New basic implementation of Curve25519 (generic i15 code, experimental).
This commit is contained in:
Thomas Pornin
parent
ef318ef83a
commit
2f9c953af4
9 changed files with 448 additions and 18 deletions
303
src/ec/ec_c25519_i15.c
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303
src/ec/ec_c25519_i15.c
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/*
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* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
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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
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* "Software"), to deal in the Software without restriction, including
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* without limitation the rights to use, copy, modify, merge, publish,
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* distribute, sublicense, and/or sell copies of the Software, and to
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* permit persons to whom the Software is furnished to do so, subject to
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* the following conditions:
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*
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* The above copyright notice and this permission notice shall be
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* included 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,
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
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* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
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* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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* SOFTWARE.
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*/
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#include "inner.h"
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/*
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* Parameters for the field:
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* - field modulus p = 2^255-19
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* - R^2 mod p (R = 2^(15k) for the smallest k such that R >= p)
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*/
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static const uint16_t C255_P[] = {
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0x0110,
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0x7FED, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
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0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
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0x7FFF
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};
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#define P0I 0x4A1B
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static const uint16_t C255_R2[] = {
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0x0110,
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0x0169, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
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0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
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0x0000
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};
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static const uint16_t C255_A24[] = {
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0x0110,
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0x45D3, 0x0046, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
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0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
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0x0000
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};
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static const unsigned char GEN[] = {
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0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
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};
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static const unsigned char ORDER[] = {
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0x10, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x14, 0xDE, 0xF9, 0xDE, 0xA2, 0xF7, 0x9C, 0xD6,
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0x58, 0x12, 0x63, 0x1A, 0x5C, 0xF5, 0xD3, 0xED
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};
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static const unsigned char *
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api_generator(int curve, size_t *len)
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{
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(void)curve;
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*len = 32;
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return GEN;
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}
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static const unsigned char *
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api_order(int curve, size_t *len)
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{
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(void)curve;
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*len = 32;
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return ORDER;
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}
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static void
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cswap(uint16_t *a, uint16_t *b, uint32_t ctl)
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{
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int i;
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ctl = -ctl;
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for (i = 0; i < 18; i ++) {
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uint32_t aw, bw, tw;
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aw = a[i];
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bw = b[i];
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tw = ctl & (aw ^ bw);
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a[i] = aw ^ tw;
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b[i] = bw ^ tw;
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}
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}
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static void
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c255_add(uint16_t *d, const uint16_t *a, const uint16_t *b)
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{
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uint32_t ctl;
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uint16_t t[18];
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memcpy(t, a, sizeof t);
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ctl = br_i15_add(t, b, 1);
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ctl |= NOT(br_i15_sub(t, C255_P, 0));
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br_i15_sub(t, C255_P, ctl);
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memcpy(d, t, sizeof t);
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}
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static void
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c255_sub(uint16_t *d, const uint16_t *a, const uint16_t *b)
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{
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uint16_t t[18];
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memcpy(t, a, sizeof t);
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br_i15_add(t, C255_P, br_i15_sub(t, b, 1));
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memcpy(d, t, sizeof t);
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}
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static void
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c255_mul(uint16_t *d, const uint16_t *a, const uint16_t *b)
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{
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uint16_t t[18];
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br_i15_montymul(t, a, b, C255_P, P0I);
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memcpy(d, t, sizeof t);
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}
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static void
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byteswap(unsigned char *G)
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{
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int i;
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for (i = 0; i < 16; i ++) {
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unsigned char t;
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t = G[i];
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G[i] = G[31 - i];
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G[31 - i] = t;
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}
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}
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static uint32_t
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api_mul(unsigned char *G, size_t Glen,
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const unsigned char *kb, size_t kblen, int curve)
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{
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uint16_t x1[18], x2[18], x3[18], z2[18], z3[18];
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uint16_t a[18], aa[18], b[18], bb[18];
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uint16_t c[18], d[18], e[18], da[18], cb[18];
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unsigned char k[32];
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uint32_t swap;
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int i;
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(void)curve;
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/*
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* Points are encoded over exactly 32 bytes. Multipliers must fit
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* in 32 bytes as well.
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* RFC 7748 mandates that the high bit of the last point byte must
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* be ignored/cleared.
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*/
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if (Glen != 32 || kblen > 32) {
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return 0;
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}
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G[31] &= 0x7F;
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/*
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* Byteswap the point encoding, because it uses little-endian, and
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* the generic decoding routine uses big-endian.
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*/
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byteswap(G);
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/*
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* Initialise variables x1, x2, z2, x3 and z3. We set all of them
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* into Montgomery representation.
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*/
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br_i15_decode_reduce(a, G, 32, C255_P);
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br_i15_montymul(x1, a, C255_R2, C255_P, P0I);
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memcpy(x3, x1, sizeof x1);
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br_i15_zero(z2, C255_P[0]);
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memcpy(x2, z2, sizeof z2);
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x2[1] = 19;
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memcpy(z3, x2, sizeof x2);
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memcpy(k, kb, kblen);
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memset(k + kblen, 0, (sizeof k) - kblen);
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k[0] &= 0xF8;
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k[31] &= 0x7F;
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k[31] |= 0x40;
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swap = 0;
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for (i = 254; i >= 0; i --) {
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uint32_t kt;
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kt = (k[i >> 3] >> (i & 7)) & 1;
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swap ^= kt;
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cswap(x2, x3, swap);
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cswap(z2, z3, swap);
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swap = kt;
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c255_add(a, x2, z2);
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c255_mul(aa, a, a);
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c255_sub(b, x2, z2);
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c255_mul(bb, b, b);
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c255_sub(e, aa, bb);
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c255_add(c, x3, z3);
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c255_sub(d, x3, z3);
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c255_mul(da, d, a);
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c255_mul(cb, c, b);
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c255_add(x3, da, cb);
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c255_mul(x3, x3, x3);
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c255_sub(z3, da, cb);
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c255_mul(z3, z3, z3);
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c255_mul(z3, z3, x1);
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c255_mul(x2, aa, bb);
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c255_mul(z2, C255_A24, e);
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c255_add(z2, z2, aa);
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c255_mul(z2, e, z2);
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}
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cswap(x2, x3, swap);
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cswap(z2, z3, swap);
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/*
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* Inverse z2 with a modular exponentiation. This is a simple
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* square-and-multiply algorithm; we mutualise most non-squarings
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* since the exponent contains almost only ones.
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*/
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memcpy(a, z2, sizeof z2);
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for (i = 0; i < 15; i ++) {
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c255_mul(a, a, a);
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c255_mul(a, a, z2);
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}
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memcpy(b, a, sizeof a);
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for (i = 0; i < 14; i ++) {
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int j;
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for (j = 0; j < 16; j ++) {
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c255_mul(b, b, b);
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}
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c255_mul(b, b, a);
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}
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for (i = 14; i >= 0; i --) {
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c255_mul(b, b, b);
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if ((0xFFEB >> i) & 1) {
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c255_mul(b, z2, b);
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}
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}
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c255_mul(x2, x2, b);
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br_i15_from_monty(x2, C255_P, P0I);
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br_i15_encode(G, 32, x2);
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byteswap(G);
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return 1;
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}
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static size_t
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api_mulgen(unsigned char *R,
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const unsigned char *x, size_t xlen, int curve)
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{
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const unsigned char *G;
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size_t Glen;
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G = api_generator(curve, &Glen);
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memcpy(R, G, Glen);
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api_mul(R, Glen, x, xlen, curve);
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return Glen;
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}
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static uint32_t
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api_muladd(unsigned char *A, const unsigned char *B, size_t len,
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const unsigned char *x, size_t xlen,
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const unsigned char *y, size_t ylen, int curve)
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{
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/*
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* We don't implement this method, since it is used for ECDSA
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* only, and there is no ECDSA over Curve25519 (which instead
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* uses EdDSA).
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*/
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(void)A;
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(void)B;
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(void)len;
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(void)x;
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(void)xlen;
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(void)y;
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(void)ylen;
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(void)curve;
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return 0;
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}
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/* see bearssl_ec.h */
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const br_ec_impl br_ec_c25519_i15 = {
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(uint32_t)0x20000000,
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&api_generator,
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&api_order,
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&api_mul,
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&api_mulgen,
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&api_muladd
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};
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46
src/ec/ec_curve25519.c
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46
src/ec/ec_curve25519.c
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@ -0,0 +1,46 @@
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/*
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* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
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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
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* "Software"), to deal in the Software without restriction, including
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* without limitation the rights to use, copy, modify, merge, publish,
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* distribute, sublicense, and/or sell copies of the Software, and to
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* permit persons to whom the Software is furnished to do so, subject to
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* the following conditions:
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*
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* The above copyright notice and this permission notice shall be
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* included 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,
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
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* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
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* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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* SOFTWARE.
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*/
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#include "inner.h"
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static const unsigned char GEN[] = {
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0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
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};
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static const unsigned char ORDER[] = {
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0x10, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x14, 0xDE, 0xF9, 0xDE, 0xA2, 0xF7, 0x9C, 0xD6,
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0x58, 0x12, 0x63, 0x1A, 0x5C, 0xF5, 0xD3, 0xED
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};
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/* see inner.h */
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const br_ec_curve_def br_curve25519 = {
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BR_EC_curve25519,
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ORDER, sizeof ORDER,
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GEN, sizeof GEN
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};
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@ -2075,7 +2075,7 @@ api_muladd(unsigned char *A, const unsigned char *B, size_t len,
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}
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/* see bearssl_ec.h */
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const br_ec_impl br_ec_p256_i15 = {
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const br_ec_impl br_ec_p256_m15 = {
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(uint32_t)0x00800000,
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&api_generator,
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&api_order,
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@ -1456,6 +1456,8 @@ extern const br_ec_curve_def br_secp256r1;
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extern const br_ec_curve_def br_secp384r1;
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extern const br_ec_curve_def br_secp521r1;
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extern const br_ec_curve_def br_curve25519;
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#if 0
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/* obsolete */
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/*
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@ -263,7 +263,8 @@ br_i15_montymul(uint16_t *d, const uint16_t *x, const uint16_t *y,
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uint32_t f, xu, r, zh;
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xu = x[u + 1];
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f = MUL15(d[1] + MUL15(x[u + 1], y[1]), m0i) & 0x7FFF;
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f = MUL15((d[1] + MUL15(x[u + 1], y[1])) & 0x7FFF, m0i)
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& 0x7FFF;
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r = 0;
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for (v = 0; v < len4; v += 4) {
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@ -297,7 +298,7 @@ br_i15_montymul(uint16_t *d, const uint16_t *x, const uint16_t *y,
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zh = dh + r;
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d[len] = zh & 0x7FFF;
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dh = zh >> 31;
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dh = zh >> 15;
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}
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/*
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