--- /dev/null
+/*
+ * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/*
+ * Parameters for the field:
+ * - field modulus p = 2^255-19
+ * - R^2 mod p (R = 2^(31k) for the smallest k such that R >= p)
+ */
+
+static const uint32_t C255_P[] = {
+ 0x00000107,
+ 0x7FFFFFED, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
+ 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x0000007F
+};
+
+#define P0I 0x286BCA1B
+
+static const uint32_t C255_R2[] = {
+ 0x00000107,
+ 0x00000000, 0x02D20000, 0x00000000, 0x00000000, 0x00000000,
+ 0x00000000, 0x00000000, 0x00000000, 0x00000000
+};
+
+static const uint32_t C255_A24[] = {
+ 0x00000107,
+ 0x53000000, 0x0000468B, 0x00000000, 0x00000000, 0x00000000,
+ 0x00000000, 0x00000000, 0x00000000, 0x00000000
+};
+
+/* obsolete
+#include <stdio.h>
+#include <stdlib.h>
+static void
+print_int_mont(const char *name, const uint32_t *x)
+{
+ uint32_t y[10];
+ unsigned char tmp[32];
+ size_t u;
+
+ printf("%s = ", name);
+ memcpy(y, x, sizeof y);
+ br_i31_from_monty(y, C255_P, P0I);
+ br_i31_encode(tmp, sizeof tmp, y);
+ for (u = 0; u < sizeof tmp; u ++) {
+ printf("%02X", tmp[u]);
+ }
+ printf("\n");
+}
+*/
+
+static const unsigned char GEN[] = {
+ 0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
+};
+
+static const unsigned char ORDER[] = {
+ 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
+};
+
+static const unsigned char *
+api_generator(int curve, size_t *len)
+{
+ (void)curve;
+ *len = 32;
+ return GEN;
+}
+
+static const unsigned char *
+api_order(int curve, size_t *len)
+{
+ (void)curve;
+ *len = 32;
+ return ORDER;
+}
+
+static size_t
+api_xoff(int curve, size_t *len)
+{
+ (void)curve;
+ *len = 32;
+ return 0;
+}
+
+static void
+cswap(uint32_t *a, uint32_t *b, uint32_t ctl)
+{
+ int i;
+
+ ctl = -ctl;
+ for (i = 0; i < 10; i ++) {
+ uint32_t aw, bw, tw;
+
+ aw = a[i];
+ bw = b[i];
+ tw = ctl & (aw ^ bw);
+ a[i] = aw ^ tw;
+ b[i] = bw ^ tw;
+ }
+}
+
+static void
+c255_add(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+ uint32_t ctl;
+ uint32_t t[10];
+
+ memcpy(t, a, sizeof t);
+ ctl = br_i31_add(t, b, 1);
+ ctl |= NOT(br_i31_sub(t, C255_P, 0));
+ br_i31_sub(t, C255_P, ctl);
+ memcpy(d, t, sizeof t);
+}
+
+static void
+c255_sub(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+ uint32_t t[10];
+
+ memcpy(t, a, sizeof t);
+ br_i31_add(t, C255_P, br_i31_sub(t, b, 1));
+ memcpy(d, t, sizeof t);
+}
+
+static void
+c255_mul(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+ uint32_t t[10];
+
+ br_i31_montymul(t, a, b, C255_P, P0I);
+ memcpy(d, t, sizeof t);
+}
+
+static void
+byteswap(unsigned char *G)
+{
+ int i;
+
+ for (i = 0; i < 16; i ++) {
+ unsigned char t;
+
+ t = G[i];
+ G[i] = G[31 - i];
+ G[31 - i] = t;
+ }
+}
+
+static uint32_t
+api_mul(unsigned char *G, size_t Glen,
+ const unsigned char *kb, size_t kblen, int curve)
+{
+ uint32_t x1[10], x2[10], x3[10], z2[10], z3[10];
+ uint32_t a[10], aa[10], b[10], bb[10];
+ uint32_t c[10], d[10], e[10], da[10], cb[10];
+ unsigned char k[32];
+ uint32_t swap;
+ int i;
+
+ (void)curve;
+
+ /*
+ * Points are encoded over exactly 32 bytes. Multipliers must fit
+ * in 32 bytes as well.
+ * RFC 7748 mandates that the high bit of the last point byte must
+ * be ignored/cleared.
+ */
+ if (Glen != 32 || kblen > 32) {
+ return 0;
+ }
+ G[31] &= 0x7F;
+
+ /*
+ * Byteswap the point encoding, because it uses little-endian, and
+ * the generic decoding routine uses big-endian.
+ */
+ byteswap(G);
+
+ /*
+ * Initialise variables x1, x2, z2, x3 and z3. We set all of them
+ * into Montgomery representation.
+ */
+ br_i31_decode_reduce(a, G, 32, C255_P);
+ br_i31_montymul(x1, a, C255_R2, C255_P, P0I);
+ memcpy(x3, x1, sizeof x1);
+ br_i31_zero(z2, C255_P[0]);
+ memcpy(x2, z2, sizeof z2);
+ x2[1] = 0x13000000;
+ memcpy(z3, x2, sizeof x2);
+
+ memcpy(k, kb, kblen);
+ memset(k + kblen, 0, (sizeof k) - kblen);
+ k[0] &= 0xF8;
+ k[31] &= 0x7F;
+ k[31] |= 0x40;
+
+ /* obsolete
+ print_int_mont("x1", x1);
+ */
+
+ swap = 0;
+ for (i = 254; i >= 0; i --) {
+ uint32_t kt;
+
+ kt = (k[i >> 3] >> (i & 7)) & 1;
+ swap ^= kt;
+ cswap(x2, x3, swap);
+ cswap(z2, z3, swap);
+ swap = kt;
+
+ /* obsolete
+ print_int_mont("x2", x2);
+ print_int_mont("z2", z2);
+ print_int_mont("x3", x3);
+ print_int_mont("z3", z3);
+ */
+
+ c255_add(a, x2, z2);
+ c255_mul(aa, a, a);
+ c255_sub(b, x2, z2);
+ c255_mul(bb, b, b);
+ c255_sub(e, aa, bb);
+ c255_add(c, x3, z3);
+ c255_sub(d, x3, z3);
+ c255_mul(da, d, a);
+ c255_mul(cb, c, b);
+
+ /* obsolete
+ print_int_mont("a ", a);
+ print_int_mont("aa", aa);
+ print_int_mont("b ", b);
+ print_int_mont("bb", bb);
+ print_int_mont("e ", e);
+ print_int_mont("c ", c);
+ print_int_mont("d ", d);
+ print_int_mont("da", da);
+ print_int_mont("cb", cb);
+ */
+
+ c255_add(x3, da, cb);
+ c255_mul(x3, x3, x3);
+ c255_sub(z3, da, cb);
+ c255_mul(z3, z3, z3);
+ c255_mul(z3, z3, x1);
+ c255_mul(x2, aa, bb);
+ c255_mul(z2, C255_A24, e);
+ c255_add(z2, z2, aa);
+ c255_mul(z2, e, z2);
+
+ /* obsolete
+ print_int_mont("x2", x2);
+ print_int_mont("z2", z2);
+ print_int_mont("x3", x3);
+ print_int_mont("z3", z3);
+ */
+ }
+ cswap(x2, x3, swap);
+ cswap(z2, z3, swap);
+
+ /*
+ * Inverse z2 with a modular exponentiation. This is a simple
+ * square-and-multiply algorithm; we mutualise most non-squarings
+ * since the exponent contains almost only ones.
+ */
+ memcpy(a, z2, sizeof z2);
+ for (i = 0; i < 15; i ++) {
+ c255_mul(a, a, a);
+ c255_mul(a, a, z2);
+ }
+ memcpy(b, a, sizeof a);
+ for (i = 0; i < 14; i ++) {
+ int j;
+
+ for (j = 0; j < 16; j ++) {
+ c255_mul(b, b, b);
+ }
+ c255_mul(b, b, a);
+ }
+ for (i = 14; i >= 0; i --) {
+ c255_mul(b, b, b);
+ if ((0xFFEB >> i) & 1) {
+ c255_mul(b, z2, b);
+ }
+ }
+ c255_mul(x2, x2, b);
+ br_i31_from_monty(x2, C255_P, P0I);
+ br_i31_encode(G, 32, x2);
+ byteswap(G);
+ return 1;
+}
+
+static size_t
+api_mulgen(unsigned char *R,
+ const unsigned char *x, size_t xlen, int curve)
+{
+ const unsigned char *G;
+ size_t Glen;
+
+ G = api_generator(curve, &Glen);
+ memcpy(R, G, Glen);
+ api_mul(R, Glen, x, xlen, curve);
+ return Glen;
+}
+
+static uint32_t
+api_muladd(unsigned char *A, const unsigned char *B, size_t len,
+ const unsigned char *x, size_t xlen,
+ const unsigned char *y, size_t ylen, int curve)
+{
+ /*
+ * We don't implement this method, since it is used for ECDSA
+ * only, and there is no ECDSA over Curve25519 (which instead
+ * uses EdDSA).
+ */
+ (void)A;
+ (void)B;
+ (void)len;
+ (void)x;
+ (void)xlen;
+ (void)y;
+ (void)ylen;
+ (void)curve;
+ return 0;
+}
+
+/* see bearssl_ec.h */
+const br_ec_impl br_ec_c25519_i31 = {
+ (uint32_t)0x20000000,
+ &api_generator,
+ &api_order,
+ &api_xoff,
+ &api_mul,
+ &api_mulgen,
+ &api_muladd
+};
--- /dev/null
+/*
+ * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining
+ * a copy of this software and associated documentation files (the
+ * "Software"), to deal in the Software without restriction, including
+ * without limitation the rights to use, copy, modify, merge, publish,
+ * distribute, sublicense, and/or sell copies of the Software, and to
+ * permit persons to whom the Software is furnished to do so, subject to
+ * the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "inner.h"
+
+/* obsolete
+#include <stdio.h>
+#include <stdlib.h>
+static void
+print_int(const char *name, const uint32_t *x)
+{
+ size_t u;
+ unsigned char tmp[40];
+
+ printf("%s = ", name);
+ for (u = 0; u < 9; u ++) {
+ if (x[u] > 0x3FFFFFFF) {
+ printf("INVALID:");
+ for (u = 0; u < 9; u ++) {
+ printf(" %08X", x[u]);
+ }
+ printf("\n");
+ return;
+ }
+ }
+ memset(tmp, 0, sizeof tmp);
+ for (u = 0; u < 9; u ++) {
+ uint64_t w;
+ int j, k;
+
+ w = x[u];
+ j = 30 * (int)u;
+ k = j & 7;
+ if (k != 0) {
+ w <<= k;
+ j -= k;
+ }
+ k = j >> 3;
+ for (j = 0; j < 8; j ++) {
+ tmp[39 - k - j] |= (unsigned char)w;
+ w >>= 8;
+ }
+ }
+ for (u = 8; u < 40; u ++) {
+ printf("%02X", tmp[u]);
+ }
+ printf("\n");
+}
+*/
+
+/*
+ * If BR_NO_ARITH_SHIFT is undefined, or defined to 0, then we _assume_
+ * that right-shifting a signed negative integer copies the sign bit
+ * (arithmetic right-shift). This is "implementation-defined behaviour",
+ * i.e. it is not undefined, but it may differ between compilers. Each
+ * compiler is supposed to document its behaviour in that respect. GCC
+ * explicitly defines that an arithmetic right shift is used. We expect
+ * all other compilers to do the same, because underlying CPU offer an
+ * arithmetic right shift opcode that could not be used otherwise.
+ */
+#if BR_NO_ARITH_SHIFT
+#define ARSH(x, n) (((uint32_t)(x) >> (n)) \
+ | ((-((uint32_t)(x) >> 31)) << (32 - (n))))
+#else
+#define ARSH(x, n) ((*(int32_t *)&(x)) >> (n))
+#endif
+
+/*
+ * Convert an integer from unsigned little-endian encoding to a sequence of
+ * 30-bit words in little-endian order. The final "partial" word is
+ * returned.
+ */
+static uint32_t
+le8_to_le30(uint32_t *dst, const unsigned char *src, size_t len)
+{
+ uint32_t acc;
+ int acc_len;
+
+ acc = 0;
+ acc_len = 0;
+ while (len -- > 0) {
+ uint32_t b;
+
+ b = *src ++;
+ if (acc_len < 22) {
+ acc |= b << acc_len;
+ acc_len += 8;
+ } else {
+ *dst ++ = (acc | (b << acc_len)) & 0x3FFFFFFF;
+ acc = b >> (30 - acc_len);
+ acc_len -= 22;
+ }
+ }
+ return acc;
+}
+
+/*
+ * Convert an integer (30-bit words, little-endian) to unsigned
+ * little-endian encoding. The total encoding length is provided; all
+ * the destination bytes will be filled.
+ */
+static void
+le30_to_le8(unsigned char *dst, size_t len, const uint32_t *src)
+{
+ uint32_t acc;
+ int acc_len;
+
+ acc = 0;
+ acc_len = 0;
+ while (len -- > 0) {
+ if (acc_len < 8) {
+ uint32_t w;
+
+ w = *src ++;
+ *dst ++ = (unsigned char)(acc | (w << acc_len));
+ acc = w >> (8 - acc_len);
+ acc_len += 22;
+ } else {
+ *dst ++ = (unsigned char)acc;
+ acc >>= 8;
+ acc_len -= 8;
+ }
+ }
+}
+
+/*
+ * Multiply two integers. Source integers are represented as arrays of
+ * nine 30-bit words, for values up to 2^270-1. Result is encoded over
+ * 18 words of 30 bits each.
+ */
+static void
+mul9(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+ /*
+ * Maximum intermediate result is no more than
+ * 10376293531797946367, which fits in 64 bits. Reason:
+ *
+ * 10376293531797946367 = 9 * (2^30-1)^2 + 9663676406
+ * 10376293531797946367 < 9663676407 * 2^30
+ *
+ * Thus, adding together 9 products of 30-bit integers, with
+ * a carry of at most 9663676406, yields an integer that fits
+ * on 64 bits and generates a carry of at most 9663676406.
+ */
+ uint64_t t[17];
+ uint64_t cc;
+ int i;
+
+ t[ 0] = MUL31(a[0], b[0]);
+ t[ 1] = MUL31(a[0], b[1])
+ + MUL31(a[1], b[0]);
+ t[ 2] = MUL31(a[0], b[2])
+ + MUL31(a[1], b[1])
+ + MUL31(a[2], b[0]);
+ t[ 3] = MUL31(a[0], b[3])
+ + MUL31(a[1], b[2])
+ + MUL31(a[2], b[1])
+ + MUL31(a[3], b[0]);
+ t[ 4] = MUL31(a[0], b[4])
+ + MUL31(a[1], b[3])
+ + MUL31(a[2], b[2])
+ + MUL31(a[3], b[1])
+ + MUL31(a[4], b[0]);
+ t[ 5] = MUL31(a[0], b[5])
+ + MUL31(a[1], b[4])
+ + MUL31(a[2], b[3])
+ + MUL31(a[3], b[2])
+ + MUL31(a[4], b[1])
+ + MUL31(a[5], b[0]);
+ t[ 6] = MUL31(a[0], b[6])
+ + MUL31(a[1], b[5])
+ + MUL31(a[2], b[4])
+ + MUL31(a[3], b[3])
+ + MUL31(a[4], b[2])
+ + MUL31(a[5], b[1])
+ + MUL31(a[6], b[0]);
+ t[ 7] = MUL31(a[0], b[7])
+ + MUL31(a[1], b[6])
+ + MUL31(a[2], b[5])
+ + MUL31(a[3], b[4])
+ + MUL31(a[4], b[3])
+ + MUL31(a[5], b[2])
+ + MUL31(a[6], b[1])
+ + MUL31(a[7], b[0]);
+ t[ 8] = MUL31(a[0], b[8])
+ + MUL31(a[1], b[7])
+ + MUL31(a[2], b[6])
+ + MUL31(a[3], b[5])
+ + MUL31(a[4], b[4])
+ + MUL31(a[5], b[3])
+ + MUL31(a[6], b[2])
+ + MUL31(a[7], b[1])
+ + MUL31(a[8], b[0]);
+ t[ 9] = MUL31(a[1], b[8])
+ + MUL31(a[2], b[7])
+ + MUL31(a[3], b[6])
+ + MUL31(a[4], b[5])
+ + MUL31(a[5], b[4])
+ + MUL31(a[6], b[3])
+ + MUL31(a[7], b[2])
+ + MUL31(a[8], b[1]);
+ t[10] = MUL31(a[2], b[8])
+ + MUL31(a[3], b[7])
+ + MUL31(a[4], b[6])
+ + MUL31(a[5], b[5])
+ + MUL31(a[6], b[4])
+ + MUL31(a[7], b[3])
+ + MUL31(a[8], b[2]);
+ t[11] = MUL31(a[3], b[8])
+ + MUL31(a[4], b[7])
+ + MUL31(a[5], b[6])
+ + MUL31(a[6], b[5])
+ + MUL31(a[7], b[4])
+ + MUL31(a[8], b[3]);
+ t[12] = MUL31(a[4], b[8])
+ + MUL31(a[5], b[7])
+ + MUL31(a[6], b[6])
+ + MUL31(a[7], b[5])
+ + MUL31(a[8], b[4]);
+ t[13] = MUL31(a[5], b[8])
+ + MUL31(a[6], b[7])
+ + MUL31(a[7], b[6])
+ + MUL31(a[8], b[5]);
+ t[14] = MUL31(a[6], b[8])
+ + MUL31(a[7], b[7])
+ + MUL31(a[8], b[6]);
+ t[15] = MUL31(a[7], b[8])
+ + MUL31(a[8], b[7]);
+ t[16] = MUL31(a[8], b[8]);
+
+ /*
+ * Propagate carries.
+ */
+ cc = 0;
+ for (i = 0; i < 17; i ++) {
+ uint64_t w;
+
+ w = t[i] + cc;
+ d[i] = (uint32_t)w & 0x3FFFFFFF;
+ cc = w >> 30;
+ }
+ d[17] = (uint32_t)cc;
+}
+
+/*
+ * Square a 270-bit integer, represented as an array of nine 30-bit words.
+ * Result uses 18 words of 30 bits each.
+ */
+static void
+square9(uint32_t *d, const uint32_t *a)
+{
+ uint64_t t[17];
+ uint64_t cc;
+ int i;
+
+ t[ 0] = MUL31(a[0], a[0]);
+ t[ 1] = ((MUL31(a[0], a[1])) << 1);
+ t[ 2] = MUL31(a[1], a[1])
+ + ((MUL31(a[0], a[2])) << 1);
+ t[ 3] = ((MUL31(a[0], a[3])
+ + MUL31(a[1], a[2])) << 1);
+ t[ 4] = MUL31(a[2], a[2])
+ + ((MUL31(a[0], a[4])
+ + MUL31(a[1], a[3])) << 1);
+ t[ 5] = ((MUL31(a[0], a[5])
+ + MUL31(a[1], a[4])
+ + MUL31(a[2], a[3])) << 1);
+ t[ 6] = MUL31(a[3], a[3])
+ + ((MUL31(a[0], a[6])
+ + MUL31(a[1], a[5])
+ + MUL31(a[2], a[4])) << 1);
+ t[ 7] = ((MUL31(a[0], a[7])
+ + MUL31(a[1], a[6])
+ + MUL31(a[2], a[5])
+ + MUL31(a[3], a[4])) << 1);
+ t[ 8] = MUL31(a[4], a[4])
+ + ((MUL31(a[0], a[8])
+ + MUL31(a[1], a[7])
+ + MUL31(a[2], a[6])
+ + MUL31(a[3], a[5])) << 1);
+ t[ 9] = ((MUL31(a[1], a[8])
+ + MUL31(a[2], a[7])
+ + MUL31(a[3], a[6])
+ + MUL31(a[4], a[5])) << 1);
+ t[10] = MUL31(a[5], a[5])
+ + ((MUL31(a[2], a[8])
+ + MUL31(a[3], a[7])
+ + MUL31(a[4], a[6])) << 1);
+ t[11] = ((MUL31(a[3], a[8])
+ + MUL31(a[4], a[7])
+ + MUL31(a[5], a[6])) << 1);
+ t[12] = MUL31(a[6], a[6])
+ + ((MUL31(a[4], a[8])
+ + MUL31(a[5], a[7])) << 1);
+ t[13] = ((MUL31(a[5], a[8])
+ + MUL31(a[6], a[7])) << 1);
+ t[14] = MUL31(a[7], a[7])
+ + ((MUL31(a[6], a[8])) << 1);
+ t[15] = ((MUL31(a[7], a[8])) << 1);
+ t[16] = MUL31(a[8], a[8]);
+
+ /*
+ * Propagate carries.
+ */
+ cc = 0;
+ for (i = 0; i < 17; i ++) {
+ uint64_t w;
+
+ w = t[i] + cc;
+ d[i] = (uint32_t)w & 0x3FFFFFFF;
+ cc = w >> 30;
+ }
+ d[17] = (uint32_t)cc;
+}
+
+/*
+ * Perform a "final reduction" in field F255 (field for Curve25519)
+ * The source value must be less than twice the modulus. If the value
+ * is not lower than the modulus, then the modulus is subtracted and
+ * this function returns 1; otherwise, it leaves it untouched and it
+ * returns 0.
+ */
+static uint32_t
+reduce_final_f255(uint32_t *d)
+{
+ uint32_t t[9];
+ uint32_t cc;
+ int i;
+
+ memcpy(t, d, sizeof t);
+ cc = 19;
+ for (i = 0; i < 9; i ++) {
+ uint32_t w;
+
+ w = t[i] + cc;
+ cc = w >> 30;
+ t[i] = w & 0x3FFFFFFF;
+ }
+ cc = t[8] >> 15;
+ t[8] &= 0x7FFF;
+ CCOPY(cc, d, t, sizeof t);
+ return cc;
+}
+
+/*
+ * Perform a multiplication of two integers modulo 2^255-19.
+ * Operands are arrays of 9 words, each containing 30 bits of data, in
+ * little-endian order. Input value may be up to 2^256-1; on output, value
+ * fits on 256 bits and is lower than twice the modulus.
+ */
+static void
+f255_mul(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+ uint32_t t[18];
+ uint64_t cc, w;
+ int i;
+
+ /*
+ * Compute raw multiplication. All result words fit in 30 bits
+ * each; upper word (t[17]) must fit on 2 bits, since the product
+ * of two 256-bit integers must fit on 512 bits.
+ */
+ mul9(t, a, b);
+
+ /*
+ * Modular reduction: each high word is added where necessary.
+ * Since the modulus is 2^255-19 and word 9 corresponds to
+ * offset 9*30 = 270, word 9+k must be added to word k with
+ * a factor of 19*2^15 = 622592. The extra bits in word 8 are also
+ * added that way.
+ */
+ cc = MUL31(t[8] >> 15, 19);
+ t[8] &= 0x7FFF;
+ for (i = 0; i < 9; i ++) {
+ w = (uint64_t)t[i] + cc + MUL31(t[i + 9], 622592);
+ t[i] = (uint32_t)w & 0x3FFFFFFF;
+ cc = w >> 30;
+ }
+ cc = MUL31(w >> 15, 19);
+ t[8] &= 0x7FFF;
+ for (i = 0; i < 9; i ++) {
+ w = t[i] + cc;
+ d[i] = (uint32_t)w & 0x3FFFFFFF;
+ cc = w >> 30;
+ }
+}
+
+/*
+ * Perform a squaring of an integer modulo 2^255-19.
+ * Operands are arrays of 9 words, each containing 30 bits of data, in
+ * little-endian order. Input value may be up to 2^256-1; on output, value
+ * fits on 256 bits and is lower than twice the modulus.
+ */
+static void
+f255_square(uint32_t *d, const uint32_t *a)
+{
+ uint32_t t[18];
+ uint64_t cc, w;
+ int i;
+
+ /*
+ * Compute raw squaring. All result words fit in 30 bits
+ * each; upper word (t[17]) must fit on 2 bits, since the square
+ * of a 256-bit integers must fit on 512 bits.
+ */
+ square9(t, a);
+
+ /*
+ * Modular reduction: each high word is added where necessary.
+ * Since the modulus is 2^255-19 and word 9 corresponds to
+ * offset 9*30 = 270, word 9+k must be added to word k with
+ * a factor of 19*2^15 = 622592. The extra bits in word 8 are also
+ * added that way.
+ */
+ cc = MUL31(t[8] >> 15, 19);
+ t[8] &= 0x7FFF;
+ for (i = 0; i < 9; i ++) {
+ w = (uint64_t)t[i] + cc + MUL31(t[i + 9], 622592);
+ t[i] = (uint32_t)w & 0x3FFFFFFF;
+ cc = w >> 30;
+ }
+ cc = MUL31(w >> 15, 19);
+ t[8] &= 0x7FFF;
+ for (i = 0; i < 9; i ++) {
+ w = t[i] + cc;
+ d[i] = (uint32_t)w & 0x3FFFFFFF;
+ cc = w >> 30;
+ }
+}
+
+/*
+ * Add two values in F255. Partial reduction is performed (down to less
+ * than twice the modulus).
+ */
+static void
+f255_add(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+ /*
+ * Since operand words fit on 30 bits, we can use 32-bit
+ * variables throughout.
+ */
+ int i;
+ uint32_t cc, w;
+
+ cc = 0;
+ for (i = 0; i < 9; i ++) {
+ w = a[i] + b[i] + cc;
+ d[i] = w & 0x3FFFFFFF;
+ cc = w >> 30;
+ }
+ cc = MUL15(w >> 15, 19);
+ d[8] &= 0x7FFF;
+ for (i = 0; i < 9; i ++) {
+ w = d[i] + cc;
+ d[i] = w & 0x3FFFFFFF;
+ cc = w >> 30;
+ }
+}
+
+/*
+ * Subtract one value from another in F255. Partial reduction is
+ * performed (down to less than twice the modulus).
+ */
+static void
+f255_sub(uint32_t *d, const uint32_t *a, const uint32_t *b)
+{
+ /*
+ * We actually compute a - b + 2*p, so that the final value is
+ * necessarily positive.
+ */
+ int i;
+ uint32_t cc, w;
+
+ cc = (uint32_t)-38;
+ for (i = 0; i < 9; i ++) {
+ w = a[i] - b[i] + cc;
+ d[i] = w & 0x3FFFFFFF;
+ cc = ARSH(w, 30);
+ }
+ cc = MUL15((w + 0x10000) >> 15, 19);
+ d[8] &= 0x7FFF;
+ for (i = 0; i < 9; i ++) {
+ w = d[i] + cc;
+ d[i] = w & 0x3FFFFFFF;
+ cc = w >> 30;
+ }
+}
+
+/*
+ * Multiply an integer by the 'A24' constant (121665). Partial reduction
+ * is performed (down to less than twice the modulus).
+ */
+static void
+f255_mul_a24(uint32_t *d, const uint32_t *a)
+{
+ int i;
+ uint64_t cc, w;
+
+ cc = 0;
+ for (i = 0; i < 9; i ++) {
+ w = MUL31(a[i], 121665) + cc;
+ d[i] = (uint32_t)w & 0x3FFFFFFF;
+ cc = w >> 30;
+ }
+ cc = MUL31((uint32_t)(w >> 15), 19);
+ d[8] &= 0x7FFF;
+ for (i = 0; i < 9; i ++) {
+ w = (uint64_t)d[i] + cc;
+ d[i] = w & 0x3FFFFFFF;
+ cc = w >> 30;
+ }
+}
+
+static const unsigned char GEN[] = {
+ 0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
+};
+
+static const unsigned char ORDER[] = {
+ 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
+};
+
+static const unsigned char *
+api_generator(int curve, size_t *len)
+{
+ (void)curve;
+ *len = 32;
+ return GEN;
+}
+
+static const unsigned char *
+api_order(int curve, size_t *len)
+{
+ (void)curve;
+ *len = 32;
+ return ORDER;
+}
+
+static size_t
+api_xoff(int curve, size_t *len)
+{
+ (void)curve;
+ *len = 32;
+ return 0;
+}
+
+static void
+cswap(uint32_t *a, uint32_t *b, uint32_t ctl)
+{
+ int i;
+
+ ctl = -ctl;
+ for (i = 0; i < 9; i ++) {
+ uint32_t aw, bw, tw;
+
+ aw = a[i];
+ bw = b[i];
+ tw = ctl & (aw ^ bw);
+ a[i] = aw ^ tw;
+ b[i] = bw ^ tw;
+ }
+}
+
+static uint32_t
+api_mul(unsigned char *G, size_t Glen,
+ const unsigned char *kb, size_t kblen, int curve)
+{
+ uint32_t x1[9], x2[9], x3[9], z2[9], z3[9];
+ uint32_t a[9], aa[9], b[9], bb[9];
+ uint32_t c[9], d[9], e[9], da[9], cb[9];
+ unsigned char k[32];
+ uint32_t swap;
+ int i;
+
+ (void)curve;
+
+ /*
+ * Points are encoded over exactly 32 bytes. Multipliers must fit
+ * in 32 bytes as well.
+ * RFC 7748 mandates that the high bit of the last point byte must
+ * be ignored/cleared.
+ */
+ if (Glen != 32 || kblen > 32) {
+ return 0;
+ }
+ G[31] &= 0x7F;
+
+ /*
+ * Initialise variables x1, x2, z2, x3 and z3. We set all of them
+ * into Montgomery representation.
+ */
+ x1[8] = le8_to_le30(x1, G, 32);
+ memcpy(x3, x1, sizeof x1);
+ memset(z2, 0, sizeof z2);
+ memset(x2, 0, sizeof x2);
+ x2[0] = 1;
+ memset(z3, 0, sizeof z3);
+ z3[0] = 1;
+
+ memcpy(k, kb, kblen);
+ memset(k + kblen, 0, (sizeof k) - kblen);
+ k[0] &= 0xF8;
+ k[31] &= 0x7F;
+ k[31] |= 0x40;
+
+ /* obsolete
+ print_int("x1", x1);
+ */
+
+ swap = 0;
+ for (i = 254; i >= 0; i --) {
+ uint32_t kt;
+
+ kt = (k[i >> 3] >> (i & 7)) & 1;
+ swap ^= kt;
+ cswap(x2, x3, swap);
+ cswap(z2, z3, swap);
+ swap = kt;
+
+ /* obsolete
+ print_int("x2", x2);
+ print_int("z2", z2);
+ print_int("x3", x3);
+ print_int("z3", z3);
+ */
+
+ f255_add(a, x2, z2);
+ f255_square(aa, a);
+ f255_sub(b, x2, z2);
+ f255_square(bb, b);
+ f255_sub(e, aa, bb);
+ f255_add(c, x3, z3);
+ f255_sub(d, x3, z3);
+ f255_mul(da, d, a);
+ f255_mul(cb, c, b);
+
+ /* obsolete
+ print_int("a ", a);
+ print_int("aa", aa);
+ print_int("b ", b);
+ print_int("bb", bb);
+ print_int("e ", e);
+ print_int("c ", c);
+ print_int("d ", d);
+ print_int("da", da);
+ print_int("cb", cb);
+ */
+
+ f255_add(x3, da, cb);
+ f255_square(x3, x3);
+ f255_sub(z3, da, cb);
+ f255_square(z3, z3);
+ f255_mul(z3, z3, x1);
+ f255_mul(x2, aa, bb);
+ f255_mul_a24(z2, e);
+ f255_add(z2, z2, aa);
+ f255_mul(z2, e, z2);
+
+ /* obsolete
+ print_int("x2", x2);
+ print_int("z2", z2);
+ print_int("x3", x3);
+ print_int("z3", z3);
+ */
+ }
+ cswap(x2, x3, swap);
+ cswap(z2, z3, swap);
+
+ /*
+ * Inverse z2 with a modular exponentiation. This is a simple
+ * square-and-multiply algorithm; we mutualise most non-squarings
+ * since the exponent contains almost only ones.
+ */
+ memcpy(a, z2, sizeof z2);
+ for (i = 0; i < 15; i ++) {
+ f255_square(a, a);
+ f255_mul(a, a, z2);
+ }
+ memcpy(b, a, sizeof a);
+ for (i = 0; i < 14; i ++) {
+ int j;
+
+ for (j = 0; j < 16; j ++) {
+ f255_square(b, b);
+ }
+ f255_mul(b, b, a);
+ }
+ for (i = 14; i >= 0; i --) {
+ f255_square(b, b);
+ if ((0xFFEB >> i) & 1) {
+ f255_mul(b, z2, b);
+ }
+ }
+ f255_mul(x2, x2, b);
+ reduce_final_f255(x2);
+ le30_to_le8(G, 32, x2);
+ return 1;
+}
+
+static size_t
+api_mulgen(unsigned char *R,
+ const unsigned char *x, size_t xlen, int curve)
+{
+ const unsigned char *G;
+ size_t Glen;
+
+ G = api_generator(curve, &Glen);
+ memcpy(R, G, Glen);
+ api_mul(R, Glen, x, xlen, curve);
+ return Glen;
+}
+
+static uint32_t
+api_muladd(unsigned char *A, const unsigned char *B, size_t len,
+ const unsigned char *x, size_t xlen,
+ const unsigned char *y, size_t ylen, int curve)
+{
+ /*
+ * We don't implement this method, since it is used for ECDSA
+ * only, and there is no ECDSA over Curve25519 (which instead
+ * uses EdDSA).
+ */
+ (void)A;
+ (void)B;
+ (void)len;
+ (void)x;
+ (void)xlen;
+ (void)y;
+ (void)ylen;
+ (void)curve;
+ return 0;
+}
+
+/* see bearssl_ec.h */
+const br_ec_impl br_ec_c25519_m31 = {
+ (uint32_t)0x20000000,
+ &api_generator,
+ &api_order,
+ &api_xoff,
+ &api_mul,
+ &api_mulgen,
+ &api_muladd
+};
projects / BearSSL / commitdiff