OBJEC = $(BUILD)/ec_all_m15.o $(BUILD)/ec_all_m31.o $(BUILD)/ec_c25519_i15.o $(BUILD)/ec_c25519_i31.o $(BUILD)/ec_c25519_m15.o $(BUILD)/ec_c25519_m31.o $(BUILD)/ec_curve25519.o $(BUILD)/ec_p256_m15.o $(BUILD)/ec_p256_m31.o $(BUILD)/ec_prime_i15.o $(BUILD)/ec_prime_i31.o $(BUILD)/ec_secp256r1.o $(BUILD)/ec_secp384r1.o $(BUILD)/ec_secp521r1.o $(BUILD)/ecdsa_atr.o $(BUILD)/ecdsa_i15_bits.o $(BUILD)/ecdsa_i15_sign_asn1.o $(BUILD)/ecdsa_i15_sign_raw.o $(BUILD)/ecdsa_i15_vrfy_asn1.o $(BUILD)/ecdsa_i15_vrfy_raw.o $(BUILD)/ecdsa_i31_bits.o $(BUILD)/ecdsa_i31_sign_asn1.o $(BUILD)/ecdsa_i31_sign_raw.o $(BUILD)/ecdsa_i31_vrfy_asn1.o $(BUILD)/ecdsa_i31_vrfy_raw.o $(BUILD)/ecdsa_rta.o
# $(BUILD)/ec_prime_i31_secp256r1.o $(BUILD)/ec_prime_i31_secp384r1.o $(BUILD)/ec_prime_i31_secp521r1.o
OBJHASH = $(BUILD)/dig_oid.o $(BUILD)/dig_size.o $(BUILD)/ghash_ctmul.o $(BUILD)/ghash_ctmul32.o $(BUILD)/ghash_ctmul64.o $(BUILD)/md5.o $(BUILD)/md5sha1.o $(BUILD)/multihash.o $(BUILD)/sha1.o $(BUILD)/sha2big.o $(BUILD)/sha2small.o
-OBJINT15 = $(BUILD)/i15_core.o $(BUILD)/i15_ext1.o $(BUILD)/i15_ext2.o
+OBJINT15 = $(BUILD)/i15_add.o $(BUILD)/i15_bitlen.o $(BUILD)/i15_decmod.o $(BUILD)/i15_decode.o $(BUILD)/i15_decred.o $(BUILD)/i15_encode.o $(BUILD)/i15_fmont.o $(BUILD)/i15_iszero.o $(BUILD)/i15_modpow.o $(BUILD)/i15_montmul.o $(BUILD)/i15_mulacc.o $(BUILD)/i15_muladd.o $(BUILD)/i15_ninv15.o $(BUILD)/i15_reduce.o $(BUILD)/i15_rshift.o $(BUILD)/i15_sub.o $(BUILD)/i15_tmont.o
OBJINT31 = $(BUILD)/i31_add.o $(BUILD)/i31_bitlen.o $(BUILD)/i31_decmod.o $(BUILD)/i31_decode.o $(BUILD)/i31_decred.o $(BUILD)/i31_encode.o $(BUILD)/i31_fmont.o $(BUILD)/i31_iszero.o $(BUILD)/i31_modpow.o $(BUILD)/i31_montmul.o $(BUILD)/i31_mulacc.o $(BUILD)/i31_muladd.o $(BUILD)/i31_ninv31.o $(BUILD)/i31_reduce.o $(BUILD)/i31_rshift.o $(BUILD)/i31_sub.o $(BUILD)/i31_tmont.o
OBJINT32 = $(BUILD)/i32_add.o $(BUILD)/i32_bitlen.o $(BUILD)/i32_decmod.o $(BUILD)/i32_decode.o $(BUILD)/i32_decred.o $(BUILD)/i32_div32.o $(BUILD)/i32_encode.o $(BUILD)/i32_fmont.o $(BUILD)/i32_iszero.o $(BUILD)/i32_modpow.o $(BUILD)/i32_montmul.o $(BUILD)/i32_mulacc.o $(BUILD)/i32_muladd.o $(BUILD)/i32_ninv32.o $(BUILD)/i32_reduce.o $(BUILD)/i32_sub.o $(BUILD)/i32_tmont.o
OBJMAC = $(BUILD)/hmac.o $(BUILD)/hmac_ct.o
$(BUILD)/sha2small.o: src/hash/sha2small.c $(HEADERS)
$(CC) $(CFLAGS) -c -o $(BUILD)/sha2small.o src/hash/sha2small.c
-$(BUILD)/i15_core.o: src/int/i15_core.c $(HEADERS)
- $(CC) $(CFLAGS) -c -o $(BUILD)/i15_core.o src/int/i15_core.c
+$(BUILD)/i15_add.o: src/int/i15_add.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_add.o src/int/i15_add.c
-$(BUILD)/i15_ext1.o: src/int/i15_ext1.c $(HEADERS)
- $(CC) $(CFLAGS) -c -o $(BUILD)/i15_ext1.o src/int/i15_ext1.c
+$(BUILD)/i15_bitlen.o: src/int/i15_bitlen.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_bitlen.o src/int/i15_bitlen.c
-$(BUILD)/i15_ext2.o: src/int/i15_ext2.c $(HEADERS)
- $(CC) $(CFLAGS) -c -o $(BUILD)/i15_ext2.o src/int/i15_ext2.c
+$(BUILD)/i15_decmod.o: src/int/i15_decmod.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_decmod.o src/int/i15_decmod.c
+
+$(BUILD)/i15_decode.o: src/int/i15_decode.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_decode.o src/int/i15_decode.c
+
+$(BUILD)/i15_decred.o: src/int/i15_decred.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_decred.o src/int/i15_decred.c
+
+$(BUILD)/i15_encode.o: src/int/i15_encode.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_encode.o src/int/i15_encode.c
+
+$(BUILD)/i15_fmont.o: src/int/i15_fmont.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_fmont.o src/int/i15_fmont.c
+
+$(BUILD)/i15_iszero.o: src/int/i15_iszero.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_iszero.o src/int/i15_iszero.c
+
+$(BUILD)/i15_modpow.o: src/int/i15_modpow.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_modpow.o src/int/i15_modpow.c
+
+$(BUILD)/i15_montmul.o: src/int/i15_montmul.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_montmul.o src/int/i15_montmul.c
+
+$(BUILD)/i15_mulacc.o: src/int/i15_mulacc.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_mulacc.o src/int/i15_mulacc.c
+
+$(BUILD)/i15_muladd.o: src/int/i15_muladd.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_muladd.o src/int/i15_muladd.c
+
+$(BUILD)/i15_ninv15.o: src/int/i15_ninv15.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_ninv15.o src/int/i15_ninv15.c
+
+$(BUILD)/i15_reduce.o: src/int/i15_reduce.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_reduce.o src/int/i15_reduce.c
+
+$(BUILD)/i15_rshift.o: src/int/i15_rshift.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_rshift.o src/int/i15_rshift.c
+
+$(BUILD)/i15_sub.o: src/int/i15_sub.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_sub.o src/int/i15_sub.c
+
+$(BUILD)/i15_tmont.o: src/int/i15_tmont.c $(HEADERS)
+ $(CC) $(CFLAGS) -c -o $(BUILD)/i15_tmont.o src/int/i15_tmont.c
$(BUILD)/i31_add.o: src/int/i31_add.c $(HEADERS)
$(CC) $(CFLAGS) -c -o $(BUILD)/i31_add.o src/int/i31_add.c
};
static const unsigned char ORDER[] = {
- 0x10, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
- 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
- 0x14, 0xDE, 0xF9, 0xDE, 0xA2, 0xF7, 0x9C, 0xD6,
- 0x58, 0x12, 0x63, 0x1A, 0x5C, 0xF5, 0xD3, 0xED
+ 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
};
/* see inner.h */
extern const br_ec_curve_def br_secp384r1;
extern const br_ec_curve_def br_secp521r1;
-extern const br_ec_curve_def br_curve25519;
-
-#if 0
-/* obsolete */
/*
- * Type for the parameters for a "prime curve":
- * coordinates are in GF(p), with p prime
- * curve equation is Y^2 = X^3 - 3*X + b
- * b is in Montgomery representation
- * curve order is n and is prime
- * base point is G (encoded) and has order n
+ * For Curve25519, the advertised "order" really is 2^255-1, since the
+ * point multipliction function really works over arbitrary 255-bit
+ * scalars. This value is only meant as a hint for ECDH key generation;
+ * only ECDSA uses the exact curve order, and ECDSA is not used with
+ * that specific curve.
*/
-typedef struct {
- const uint32_t *p;
- const uint32_t *b;
- const uint32_t p0i;
-} br_ec_prime_i31_curve;
-
-extern const br_ec_prime_i31_curve br_ec_prime_i31_secp256r1;
-extern const br_ec_prime_i31_curve br_ec_prime_i31_secp384r1;
-extern const br_ec_prime_i31_curve br_ec_prime_i31_secp521r1;
-
-#define BR_EC_I31_LEN ((BR_MAX_EC_SIZE + 61) / 31)
-#endif
+extern const br_ec_curve_def br_curve25519;
/*
* Decode some bytes as an i31 integer, with truncation (corresponding
/*
- * Copyright (c) 201
6 Thomas Pornin <pornin@bolet.org>
+ * Copyright (c) 201
7 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
#include "inner.h"
-static const uint32_t P256_P[] = {
- 0x00000108,
- 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x00000007,
- 0x00000000, 0x00000000, 0x00000040, 0x7FFFFF80,
- 0x000000FF
-};
+/* see inner.h */
+uint32_t
+br_i15_add(uint16_t *a, const uint16_t *b, uint32_t ctl)
+{
+ uint32_t cc;
+ size_t u, m;
-static const uint32_t P256_B[] = {
- 0x00000108,
- 0x6FEE1803, 0x6229C4BD, 0x21B139BE, 0x327150AA,
- 0x3567802E, 0x3F7212ED, 0x012E4355, 0x782DD38D,
- 0x0000000E
-};
+ cc = 0;
+ m = (a[0] + 31) >> 4;
+ for (u = 1; u < m; u ++) {
+ uint32_t aw, bw, naw;
-/* see inner.h */
-const br_ec_prime_i31_curve br_ec_prime_i31_secp256r1 = {
- P256_P,
- P256_B,
- 0x00000001
-};
+ aw = a[u];
+ bw = b[u];
+ naw = aw + bw + cc;
+ cc = naw >> 15;
+ a[u] = MUX(ctl, naw & 0x7FFF, aw);
+ }
+ return cc;
+}
/*
- * Copyright (c) 201
6 Thomas Pornin <pornin@bolet.org>
+ * Copyright (c) 201
7 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
#include "inner.h"
-static const uint32_t P384_P[] = {
- 0x0000018C,
- 0x7FFFFFFF, 0x00000001, 0x00000000, 0x7FFFFFF8,
- 0x7FFFFFEF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
- 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
- 0x00000FFF
-};
+/* see inner.h */
+uint32_t
+br_i15_bit_length(uint16_t *x, size_t xlen)
+{
+ uint32_t tw, twk;
-static const uint32_t P384_B[] = {
- 0x0000018C,
- 0x6E666840, 0x070D0392, 0x5D810231, 0x7651D50C,
- 0x17E218D6, 0x1B192002, 0x44EFE441, 0x3A524E2B,
- 0x2719BA5F, 0x41F02209, 0x36C5643E, 0x5813EFFE,
- 0x000008A5
-};
+ tw = 0;
+ twk = 0;
+ while (xlen -- > 0) {
+ uint32_t w, c;
-/* see inner.h */
-const br_ec_prime_i31_curve br_ec_prime_i31_secp384r1 = {
- P384_P,
- P384_B,
- 0x00000001
-};
+ c = EQ(tw, 0);
+ w = x[xlen];
+ tw = MUX(c, w, tw);
+ twk = MUX(c, (uint32_t)xlen, twk);
+ }
+ return (twk << 4) + BIT_LENGTH(tw);
+}
+++ /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"
-
-/*
- * This file contains the core "big integer" functions for the i15
- * implementation, that represents integers as sequences of 15-bit
- * words.
- */
-
-/* see inner.h */
-uint32_t
-br_i15_iszero(const uint16_t *x)
-{
- uint32_t z;
- size_t u;
-
- z = 0;
- for (u = (x[0] + 15) >> 4; u > 0; u --) {
- z |= x[u];
- }
- return ~(z | -z) >> 31;
-}
-
-/* see inner.h */
-uint16_t
-br_i15_ninv15(uint16_t x)
-{
- uint32_t y;
-
- y = 2 - x;
- y = MUL15(y, 2 - MUL15(x, y));
- y = MUL15(y, 2 - MUL15(x, y));
- y = MUL15(y, 2 - MUL15(x, y));
- return MUX(x & 1, -y, 0) & 0x7FFF;
-}
-
-/* see inner.h */
-uint32_t
-br_i15_add(uint16_t *a, const uint16_t *b, uint32_t ctl)
-{
- uint32_t cc;
- size_t u, m;
-
- cc = 0;
- m = (a[0] + 31) >> 4;
- for (u = 1; u < m; u ++) {
- uint32_t aw, bw, naw;
-
- aw = a[u];
- bw = b[u];
- naw = aw + bw + cc;
- cc = naw >> 15;
- a[u] = MUX(ctl, naw & 0x7FFF, aw);
- }
- return cc;
-}
-
-/* see inner.h */
-uint32_t
-br_i15_sub(uint16_t *a, const uint16_t *b, uint32_t ctl)
-{
- uint32_t cc;
- size_t u, m;
-
- cc = 0;
- m = (a[0] + 31) >> 4;
- for (u = 1; u < m; u ++) {
- uint32_t aw, bw, naw;
-
- aw = a[u];
- bw = b[u];
- naw = aw - bw - cc;
- cc = naw >> 31;
- a[u] = MUX(ctl, naw & 0x7FFF, aw);
- }
- return cc;
-}
-
-/*
- * Constant-time division. The divisor must not be larger than 16 bits,
- * and the quotient must fit on 17 bits.
- */
-static uint32_t
-divrem16(uint32_t x, uint32_t d, uint32_t *r)
-{
- int i;
- uint32_t q;
-
- q = 0;
- d <<= 16;
- for (i = 16; i >= 0; i --) {
- uint32_t ctl;
-
- ctl = LE(d, x);
- q |= ctl << i;
- x -= (-ctl) & d;
- d >>= 1;
- }
- if (r != NULL) {
- *r = x;
- }
- return q;
-}
-
-/* see inner.h */
-void
-br_i15_muladd_small(uint16_t *x, uint16_t z, const uint16_t *m)
-{
- /*
- * Constant-time: we accept to leak the exact bit length of the
- * modulus m.
- */
- unsigned m_bitlen, mblr;
- size_t u, mlen;
- uint32_t hi, a0, a, b, q;
- uint32_t cc, tb, over, under;
-
- /*
- * Simple case: the modulus fits on one word.
- */
- m_bitlen = m[0];
- if (m_bitlen == 0) {
- return;
- }
- if (m_bitlen <= 15) {
- uint32_t rem;
-
- divrem16(((uint32_t)x[1] << 15) | z, m[1], &rem);
- x[1] = rem;
- return;
- }
- mlen = (m_bitlen + 15) >> 4;
- mblr = m_bitlen & 15;
-
- /*
- * Principle: we estimate the quotient (x*2^15+z)/m by
- * doing a 30/15 division with the high words.
- *
- * Let:
- * w = 2^15
- * a = (w*a0 + a1) * w^N + a2
- * b = b0 * w^N + b2
- * such that:
- * 0 <= a0 < w
- * 0 <= a1 < w
- * 0 <= a2 < w^N
- * w/2 <= b0 < w
- * 0 <= b2 < w^N
- * a < w*b
- * I.e. the two top words of a are a0:a1, the top word of b is
- * b0, we ensured that b0 is "full" (high bit set), and a is
- * such that the quotient q = a/b fits on one word (0 <= q < w).
- *
- * If a = b*q + r (with 0 <= r < q), then we can estimate q by
- * using a division on the top words:
- * a0*w + a1 = b0*u + v (with 0 <= v < b0)
- * Then the following holds:
- * 0 <= u <= w
- * u-2 <= q <= u
- */
- hi = x[mlen];
- if (mblr == 0) {
- a0 = x[mlen];
- memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
- x[1] = z;
- a = (a0 << 15) + x[mlen];
- b = m[mlen];
- } else {
- a0 = (x[mlen] << (15 - mblr)) | (x[mlen - 1] >> mblr);
- memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
- x[1] = z;
- a = (a0 << 15) | (((x[mlen] << (15 - mblr))
- | (x[mlen - 1] >> mblr)) & 0x7FFF);
- b = (m[mlen] << (15 - mblr)) | (m[mlen - 1] >> mblr);
- }
- q = divrem16(a, b, NULL);
-
- /*
- * We computed an estimate for q, but the real one may be q,
- * q-1 or q-2; moreover, the division may have returned a value
- * 8000 or even 8001 if the two high words were identical, and
- * we want to avoid values beyond 7FFF. We thus adjust q so
- * that the "true" multiplier will be q+1, q or q-1, and q is
- * in the 0000..7FFF range.
- */
- q = MUX(EQ(b, a0), 0x7FFF, q - 1 + ((q - 1) >> 31));
-
- /*
- * We subtract q*m from x (x has an extra high word of value 'hi').
- * Since q may be off by 1 (in either direction), we may have to
- * add or subtract m afterwards.
- *
- * The 'tb' flag will be true (1) at the end of the loop if the
- * result is greater than or equal to the modulus (not counting
- * 'hi' or the carry).
- */
- cc = 0;
- tb = 1;
- for (u = 1; u <= mlen; u ++) {
- uint32_t mw, zl, xw, nxw;
-
- mw = m[u];
- zl = MUL15(mw, q) + cc;
- cc = zl >> 15;
- zl &= 0x7FFF;
- xw = x[u];
- nxw = xw - zl;
- cc += nxw >> 31;
- nxw &= 0x7FFF;
- x[u] = nxw;
- tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw));
- }
-
- /*
- * If we underestimated q, then either cc < hi (one extra bit
- * beyond the top array word), or cc == hi and tb is true (no
- * extra bit, but the result is not lower than the modulus).
- *
- * If we overestimated q, then cc > hi.
- */
- over = GT(cc, hi);
- under = ~over & (tb | LT(cc, hi));
- br_i15_add(x, m, over);
- br_i15_sub(x, m, under);
-}
-
-/* see inner.h */
-void
-br_i15_montymul(uint16_t *d, const uint16_t *x, const uint16_t *y,
- const uint16_t *m, uint16_t m0i)
-{
- size_t len, len4, u, v;
- uint32_t dh;
-
- len = (m[0] + 15) >> 4;
- len4 = len & ~(size_t)3;
- br_i15_zero(d, m[0]);
- dh = 0;
- for (u = 0; u < len; u ++) {
- uint32_t f, xu, r, zh;
-
- xu = x[u + 1];
- f = MUL15((d[1] + MUL15(x[u + 1], y[1])) & 0x7FFF, m0i)
- & 0x7FFF;
-
- r = 0;
- for (v = 0; v < len4; v += 4) {
- uint32_t z;
-
- z = d[v + 1] + MUL15(xu, y[v + 1])
- + MUL15(f, m[v + 1]) + r;
- r = z >> 15;
- d[v + 0] = z & 0x7FFF;
- z = d[v + 2] + MUL15(xu, y[v + 2])
- + MUL15(f, m[v + 2]) + r;
- r = z >> 15;
- d[v + 1] = z & 0x7FFF;
- z = d[v + 3] + MUL15(xu, y[v + 3])
- + MUL15(f, m[v + 3]) + r;
- r = z >> 15;
- d[v + 2] = z & 0x7FFF;
- z = d[v + 4] + MUL15(xu, y[v + 4])
- + MUL15(f, m[v + 4]) + r;
- r = z >> 15;
- d[v + 3] = z & 0x7FFF;
- }
- for (; v < len; v ++) {
- uint32_t z;
-
- z = d[v + 1] + MUL15(xu, y[v + 1])
- + MUL15(f, m[v + 1]) + r;
- r = z >> 15;
- d[v + 0] = z & 0x7FFF;
- }
-
- zh = dh + r;
- d[len] = zh & 0x7FFF;
- dh = zh >> 15;
- }
-
- /*
- * Restore the bit length (it was overwritten in the loop above).
- */
- d[0] = m[0];
-
- /*
- * d[] may be greater than m[], but it is still lower than twice
- * the modulus.
- */
- br_i15_sub(d, m, NEQ(dh, 0) | NOT(br_i15_sub(d, m, 0)));
-}
-
-/* see inner.h */
-void
-br_i15_to_monty(uint16_t *x, const uint16_t *m)
-{
- unsigned k;
-
- for (k = (m[0] + 15) >> 4; k > 0; k --) {
- br_i15_muladd_small(x, 0, m);
- }
-}
-
-/* see inner.h */
-void
-br_i15_modpow(uint16_t *x,
- const unsigned char *e, size_t elen,
- const uint16_t *m, uint16_t m0i, uint16_t *t1, uint16_t *t2)
-{
- size_t mlen;
- unsigned k;
-
- mlen = ((m[0] + 31) >> 4) * sizeof m[0];
- memcpy(t1, x, mlen);
- br_i15_to_monty(t1, m);
- br_i15_zero(x, m[0]);
- x[1] = 1;
- for (k = 0; k < ((unsigned)elen << 3); k ++) {
- uint32_t ctl;
-
- ctl = (e[elen - 1 - (k >> 3)] >> (k & 7)) & 1;
- br_i15_montymul(t2, x, t1, m, m0i);
- CCOPY(ctl, x, t2, mlen);
- br_i15_montymul(t2, t1, t1, m, m0i);
- memcpy(t1, t2, mlen);
- }
-}
-
-/* see inner.h */
-void
-br_i15_encode(void *dst, size_t len, const uint16_t *x)
-{
- unsigned char *buf;
- size_t u, xlen;
- uint32_t acc;
- int acc_len;
-
- xlen = (x[0] + 15) >> 4;
- if (xlen == 0) {
- memset(dst, 0, len);
- return;
- }
- u = 1;
- acc = 0;
- acc_len = 0;
- buf = dst;
- while (len -- > 0) {
- if (acc_len < 8) {
- if (u <= xlen) {
- acc += (uint32_t)x[u ++] << acc_len;
- }
- acc_len += 15;
- }
- buf[len] = (unsigned char)acc;
- acc >>= 8;
- acc_len -= 8;
- }
-}
-
-/* see inner.h */
-uint32_t
-br_i15_decode_mod(uint16_t *x, const void *src, size_t len, const uint16_t *m)
-{
- /*
- * Two-pass algorithm: in the first pass, we determine whether the
- * value fits; in the second pass, we do the actual write.
- *
- * During the first pass, 'r' contains the comparison result so
- * far:
- * 0x00000000 value is equal to the modulus
- * 0x00000001 value is greater than the modulus
- * 0xFFFFFFFF value is lower than the modulus
- *
- * Since we iterate starting with the least significant bytes (at
- * the end of src[]), each new comparison overrides the previous
- * except when the comparison yields 0 (equal).
- *
- * During the second pass, 'r' is either 0xFFFFFFFF (value fits)
- * or 0x00000000 (value does not fit).
- *
- * We must iterate over all bytes of the source, _and_ possibly
- * some extra virutal bytes (with value 0) so as to cover the
- * complete modulus as well. We also add 4 such extra bytes beyond
- * the modulus length because it then guarantees that no accumulated
- * partial word remains to be processed.
- */
- const unsigned char *buf;
- size_t mlen, tlen;
- int pass;
- uint32_t r;
-
- buf = src;
- mlen = (m[0] + 15) >> 4;
- tlen = (mlen << 1);
- if (tlen < len) {
- tlen = len;
- }
- tlen += 4;
- r = 0;
- for (pass = 0; pass < 2; pass ++) {
- size_t u, v;
- uint32_t acc;
- int acc_len;
-
- v = 1;
- acc = 0;
- acc_len = 0;
- for (u = 0; u < tlen; u ++) {
- uint32_t b;
-
- if (u < len) {
- b = buf[len - 1 - u];
- } else {
- b = 0;
- }
- acc |= (b << acc_len);
- acc_len += 8;
- if (acc_len >= 15) {
- uint32_t xw;
-
- xw = acc & (uint32_t)0x7FFF;
- acc_len -= 15;
- acc = b >> (8 - acc_len);
- if (v <= mlen) {
- if (pass) {
- x[v] = r & xw;
- } else {
- uint32_t cc;
-
- cc = (uint32_t)CMP(xw, m[v]);
- r = MUX(EQ(cc, 0), r, cc);
- }
- } else {
- if (!pass) {
- r = MUX(EQ(xw, 0), r, 1);
- }
- }
- v ++;
- }
- }
-
- /*
- * When we reach this point at the end of the first pass:
- * r is either 0, 1 or -1; we want to set r to 0 if it
- * is equal to 0 or 1, and leave it to -1 otherwise.
- *
- * When we reach this point at the end of the second pass:
- * r is either 0 or -1; we want to leave that value
- * untouched. This is a subcase of the previous.
- */
- r >>= 1;
- r |= (r << 1);
- }
-
- x[0] = m[0];
- return r & (uint32_t)1;
-}
--- /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"
+
+/* see inner.h */
+uint32_t
+br_i15_decode_mod(uint16_t *x, const void *src, size_t len, const uint16_t *m)
+{
+ /*
+ * Two-pass algorithm: in the first pass, we determine whether the
+ * value fits; in the second pass, we do the actual write.
+ *
+ * During the first pass, 'r' contains the comparison result so
+ * far:
+ * 0x00000000 value is equal to the modulus
+ * 0x00000001 value is greater than the modulus
+ * 0xFFFFFFFF value is lower than the modulus
+ *
+ * Since we iterate starting with the least significant bytes (at
+ * the end of src[]), each new comparison overrides the previous
+ * except when the comparison yields 0 (equal).
+ *
+ * During the second pass, 'r' is either 0xFFFFFFFF (value fits)
+ * or 0x00000000 (value does not fit).
+ *
+ * We must iterate over all bytes of the source, _and_ possibly
+ * some extra virutal bytes (with value 0) so as to cover the
+ * complete modulus as well. We also add 4 such extra bytes beyond
+ * the modulus length because it then guarantees that no accumulated
+ * partial word remains to be processed.
+ */
+ const unsigned char *buf;
+ size_t mlen, tlen;
+ int pass;
+ uint32_t r;
+
+ buf = src;
+ mlen = (m[0] + 15) >> 4;
+ tlen = (mlen << 1);
+ if (tlen < len) {
+ tlen = len;
+ }
+ tlen += 4;
+ r = 0;
+ for (pass = 0; pass < 2; pass ++) {
+ size_t u, v;
+ uint32_t acc;
+ int acc_len;
+
+ v = 1;
+ acc = 0;
+ acc_len = 0;
+ for (u = 0; u < tlen; u ++) {
+ uint32_t b;
+
+ if (u < len) {
+ b = buf[len - 1 - u];
+ } else {
+ b = 0;
+ }
+ acc |= (b << acc_len);
+ acc_len += 8;
+ if (acc_len >= 15) {
+ uint32_t xw;
+
+ xw = acc & (uint32_t)0x7FFF;
+ acc_len -= 15;
+ acc = b >> (8 - acc_len);
+ if (v <= mlen) {
+ if (pass) {
+ x[v] = r & xw;
+ } else {
+ uint32_t cc;
+
+ cc = (uint32_t)CMP(xw, m[v]);
+ r = MUX(EQ(cc, 0), r, cc);
+ }
+ } else {
+ if (!pass) {
+ r = MUX(EQ(xw, 0), r, 1);
+ }
+ }
+ v ++;
+ }
+ }
+
+ /*
+ * When we reach this point at the end of the first pass:
+ * r is either 0, 1 or -1; we want to set r to 0 if it
+ * is equal to 0 or 1, and leave it to -1 otherwise.
+ *
+ * When we reach this point at the end of the second pass:
+ * r is either 0 or -1; we want to leave that value
+ * untouched. This is a subcase of the previous.
+ */
+ r >>= 1;
+ r |= (r << 1);
+ }
+
+ x[0] = m[0];
+ return r & (uint32_t)1;
+}
/*
- * Copyright (c) 201
6 Thomas Pornin <pornin@bolet.org>
+ * Copyright (c) 201
7 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
#include "inner.h"
-static const uint32_t P521_P[] = {
- 0x00000219,
- 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
- 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
- 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
- 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
- 0x01FFFFFF
-};
+/* see inner.h */
+void
+br_i15_decode(uint16_t *x, const void *src, size_t len)
+{
+ const unsigned char *buf;
+ size_t v;
+ uint32_t acc;
+ int acc_len;
-static const uint32_t P521_B[] = {
- 0x00000219,
- 0x540FC00A, 0x228FEA35, 0x2C34F1EF, 0x67BF107A,
- 0x46FC1CD5, 0x1605E9DD, 0x6937B165, 0x272A3D8F,
- 0x42785586, 0x44C8C778, 0x15F3B8B4, 0x64B73366,
- 0x03BA8B69, 0x0D05B42A, 0x21F929A2, 0x2C31C393,
- 0x00654FAE
-};
+ buf = src;
+ v = 1;
+ acc = 0;
+ acc_len = 0;
+ while (len -- > 0) {
+ uint32_t b;
-/* see inner.h */
-const br_ec_prime_i31_curve br_ec_prime_i31_secp521r1 = {
- P521_P,
- P521_B,
- 0x00000001
-};
+ b = buf[len];
+ acc |= (b << acc_len);
+ acc_len += 8;
+ if (acc_len >= 15) {
+ x[v ++] = acc & 0x7FFF;
+ acc_len -= 15;
+ acc >>= 15;
+ }
+ }
+ if (acc_len != 0) {
+ x[v ++] = acc;
+ }
+ x[0] = br_i15_bit_length(x + 1, v - 1);
+}
#include "inner.h"
-/*
- * This file contains some additional functions for "i15" big integers.
- * These functions are needed to support RSA.
- */
-
/* see inner.h */
void
br_i15_decode_reduce(uint16_t *x,
br_i15_muladd_small(x, acc, m);
}
}
-
-/* see inner.h */
-void
-br_i15_reduce(uint16_t *x, const uint16_t *a, const uint16_t *m)
-{
- uint32_t m_bitlen, a_bitlen;
- size_t mlen, alen, u;
-
- m_bitlen = m[0];
- mlen = (m_bitlen + 15) >> 4;
-
- x[0] = m_bitlen;
- if (m_bitlen == 0) {
- return;
- }
-
- /*
- * If the source is shorter, then simply copy all words from a[]
- * and zero out the upper words.
- */
- a_bitlen = a[0];
- alen = (a_bitlen + 15) >> 4;
- if (a_bitlen < m_bitlen) {
- memcpy(x + 1, a + 1, alen * sizeof *a);
- for (u = alen; u < mlen; u ++) {
- x[u + 1] = 0;
- }
- return;
- }
-
- /*
- * The source length is at least equal to that of the modulus.
- * We must thus copy N-1 words, and input the remaining words
- * one by one.
- */
- memcpy(x + 1, a + 2 + (alen - mlen), (mlen - 1) * sizeof *a);
- x[mlen] = 0;
- for (u = 1 + alen - mlen; u > 0; u --) {
- br_i15_muladd_small(x, a[u], m);
- }
-}
-
-/* see inner.h */
-void
-br_i15_mulacc(uint16_t *d, const uint16_t *a, const uint16_t *b)
-{
- size_t alen, blen, u;
-
- alen = (a[0] + 15) >> 4;
- blen = (b[0] + 15) >> 4;
- d[0] = a[0] + b[0];
- for (u = 0; u < blen; u ++) {
- uint32_t f;
- size_t v;
- uint32_t cc;
-
- f = b[1 + u];
- cc = 0;
- for (v = 0; v < alen; v ++) {
- uint32_t z;
-
- z = (uint32_t)d[1 + u + v] + MUL15(f, a[1 + v]) + cc;
- cc = z >> 15;
- d[1 + u + v] = z & 0x7FFF;
- }
- d[1 + u + alen] = cc;
- }
-}
--- /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"
+
+/* see inner.h */
+void
+br_i15_encode(void *dst, size_t len, const uint16_t *x)
+{
+ unsigned char *buf;
+ size_t u, xlen;
+ uint32_t acc;
+ int acc_len;
+
+ xlen = (x[0] + 15) >> 4;
+ if (xlen == 0) {
+ memset(dst, 0, len);
+ return;
+ }
+ u = 1;
+ acc = 0;
+ acc_len = 0;
+ buf = dst;
+ while (len -- > 0) {
+ if (acc_len < 8) {
+ if (u <= xlen) {
+ acc += (uint32_t)x[u ++] << acc_len;
+ }
+ acc_len += 15;
+ }
+ buf[len] = (unsigned char)acc;
+ acc >>= 8;
+ acc_len -= 8;
+ }
+}
#include "inner.h"
-/*
- * This file contains some additional functions for "i15" big integers.
- * These functions are needed to support ECDSA.
- */
-
-/* see inner.h */
-void
-br_i15_rshift(uint16_t *x, int count)
-{
- size_t u, len;
- unsigned r;
-
- len = (x[0] + 15) >> 4;
- if (len == 0) {
- return;
- }
- r = x[1] >> count;
- for (u = 2; u <= len; u ++) {
- unsigned w;
-
- w = x[u];
- x[u - 1] = ((w << (15 - count)) | r) & 0x7FFF;
- r = w >> count;
- }
- x[len] = r;
-}
-
-/* see inner.h */
-uint32_t
-br_i15_bit_length(uint16_t *x, size_t xlen)
-{
- uint32_t tw, twk;
-
- tw = 0;
- twk = 0;
- while (xlen -- > 0) {
- uint32_t w, c;
-
- c = EQ(tw, 0);
- w = x[xlen];
- tw = MUX(c, w, tw);
- twk = MUX(c, (uint32_t)xlen, twk);
- }
- return (twk << 4) + BIT_LENGTH(tw);
-}
-
-/* see inner.h */
-void
-br_i15_decode(uint16_t *x, const void *src, size_t len)
-{
- const unsigned char *buf;
- size_t v;
- uint32_t acc;
- int acc_len;
-
- buf = src;
- v = 1;
- acc = 0;
- acc_len = 0;
- while (len -- > 0) {
- uint32_t b;
-
- b = buf[len];
- acc |= (b << acc_len);
- acc_len += 8;
- if (acc_len >= 15) {
- x[v ++] = acc & 0x7FFF;
- acc_len -= 15;
- acc >>= 15;
- }
- }
- if (acc_len != 0) {
- x[v ++] = acc;
- }
- x[0] = br_i15_bit_length(x + 1, v - 1);
-}
-
/* see inner.h */
void
br_i15_from_monty(uint16_t *x, const uint16_t *m, uint16_t m0i)
--- /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"
+
+/* see inner.h */
+uint32_t
+br_i15_iszero(const uint16_t *x)
+{
+ uint32_t z;
+ size_t u;
+
+ z = 0;
+ for (u = (x[0] + 15) >> 4; u > 0; u --) {
+ z |= x[u];
+ }
+ return ~(z | -z) >> 31;
+}
--- /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"
+
+/* see inner.h */
+void
+br_i15_modpow(uint16_t *x,
+ const unsigned char *e, size_t elen,
+ const uint16_t *m, uint16_t m0i, uint16_t *t1, uint16_t *t2)
+{
+ size_t mlen;
+ unsigned k;
+
+ mlen = ((m[0] + 31) >> 4) * sizeof m[0];
+ memcpy(t1, x, mlen);
+ br_i15_to_monty(t1, m);
+ br_i15_zero(x, m[0]);
+ x[1] = 1;
+ for (k = 0; k < ((unsigned)elen << 3); k ++) {
+ uint32_t ctl;
+
+ ctl = (e[elen - 1 - (k >> 3)] >> (k & 7)) & 1;
+ br_i15_montymul(t2, x, t1, m, m0i);
+ CCOPY(ctl, x, t2, mlen);
+ br_i15_montymul(t2, t1, t1, m, m0i);
+ memcpy(t1, t2, mlen);
+ }
+}
--- /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"
+
+/* see inner.h */
+void
+br_i15_montymul(uint16_t *d, const uint16_t *x, const uint16_t *y,
+ const uint16_t *m, uint16_t m0i)
+{
+ size_t len, len4, u, v;
+ uint32_t dh;
+
+ len = (m[0] + 15) >> 4;
+ len4 = len & ~(size_t)3;
+ br_i15_zero(d, m[0]);
+ dh = 0;
+ for (u = 0; u < len; u ++) {
+ uint32_t f, xu, r, zh;
+
+ xu = x[u + 1];
+ f = MUL15((d[1] + MUL15(x[u + 1], y[1])) & 0x7FFF, m0i)
+ & 0x7FFF;
+
+ r = 0;
+ for (v = 0; v < len4; v += 4) {
+ uint32_t z;
+
+ z = d[v + 1] + MUL15(xu, y[v + 1])
+ + MUL15(f, m[v + 1]) + r;
+ r = z >> 15;
+ d[v + 0] = z & 0x7FFF;
+ z = d[v + 2] + MUL15(xu, y[v + 2])
+ + MUL15(f, m[v + 2]) + r;
+ r = z >> 15;
+ d[v + 1] = z & 0x7FFF;
+ z = d[v + 3] + MUL15(xu, y[v + 3])
+ + MUL15(f, m[v + 3]) + r;
+ r = z >> 15;
+ d[v + 2] = z & 0x7FFF;
+ z = d[v + 4] + MUL15(xu, y[v + 4])
+ + MUL15(f, m[v + 4]) + r;
+ r = z >> 15;
+ d[v + 3] = z & 0x7FFF;
+ }
+ for (; v < len; v ++) {
+ uint32_t z;
+
+ z = d[v + 1] + MUL15(xu, y[v + 1])
+ + MUL15(f, m[v + 1]) + r;
+ r = z >> 15;
+ d[v + 0] = z & 0x7FFF;
+ }
+
+ zh = dh + r;
+ d[len] = zh & 0x7FFF;
+ dh = zh >> 15;
+ }
+
+ /*
+ * Restore the bit length (it was overwritten in the loop above).
+ */
+ d[0] = m[0];
+
+ /*
+ * d[] may be greater than m[], but it is still lower than twice
+ * the modulus.
+ */
+ br_i15_sub(d, m, NEQ(dh, 0) | NOT(br_i15_sub(d, m, 0)));
+}
--- /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"
+
+/* see inner.h */
+void
+br_i15_mulacc(uint16_t *d, const uint16_t *a, const uint16_t *b)
+{
+ size_t alen, blen, u;
+
+ alen = (a[0] + 15) >> 4;
+ blen = (b[0] + 15) >> 4;
+ d[0] = a[0] + b[0];
+ for (u = 0; u < blen; u ++) {
+ uint32_t f;
+ size_t v;
+ uint32_t cc;
+
+ f = b[1 + u];
+ cc = 0;
+ for (v = 0; v < alen; v ++) {
+ uint32_t z;
+
+ z = (uint32_t)d[1 + u + v] + MUL15(f, a[1 + v]) + cc;
+ cc = z >> 15;
+ d[1 + u + v] = z & 0x7FFF;
+ }
+ d[1 + u + alen] = cc;
+ }
+}
--- /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"
+
+/*
+ * Constant-time division. The divisor must not be larger than 16 bits,
+ * and the quotient must fit on 17 bits.
+ */
+static uint32_t
+divrem16(uint32_t x, uint32_t d, uint32_t *r)
+{
+ int i;
+ uint32_t q;
+
+ q = 0;
+ d <<= 16;
+ for (i = 16; i >= 0; i --) {
+ uint32_t ctl;
+
+ ctl = LE(d, x);
+ q |= ctl << i;
+ x -= (-ctl) & d;
+ d >>= 1;
+ }
+ if (r != NULL) {
+ *r = x;
+ }
+ return q;
+}
+
+/* see inner.h */
+void
+br_i15_muladd_small(uint16_t *x, uint16_t z, const uint16_t *m)
+{
+ /*
+ * Constant-time: we accept to leak the exact bit length of the
+ * modulus m.
+ */
+ unsigned m_bitlen, mblr;
+ size_t u, mlen;
+ uint32_t hi, a0, a, b, q;
+ uint32_t cc, tb, over, under;
+
+ /*
+ * Simple case: the modulus fits on one word.
+ */
+ m_bitlen = m[0];
+ if (m_bitlen == 0) {
+ return;
+ }
+ if (m_bitlen <= 15) {
+ uint32_t rem;
+
+ divrem16(((uint32_t)x[1] << 15) | z, m[1], &rem);
+ x[1] = rem;
+ return;
+ }
+ mlen = (m_bitlen + 15) >> 4;
+ mblr = m_bitlen & 15;
+
+ /*
+ * Principle: we estimate the quotient (x*2^15+z)/m by
+ * doing a 30/15 division with the high words.
+ *
+ * Let:
+ * w = 2^15
+ * a = (w*a0 + a1) * w^N + a2
+ * b = b0 * w^N + b2
+ * such that:
+ * 0 <= a0 < w
+ * 0 <= a1 < w
+ * 0 <= a2 < w^N
+ * w/2 <= b0 < w
+ * 0 <= b2 < w^N
+ * a < w*b
+ * I.e. the two top words of a are a0:a1, the top word of b is
+ * b0, we ensured that b0 is "full" (high bit set), and a is
+ * such that the quotient q = a/b fits on one word (0 <= q < w).
+ *
+ * If a = b*q + r (with 0 <= r < q), then we can estimate q by
+ * using a division on the top words:
+ * a0*w + a1 = b0*u + v (with 0 <= v < b0)
+ * Then the following holds:
+ * 0 <= u <= w
+ * u-2 <= q <= u
+ */
+ hi = x[mlen];
+ if (mblr == 0) {
+ a0 = x[mlen];
+ memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
+ x[1] = z;
+ a = (a0 << 15) + x[mlen];
+ b = m[mlen];
+ } else {
+ a0 = (x[mlen] << (15 - mblr)) | (x[mlen - 1] >> mblr);
+ memmove(x + 2, x + 1, (mlen - 1) * sizeof *x);
+ x[1] = z;
+ a = (a0 << 15) | (((x[mlen] << (15 - mblr))
+ | (x[mlen - 1] >> mblr)) & 0x7FFF);
+ b = (m[mlen] << (15 - mblr)) | (m[mlen - 1] >> mblr);
+ }
+ q = divrem16(a, b, NULL);
+
+ /*
+ * We computed an estimate for q, but the real one may be q,
+ * q-1 or q-2; moreover, the division may have returned a value
+ * 8000 or even 8001 if the two high words were identical, and
+ * we want to avoid values beyond 7FFF. We thus adjust q so
+ * that the "true" multiplier will be q+1, q or q-1, and q is
+ * in the 0000..7FFF range.
+ */
+ q = MUX(EQ(b, a0), 0x7FFF, q - 1 + ((q - 1) >> 31));
+
+ /*
+ * We subtract q*m from x (x has an extra high word of value 'hi').
+ * Since q may be off by 1 (in either direction), we may have to
+ * add or subtract m afterwards.
+ *
+ * The 'tb' flag will be true (1) at the end of the loop if the
+ * result is greater than or equal to the modulus (not counting
+ * 'hi' or the carry).
+ */
+ cc = 0;
+ tb = 1;
+ for (u = 1; u <= mlen; u ++) {
+ uint32_t mw, zl, xw, nxw;
+
+ mw = m[u];
+ zl = MUL15(mw, q) + cc;
+ cc = zl >> 15;
+ zl &= 0x7FFF;
+ xw = x[u];
+ nxw = xw - zl;
+ cc += nxw >> 31;
+ nxw &= 0x7FFF;
+ x[u] = nxw;
+ tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw));
+ }
+
+ /*
+ * If we underestimated q, then either cc < hi (one extra bit
+ * beyond the top array word), or cc == hi and tb is true (no
+ * extra bit, but the result is not lower than the modulus).
+ *
+ * If we overestimated q, then cc > hi.
+ */
+ over = GT(cc, hi);
+ under = ~over & (tb | LT(cc, hi));
+ br_i15_add(x, m, over);
+ br_i15_sub(x, m, under);
+}
--- /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"
+
+/* see inner.h */
+uint16_t
+br_i15_ninv15(uint16_t x)
+{
+ uint32_t y;
+
+ y = 2 - x;
+ y = MUL15(y, 2 - MUL15(x, y));
+ y = MUL15(y, 2 - MUL15(x, y));
+ y = MUL15(y, 2 - MUL15(x, y));
+ return MUX(x & 1, -y, 0) & 0x7FFF;
+}
--- /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"
+
+/* see inner.h */
+void
+br_i15_reduce(uint16_t *x, const uint16_t *a, const uint16_t *m)
+{
+ uint32_t m_bitlen, a_bitlen;
+ size_t mlen, alen, u;
+
+ m_bitlen = m[0];
+ mlen = (m_bitlen + 15) >> 4;
+
+ x[0] = m_bitlen;
+ if (m_bitlen == 0) {
+ return;
+ }
+
+ /*
+ * If the source is shorter, then simply copy all words from a[]
+ * and zero out the upper words.
+ */
+ a_bitlen = a[0];
+ alen = (a_bitlen + 15) >> 4;
+ if (a_bitlen < m_bitlen) {
+ memcpy(x + 1, a + 1, alen * sizeof *a);
+ for (u = alen; u < mlen; u ++) {
+ x[u + 1] = 0;
+ }
+ return;
+ }
+
+ /*
+ * The source length is at least equal to that of the modulus.
+ * We must thus copy N-1 words, and input the remaining words
+ * one by one.
+ */
+ memcpy(x + 1, a + 2 + (alen - mlen), (mlen - 1) * sizeof *a);
+ x[mlen] = 0;
+ for (u = 1 + alen - mlen; u > 0; u --) {
+ br_i15_muladd_small(x, a[u], m);
+ }
+}
--- /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"
+
+/* see inner.h */
+void
+br_i15_rshift(uint16_t *x, int count)
+{
+ size_t u, len;
+ unsigned r;
+
+ len = (x[0] + 15) >> 4;
+ if (len == 0) {
+ return;
+ }
+ r = x[1] >> count;
+ for (u = 2; u <= len; u ++) {
+ unsigned w;
+
+ w = x[u];
+ x[u - 1] = ((w << (15 - count)) | r) & 0x7FFF;
+ r = w >> count;
+ }
+ x[len] = r;
+}
--- /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"
+
+/* see inner.h */
+uint32_t
+br_i15_sub(uint16_t *a, const uint16_t *b, uint32_t ctl)
+{
+ uint32_t cc;
+ size_t u, m;
+
+ cc = 0;
+ m = (a[0] + 31) >> 4;
+ for (u = 1; u < m; u ++) {
+ uint32_t aw, bw, naw;
+
+ aw = a[u];
+ bw = b[u];
+ naw = aw - bw - cc;
+ cc = naw >> 31;
+ a[u] = MUX(ctl, naw & 0x7FFF, aw);
+ }
+ return cc;
+}
--- /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"
+
+/* see inner.h */
+void
+br_i15_to_monty(uint16_t *x, const uint16_t *m)
+{
+ unsigned k;
+
+ for (k = (m[0] + 15) >> 4; k > 0; k --) {
+ br_i15_muladd_small(x, 0, m);
+ }
+}
&br_ecdsa_i31_vrfy_asn1);
}
-#if 0
-/* obsolete */
-static void
-test_speed_ec_prime_i31_inner(const char *name,
- const unsigned char *bg, const br_ec_prime_i31_curve *cc)
-{
- unsigned char bx[80], point[160];
- uint32_t x[BR_EC_I31_LEN];
- br_ec_prime_i31_jacobian P;
- uint32_t xbl;
- size_t plen;
- int i;
- long num;
-
- xbl = cc->p[0];
- xbl -= (xbl >> 5);
- plen = (xbl + 7) >> 3;
- memset(bx, 'T', sizeof bx);
- br_i31_decode_reduce(x, bx, sizeof bx, cc->p);
- br_i31_encode(bx, plen, x);
- br_ec_prime_i31_decode(&P, bg, 1 + (plen << 1), cc);
- for (i = 0; i < 10; i ++) {
- br_ec_prime_i31_mul(&P, bx, plen, cc);
- br_ec_prime_i31_encode(point, &P, cc);
- }
- num = 10;
- for (;;) {
- clock_t begin, end;
- double tt;
- long k;
-
- begin = clock();
- for (k = num; k > 0; k --) {
- br_ec_prime_i31_mul(&P, bx, plen, cc);
- br_ec_prime_i31_encode(point, &P, cc);
- }
- end = clock();
- tt = (double)(end - begin) / CLOCKS_PER_SEC;
- if (tt >= 2.0) {
- printf("%-30s %8.2f mul/s\n", name,
- (double)num / tt);
- fflush(stdout);
- break;
- }
- num <<= 1;
- }
-}
-
-static void
-test_speed_ec_prime_i31(void)
-{
- test_speed_ec_prime_i31_inner("EC i31 P-256",
- br_g_secp256r1, &br_ec_prime_i31_secp256r1);
- test_speed_ec_prime_i31_inner("EC i31 P-384",
- br_g_secp384r1, &br_ec_prime_i31_secp384r1);
- test_speed_ec_prime_i31_inner("EC i31 P-521",
- br_g_secp521r1, &br_ec_prime_i31_secp521r1);
-}
-
-static void
-test_speed_ec_prime_i32_inner(const char *name,
- const unsigned char *bg, const br_ec_prime_i32_curve *cc)
-{
- unsigned char bx[80], point[160];
- uint32_t x[BR_EC_I32_LEN];
- br_ec_prime_i32_jacobian P;
- size_t plen;
- int i;
- long num;
-
- plen = (cc->p[0] + 7) >> 3;
- memset(bx, 'T', sizeof bx);
- br_i32_decode_reduce(x, bx, sizeof bx, cc->p);
- br_i32_encode(bx, plen, x);
- br_ec_prime_i32_decode(&P, bg, 1 + (plen << 1), cc);
- for (i = 0; i < 10; i ++) {
- br_ec_prime_i32_mul(&P, bx, plen, cc);
- br_ec_prime_i32_encode(point, &P, cc);
- }
- num = 10;
- for (;;) {
- clock_t begin, end;
- double tt;
- long k;
-
- begin = clock();
- for (k = num; k > 0; k --) {
- br_ec_prime_i32_mul(&P, bx, plen, cc);
- br_ec_prime_i32_encode(point, &P, cc);
- }
- end = clock();
- tt = (double)(end - begin) / CLOCKS_PER_SEC;
- if (tt >= 2.0) {
- printf("%-30s %8.2f mul/s\n", name,
- (double)num / tt);
- fflush(stdout);
- break;
- }
- num <<= 1;
- }
-}
-
-static void
-test_speed_ec_prime_i32(void)
-{
- test_speed_ec_prime_i32_inner("EC i32 P-256",
- br_g_secp256r1, &br_ec_prime_i32_secp256r1);
- test_speed_ec_prime_i32_inner("EC i32 P-384",
- br_g_secp384r1, &br_ec_prime_i32_secp384r1);
- test_speed_ec_prime_i32_inner("EC i32 P-521",
- br_g_secp521r1, &br_ec_prime_i32_secp521r1);
-}
-#endif
-
static void
test_speed_i31(void)
{
projects / BearSSL / commitdiff