k1)) ||
|
|
(!bn_is_less(&s, &order256k1))) return 2;
|
|
|
|
bn_inverse(&s, &order256k1); // s^-1
|
|
bn_multiply(&s, &z, &order256k1); // z*s^-1
|
|
bn_mod(&z, &order256k1);
|
|
bn_multiply(&r, &s, &order256k1); // r*s^-1
|
|
bn_mod(&s, &order256k1);
|
|
if (bn_is_zero(&z)) {
|
|
// our message hashes to zero
|
|
// I don't expect this to happen any time soon
|
|
return 3;
|
|
} else {
|
|
scalar_multiply(&z, &res);
|
|
}
|
|
|
|
// both pub and res can be infinity, can have y = 0 OR can be equal -> false negative
|
|
point_multiply(&s, &pub, &pub);
|
|
point_add(&pub, &res);
|
|
bn_mod(&(res.x), &order256k1);
|
|
|
|
// signature does not match
|
|
if (!bn_is_equal(&res.x, &r)) return 5;
|
|
|
|
// all OK
|
|
return 0;
|
|
}
|
|
|
|
int ecdsa_sig_to_der(const uint8_t *sig, uint8_t *der)
|
|
{
|
|
int i;
|
|
uint8_t *p = der, *len, *len1, *len2;
|
|
*p = 0x30; p++; // sequence
|
|
*p = 0x00; len = p; p++; // len(sequence)
|
|
|
|
*p = 0x02; p++; // integer
|
|
*p = 0x00; len1 = p; p++; // len(integer)
|
|
|
|
// process R
|
|
i = 0;
|
|
while (sig[i] == 0 && i < 32) { i++; } // skip leading zeroes
|
|
if (sig[i] >= 0x80) { // put zero in output if MSB set
|
|
*p = 0x00; p++; *len1 = *len1 + 1;
|
|
}
|
|
while (i < 32) { // copy bytes to output
|
|
*p = sig[i]; p++; *len1 = *len1 + 1; i++;
|
|
}
|
|
|
|
*p = 0x02; p++; // integer
|
|
*p = 0x00; len2 = p; p++; // len(integer)
|
|
|
|
// process S
|
|
i = 32;
|
|
while (sig[i] == 0 && i < 64) { i++; } // skip leading zeroes
|
|
if (sig[i] >= 0x80) { // put zero in output if MSB set
|
|
*p = 0x00; p++; *len2 = *len2 + 1;
|
|
}
|
|
while (i < 64) { // copy bytes to output
|
|
*p = sig[i]; p++; *len2 = *len2 + 1; i++;
|
|
}
|
|
|
|
*len = *len1 + *len2 + 4;
|
|
return *len + 2;
|
|
}
|