289 lines
8.2 KiB
C
289 lines
8.2 KiB
C
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/**********************************************************************
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* Copyright (c) 2013, 2014 Pieter Wuille *
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* Distributed under the MIT software license, see the accompanying *
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* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
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**********************************************************************/
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#ifndef SECP256K1_NUM_REPR_IMPL_H
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#define SECP256K1_NUM_REPR_IMPL_H
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#include <string.h>
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#include <stdlib.h>
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#include <gmp.h>
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#include "util.h"
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#include "num.h"
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#ifdef VERIFY
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static void secp256k1_num_sanity(const secp256k1_num *a) {
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VERIFY_CHECK(a->limbs == 1 || (a->limbs > 1 && a->data[a->limbs-1] != 0));
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}
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#else
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#define secp256k1_num_sanity(a) do { } while(0)
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#endif
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static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a) {
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*r = *a;
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}
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static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a) {
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unsigned char tmp[65];
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int len = 0;
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int shift = 0;
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if (a->limbs>1 || a->data[0] != 0) {
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len = mpn_get_str(tmp, 256, (mp_limb_t*)a->data, a->limbs);
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}
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while (shift < len && tmp[shift] == 0) shift++;
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VERIFY_CHECK(len-shift <= (int)rlen);
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memset(r, 0, rlen - len + shift);
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if (len > shift) {
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memcpy(r + rlen - len + shift, tmp + shift, len - shift);
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}
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memset(tmp, 0, sizeof(tmp));
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}
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static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen) {
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int len;
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VERIFY_CHECK(alen > 0);
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VERIFY_CHECK(alen <= 64);
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len = mpn_set_str(r->data, a, alen, 256);
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if (len == 0) {
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r->data[0] = 0;
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len = 1;
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}
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VERIFY_CHECK(len <= NUM_LIMBS*2);
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r->limbs = len;
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r->neg = 0;
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while (r->limbs > 1 && r->data[r->limbs-1]==0) {
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r->limbs--;
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}
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}
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static void secp256k1_num_add_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
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mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs);
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r->limbs = a->limbs;
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if (c != 0) {
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VERIFY_CHECK(r->limbs < 2*NUM_LIMBS);
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r->data[r->limbs++] = c;
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}
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}
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static void secp256k1_num_sub_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
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mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs);
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(void)c;
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VERIFY_CHECK(c == 0);
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r->limbs = a->limbs;
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while (r->limbs > 1 && r->data[r->limbs-1]==0) {
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r->limbs--;
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}
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}
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static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m) {
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secp256k1_num_sanity(r);
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secp256k1_num_sanity(m);
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if (r->limbs >= m->limbs) {
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mp_limb_t t[2*NUM_LIMBS];
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mpn_tdiv_qr(t, r->data, 0, r->data, r->limbs, m->data, m->limbs);
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memset(t, 0, sizeof(t));
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r->limbs = m->limbs;
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while (r->limbs > 1 && r->data[r->limbs-1]==0) {
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r->limbs--;
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}
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}
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if (r->neg && (r->limbs > 1 || r->data[0] != 0)) {
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secp256k1_num_sub_abs(r, m, r);
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r->neg = 0;
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}
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}
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static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m) {
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int i;
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mp_limb_t g[NUM_LIMBS+1];
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mp_limb_t u[NUM_LIMBS+1];
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mp_limb_t v[NUM_LIMBS+1];
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mp_size_t sn;
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mp_size_t gn;
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secp256k1_num_sanity(a);
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secp256k1_num_sanity(m);
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/** mpn_gcdext computes: (G,S) = gcdext(U,V), where
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* * G = gcd(U,V)
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* * G = U*S + V*T
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* * U has equal or more limbs than V, and V has no padding
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* If we set U to be (a padded version of) a, and V = m:
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* G = a*S + m*T
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* G = a*S mod m
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* Assuming G=1:
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* S = 1/a mod m
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*/
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VERIFY_CHECK(m->limbs <= NUM_LIMBS);
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VERIFY_CHECK(m->data[m->limbs-1] != 0);
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for (i = 0; i < m->limbs; i++) {
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u[i] = (i < a->limbs) ? a->data[i] : 0;
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v[i] = m->data[i];
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}
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sn = NUM_LIMBS+1;
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gn = mpn_gcdext(g, r->data, &sn, u, m->limbs, v, m->limbs);
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(void)gn;
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VERIFY_CHECK(gn == 1);
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VERIFY_CHECK(g[0] == 1);
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r->neg = a->neg ^ m->neg;
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if (sn < 0) {
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mpn_sub(r->data, m->data, m->limbs, r->data, -sn);
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r->limbs = m->limbs;
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while (r->limbs > 1 && r->data[r->limbs-1]==0) {
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r->limbs--;
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}
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} else {
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r->limbs = sn;
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}
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memset(g, 0, sizeof(g));
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memset(u, 0, sizeof(u));
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memset(v, 0, sizeof(v));
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}
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static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b) {
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int ret;
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mpz_t ga, gb;
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secp256k1_num_sanity(a);
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secp256k1_num_sanity(b);
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VERIFY_CHECK(!b->neg && (b->limbs > 0) && (b->data[0] & 1));
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mpz_inits(ga, gb, NULL);
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mpz_import(gb, b->limbs, -1, sizeof(mp_limb_t), 0, 0, b->data);
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mpz_import(ga, a->limbs, -1, sizeof(mp_limb_t), 0, 0, a->data);
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if (a->neg) {
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mpz_neg(ga, ga);
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}
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ret = mpz_jacobi(ga, gb);
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mpz_clears(ga, gb, NULL);
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return ret;
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}
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static int secp256k1_num_is_one(const secp256k1_num *a) {
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return (a->limbs == 1 && a->data[0] == 1);
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}
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static int secp256k1_num_is_zero(const secp256k1_num *a) {
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return (a->limbs == 1 && a->data[0] == 0);
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}
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static int secp256k1_num_is_neg(const secp256k1_num *a) {
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return (a->limbs > 1 || a->data[0] != 0) && a->neg;
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}
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static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b) {
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if (a->limbs > b->limbs) {
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return 1;
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}
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if (a->limbs < b->limbs) {
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return -1;
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}
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return mpn_cmp(a->data, b->data, a->limbs);
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}
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static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b) {
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if (a->limbs > b->limbs) {
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return 0;
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}
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if (a->limbs < b->limbs) {
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return 0;
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}
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if ((a->neg && !secp256k1_num_is_zero(a)) != (b->neg && !secp256k1_num_is_zero(b))) {
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return 0;
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}
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return mpn_cmp(a->data, b->data, a->limbs) == 0;
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}
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static void secp256k1_num_subadd(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b, int bneg) {
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if (!(b->neg ^ bneg ^ a->neg)) { /* a and b have the same sign */
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r->neg = a->neg;
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if (a->limbs >= b->limbs) {
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secp256k1_num_add_abs(r, a, b);
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} else {
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secp256k1_num_add_abs(r, b, a);
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}
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} else {
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if (secp256k1_num_cmp(a, b) > 0) {
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r->neg = a->neg;
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secp256k1_num_sub_abs(r, a, b);
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} else {
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r->neg = b->neg ^ bneg;
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secp256k1_num_sub_abs(r, b, a);
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}
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}
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}
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static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
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secp256k1_num_sanity(a);
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secp256k1_num_sanity(b);
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secp256k1_num_subadd(r, a, b, 0);
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}
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static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
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secp256k1_num_sanity(a);
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secp256k1_num_sanity(b);
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secp256k1_num_subadd(r, a, b, 1);
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}
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static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) {
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mp_limb_t tmp[2*NUM_LIMBS+1];
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secp256k1_num_sanity(a);
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secp256k1_num_sanity(b);
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VERIFY_CHECK(a->limbs + b->limbs <= 2*NUM_LIMBS+1);
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if ((a->limbs==1 && a->data[0]==0) || (b->limbs==1 && b->data[0]==0)) {
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r->limbs = 1;
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r->neg = 0;
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r->data[0] = 0;
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return;
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}
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if (a->limbs >= b->limbs) {
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mpn_mul(tmp, a->data, a->limbs, b->data, b->limbs);
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} else {
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mpn_mul(tmp, b->data, b->limbs, a->data, a->limbs);
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}
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r->limbs = a->limbs + b->limbs;
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if (r->limbs > 1 && tmp[r->limbs - 1]==0) {
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r->limbs--;
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}
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VERIFY_CHECK(r->limbs <= 2*NUM_LIMBS);
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mpn_copyi(r->data, tmp, r->limbs);
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r->neg = a->neg ^ b->neg;
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memset(tmp, 0, sizeof(tmp));
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}
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static void secp256k1_num_shift(secp256k1_num *r, int bits) {
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if (bits % GMP_NUMB_BITS) {
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/* Shift within limbs. */
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mpn_rshift(r->data, r->data, r->limbs, bits % GMP_NUMB_BITS);
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}
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if (bits >= GMP_NUMB_BITS) {
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int i;
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/* Shift full limbs. */
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for (i = 0; i < r->limbs; i++) {
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int index = i + (bits / GMP_NUMB_BITS);
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if (index < r->limbs && index < 2*NUM_LIMBS) {
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r->data[i] = r->data[index];
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} else {
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r->data[i] = 0;
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}
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}
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}
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while (r->limbs>1 && r->data[r->limbs-1]==0) {
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r->limbs--;
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}
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}
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static void secp256k1_num_negate(secp256k1_num *r) {
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r->neg ^= 1;
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}
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#endif /* SECP256K1_NUM_REPR_IMPL_H */
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