diff options
Diffstat (limited to 'common')
| -rw-r--r-- | common/build.mk | 3 | ||||
| -rw-r--r-- | common/curve25519-generic.c | 821 | ||||
| -rw-r--r-- | common/curve25519.c | 805 |
3 files changed, 825 insertions, 804 deletions
diff --git a/common/build.mk b/common/build.mk index 9954798988..7907a87e30 100644 --- a/common/build.mk +++ b/common/build.mk @@ -45,6 +45,9 @@ common-$(CONFIG_COMMON_RUNTIME)+=hooks.o main.o system.o common-$(CONFIG_COMMON_TIMER)+=timer.o common-$(CONFIG_CRC8)+= crc8.o common-$(CONFIG_CURVE25519)+=curve25519.o +ifneq ($(CORE),cortex-m0) +common-$(CONFIG_CURVE25519)+=curve25519-generic.o +endif common-$(CONFIG_DEVICE_EVENT)+=device_event.o common-$(CONFIG_DEVICE_STATE)+=device_state.o common-$(CONFIG_DPTF)+=dptf.o diff --git a/common/curve25519-generic.c b/common/curve25519-generic.c new file mode 100644 index 0000000000..4bc1114546 --- /dev/null +++ b/common/curve25519-generic.c @@ -0,0 +1,821 @@ +/* Copyright (c) 2015, Google Inc. + * + * Permission to use, copy, modify, and/or distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY + * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION + * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN + * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ + +/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP + * 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as + * public domain but this file has the ISC license just to keep licencing + * simple. + * + * The field functions are shared by Ed25519 and X25519 where possible. */ + +#include "curve25519.h" +#include "util.h" + +/* + * fe means field element. Here the field is \Z/(2^255-19). An element t, + * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 + * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on + * context. + */ +typedef int32_t fe[10]; + +static const int64_t kBottom25Bits = INT64_C(0x1ffffff); +static const int64_t kBottom26Bits = INT64_C(0x3ffffff); +static const int64_t kTop39Bits = INT64_C(0xfffffffffe000000); +static const int64_t kTop38Bits = INT64_C(0xfffffffffc000000); + +static uint64_t load_3(const uint8_t *in) { + uint64_t result; + result = (uint64_t)in[0]; + result |= ((uint64_t)in[1]) << 8; + result |= ((uint64_t)in[2]) << 16; + return result; +} + +static uint64_t load_4(const uint8_t *in) { + uint64_t result; + result = (uint64_t)in[0]; + result |= ((uint64_t)in[1]) << 8; + result |= ((uint64_t)in[2]) << 16; + result |= ((uint64_t)in[3]) << 24; + return result; +} + +static void fe_frombytes(fe h, const uint8_t *s) { + /* Ignores top bit of h. */ + int64_t h0 = load_4(s); + int64_t h1 = load_3(s + 4) << 6; + int64_t h2 = load_3(s + 7) << 5; + int64_t h3 = load_3(s + 10) << 3; + int64_t h4 = load_3(s + 13) << 2; + int64_t h5 = load_4(s + 16); + int64_t h6 = load_3(s + 20) << 7; + int64_t h7 = load_3(s + 23) << 5; + int64_t h8 = load_3(s + 26) << 4; + int64_t h9 = (load_3(s + 29) & 8388607) << 2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* Preconditions: + * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + * + * Write p=2^255-19; q=floor(h/p). + * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). + * + * Proof: + * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. + * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. + * + * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). + * Then 0<y<1. + * + * Write r=h-pq. + * Have 0<=r<=p-1=2^255-20. + * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. + * + * Write x=r+19(2^-255)r+y. + * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. + * + * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) + * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */ +static void fe_tobytes(uint8_t *s, const fe h) { + int32_t h0 = h[0]; + int32_t h1 = h[1]; + int32_t h2 = h[2]; + int32_t h3 = h[3]; + int32_t h4 = h[4]; + int32_t h5 = h[5]; + int32_t h6 = h[6]; + int32_t h7 = h[7]; + int32_t h8 = h[8]; + int32_t h9 = h[9]; + int32_t q; + + q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; + q = (h0 + q) >> 26; + q = (h1 + q) >> 25; + q = (h2 + q) >> 26; + q = (h3 + q) >> 25; + q = (h4 + q) >> 26; + q = (h5 + q) >> 25; + q = (h6 + q) >> 26; + q = (h7 + q) >> 25; + q = (h8 + q) >> 26; + q = (h9 + q) >> 25; + + /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ + h0 += 19 * q; + /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ + + h1 += h0 >> 26; h0 &= kBottom26Bits; + h2 += h1 >> 25; h1 &= kBottom25Bits; + h3 += h2 >> 26; h2 &= kBottom26Bits; + h4 += h3 >> 25; h3 &= kBottom25Bits; + h5 += h4 >> 26; h4 &= kBottom26Bits; + h6 += h5 >> 25; h5 &= kBottom25Bits; + h7 += h6 >> 26; h6 &= kBottom26Bits; + h8 += h7 >> 25; h7 &= kBottom25Bits; + h9 += h8 >> 26; h8 &= kBottom26Bits; + h9 &= kBottom25Bits; + /* h10 = carry9 */ + + /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + * Have h0+...+2^230 h9 between 0 and 2^255-1; + * evidently 2^255 h10-2^255 q = 0. + * Goal: Output h0+...+2^230 h9. */ + + s[0] = h0 >> 0; + s[1] = h0 >> 8; + s[2] = h0 >> 16; + s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2); + s[4] = h1 >> 6; + s[5] = h1 >> 14; + s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3); + s[7] = h2 >> 5; + s[8] = h2 >> 13; + s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5); + s[10] = h3 >> 3; + s[11] = h3 >> 11; + s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6); + s[13] = h4 >> 2; + s[14] = h4 >> 10; + s[15] = h4 >> 18; + s[16] = h5 >> 0; + s[17] = h5 >> 8; + s[18] = h5 >> 16; + s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1); + s[20] = h6 >> 7; + s[21] = h6 >> 15; + s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3); + s[23] = h7 >> 5; + s[24] = h7 >> 13; + s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4); + s[26] = h8 >> 4; + s[27] = h8 >> 12; + s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6); + s[29] = h9 >> 2; + s[30] = h9 >> 10; + s[31] = h9 >> 18; +} + +/* h = f */ +static void fe_copy(fe h, const fe f) { + memmove(h, f, sizeof(int32_t) * 10); +} + +/* h = 0 */ +static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); } + +/* h = 1 */ +static void fe_1(fe h) { + memset(h, 0, sizeof(int32_t) * 10); + h[0] = 1; +} + +/* h = f + g + * Can overlap h with f or g. + * + * Preconditions: + * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ +static void fe_add(fe h, const fe f, const fe g) { + unsigned i; + for (i = 0; i < 10; i++) { + h[i] = f[i] + g[i]; + } +} + +/* h = f - g + * Can overlap h with f or g. + * + * Preconditions: + * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ +static void fe_sub(fe h, const fe f, const fe g) { + unsigned i; + for (i = 0; i < 10; i++) { + h[i] = f[i] - g[i]; + } +} + +/* h = f * g + * Can overlap h with f or g. + * + * Preconditions: + * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + * + * Notes on implementation strategy: + * + * Using schoolbook multiplication. + * Karatsuba would save a little in some cost models. + * + * Most multiplications by 2 and 19 are 32-bit precomputations; + * cheaper than 64-bit postcomputations. + * + * There is one remaining multiplication by 19 in the carry chain; + * one *19 precomputation can be merged into this, + * but the resulting data flow is considerably less clean. + * + * There are 12 carries below. + * 10 of them are 2-way parallelizable and vectorizable. + * Can get away with 11 carries, but then data flow is much deeper. + * + * With tighter constraints on inputs can squeeze carries into int32. */ +static void fe_mul(fe h, const fe f, const fe g) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ + int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ + int32_t g3_19 = 19 * g3; + int32_t g4_19 = 19 * g4; + int32_t g5_19 = 19 * g5; + int32_t g6_19 = 19 * g6; + int32_t g7_19 = 19 * g7; + int32_t g8_19 = 19 * g8; + int32_t g9_19 = 19 * g9; + int32_t f1_2 = 2 * f1; + int32_t f3_2 = 2 * f3; + int32_t f5_2 = 2 * f5; + int32_t f7_2 = 2 * f7; + int32_t f9_2 = 2 * f9; + int64_t f0g0 = f0 * (int64_t) g0; + int64_t f0g1 = f0 * (int64_t) g1; + int64_t f0g2 = f0 * (int64_t) g2; + int64_t f0g3 = f0 * (int64_t) g3; + int64_t f0g4 = f0 * (int64_t) g4; + int64_t f0g5 = f0 * (int64_t) g5; + int64_t f0g6 = f0 * (int64_t) g6; + int64_t f0g7 = f0 * (int64_t) g7; + int64_t f0g8 = f0 * (int64_t) g8; + int64_t f0g9 = f0 * (int64_t) g9; + int64_t f1g0 = f1 * (int64_t) g0; + int64_t f1g1_2 = f1_2 * (int64_t) g1; + int64_t f1g2 = f1 * (int64_t) g2; + int64_t f1g3_2 = f1_2 * (int64_t) g3; + int64_t f1g4 = f1 * (int64_t) g4; + int64_t f1g5_2 = f1_2 * (int64_t) g5; + int64_t f1g6 = f1 * (int64_t) g6; + int64_t f1g7_2 = f1_2 * (int64_t) g7; + int64_t f1g8 = f1 * (int64_t) g8; + int64_t f1g9_38 = f1_2 * (int64_t) g9_19; + int64_t f2g0 = f2 * (int64_t) g0; + int64_t f2g1 = f2 * (int64_t) g1; + int64_t f2g2 = f2 * (int64_t) g2; + int64_t f2g3 = f2 * (int64_t) g3; + int64_t f2g4 = f2 * (int64_t) g4; + int64_t f2g5 = f2 * (int64_t) g5; + int64_t f2g6 = f2 * (int64_t) g6; + int64_t f2g7 = f2 * (int64_t) g7; + int64_t f2g8_19 = f2 * (int64_t) g8_19; + int64_t f2g9_19 = f2 * (int64_t) g9_19; + int64_t f3g0 = f3 * (int64_t) g0; + int64_t f3g1_2 = f3_2 * (int64_t) g1; + int64_t f3g2 = f3 * (int64_t) g2; + int64_t f3g3_2 = f3_2 * (int64_t) g3; + int64_t f3g4 = f3 * (int64_t) g4; + int64_t f3g5_2 = f3_2 * (int64_t) g5; + int64_t f3g6 = f3 * (int64_t) g6; + int64_t f3g7_38 = f3_2 * (int64_t) g7_19; + int64_t f3g8_19 = f3 * (int64_t) g8_19; + int64_t f3g9_38 = f3_2 * (int64_t) g9_19; + int64_t f4g0 = f4 * (int64_t) g0; + int64_t f4g1 = f4 * (int64_t) g1; + int64_t f4g2 = f4 * (int64_t) g2; + int64_t f4g3 = f4 * (int64_t) g3; + int64_t f4g4 = f4 * (int64_t) g4; + int64_t f4g5 = f4 * (int64_t) g5; + int64_t f4g6_19 = f4 * (int64_t) g6_19; + int64_t f4g7_19 = f4 * (int64_t) g7_19; + int64_t f4g8_19 = f4 * (int64_t) g8_19; + int64_t f4g9_19 = f4 * (int64_t) g9_19; + int64_t f5g0 = f5 * (int64_t) g0; + int64_t f5g1_2 = f5_2 * (int64_t) g1; + int64_t f5g2 = f5 * (int64_t) g2; + int64_t f5g3_2 = f5_2 * (int64_t) g3; + int64_t f5g4 = f5 * (int64_t) g4; + int64_t f5g5_38 = f5_2 * (int64_t) g5_19; + int64_t f5g6_19 = f5 * (int64_t) g6_19; + int64_t f5g7_38 = f5_2 * (int64_t) g7_19; + int64_t f5g8_19 = f5 * (int64_t) g8_19; + int64_t f5g9_38 = f5_2 * (int64_t) g9_19; + int64_t f6g0 = f6 * (int64_t) g0; + int64_t f6g1 = f6 * (int64_t) g1; + int64_t f6g2 = f6 * (int64_t) g2; + int64_t f6g3 = f6 * (int64_t) g3; + int64_t f6g4_19 = f6 * (int64_t) g4_19; + int64_t f6g5_19 = f6 * (int64_t) g5_19; + int64_t f6g6_19 = f6 * (int64_t) g6_19; + int64_t f6g7_19 = f6 * (int64_t) g7_19; + int64_t f6g8_19 = f6 * (int64_t) g8_19; + int64_t f6g9_19 = f6 * (int64_t) g9_19; + int64_t f7g0 = f7 * (int64_t) g0; + int64_t f7g1_2 = f7_2 * (int64_t) g1; + int64_t f7g2 = f7 * (int64_t) g2; + int64_t f7g3_38 = f7_2 * (int64_t) g3_19; + int64_t f7g4_19 = f7 * (int64_t) g4_19; + int64_t f7g5_38 = f7_2 * (int64_t) g5_19; + int64_t f7g6_19 = f7 * (int64_t) g6_19; + int64_t f7g7_38 = f7_2 * (int64_t) g7_19; + int64_t f7g8_19 = f7 * (int64_t) g8_19; + int64_t f7g9_38 = f7_2 * (int64_t) g9_19; + int64_t f8g0 = f8 * (int64_t) g0; + int64_t f8g1 = f8 * (int64_t) g1; + int64_t f8g2_19 = f8 * (int64_t) g2_19; + int64_t f8g3_19 = f8 * (int64_t) g3_19; + int64_t f8g4_19 = f8 * (int64_t) g4_19; + int64_t f8g5_19 = f8 * (int64_t) g5_19; + int64_t f8g6_19 = f8 * (int64_t) g6_19; + int64_t f8g7_19 = f8 * (int64_t) g7_19; + int64_t f8g8_19 = f8 * (int64_t) g8_19; + int64_t f8g9_19 = f8 * (int64_t) g9_19; + int64_t f9g0 = f9 * (int64_t) g0; + int64_t f9g1_38 = f9_2 * (int64_t) g1_19; + int64_t f9g2_19 = f9 * (int64_t) g2_19; + int64_t f9g3_38 = f9_2 * (int64_t) g3_19; + int64_t f9g4_19 = f9 * (int64_t) g4_19; + int64_t f9g5_38 = f9_2 * (int64_t) g5_19; + int64_t f9g6_19 = f9 * (int64_t) g6_19; + int64_t f9g7_38 = f9_2 * (int64_t) g7_19; + int64_t f9g8_19 = f9 * (int64_t) g8_19; + int64_t f9g9_38 = f9_2 * (int64_t) g9_19; + int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; + int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; + int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; + int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; + int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; + int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; + int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; + int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; + int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; + int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) + * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 + * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) + * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + /* |h5| <= 1.71*2^59 */ + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.41*2^60 */ + /* |h6| <= 1.41*2^60 */ + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.71*2^59 */ + /* |h7| <= 1.71*2^59 */ + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.72*2^34 */ + /* |h8| <= 1.41*2^60 */ + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + /* |h9| <= 1.71*2^59 */ + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.1*2^39 */ + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* h = f * f + * Can overlap h with f. + * + * Preconditions: + * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + * + * See fe_mul.c for discussion of implementation strategy. */ +static void fe_sq(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +static void fe_invert(fe out, const fe z) { + fe t0; + fe t1; + fe t2; + fe t3; + int i; + + fe_sq(t0, z); + fe_sq(t1, t0); + for (i = 1; i < 2; ++i) { + fe_sq(t1, t1); + } + fe_mul(t1, z, t1); + fe_mul(t0, t0, t1); + fe_sq(t2, t0); + fe_mul(t1, t1, t2); + fe_sq(t2, t1); + for (i = 1; i < 5; ++i) { + fe_sq(t2, t2); + } + fe_mul(t1, t2, t1); + fe_sq(t2, t1); + for (i = 1; i < 10; ++i) { + fe_sq(t2, t2); + } + fe_mul(t2, t2, t1); + fe_sq(t3, t2); + for (i = 1; i < 20; ++i) { + fe_sq(t3, t3); + } + fe_mul(t2, t3, t2); + fe_sq(t2, t2); + for (i = 1; i < 10; ++i) { + fe_sq(t2, t2); + } + fe_mul(t1, t2, t1); + fe_sq(t2, t1); + for (i = 1; i < 50; ++i) { + fe_sq(t2, t2); + } + fe_mul(t2, t2, t1); + fe_sq(t3, t2); + for (i = 1; i < 100; ++i) { + fe_sq(t3, t3); + } + fe_mul(t2, t3, t2); + fe_sq(t2, t2); + for (i = 1; i < 50; ++i) { + fe_sq(t2, t2); + } + fe_mul(t1, t2, t1); + fe_sq(t1, t1); + for (i = 1; i < 5; ++i) { + fe_sq(t1, t1); + } + fe_mul(out, t1, t0); +} + +/* Replace (f,g) with (g,f) if b == 1; + * replace (f,g) with (f,g) if b == 0. + * + * Preconditions: b in {0,1}. */ +static void fe_cswap(fe f, fe g, unsigned int b) { + unsigned i; + b = 0-b; + for (i = 0; i < 10; i++) { + int32_t x = f[i] ^ g[i]; + x &= b; + f[i] ^= x; + g[i] ^= x; + } +} + +/* h = f * 121666 + * Can overlap h with f. + * + * Preconditions: + * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ +static void fe_mul121666(fe h, fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int64_t h0 = f0 * (int64_t) 121666; + int64_t h1 = f1 * (int64_t) 121666; + int64_t h2 = f2 * (int64_t) 121666; + int64_t h3 = f3 * (int64_t) 121666; + int64_t h4 = f4 * (int64_t) 121666; + int64_t h5 = f5 * (int64_t) 121666; + int64_t h6 = f6 * (int64_t) 121666; + int64_t h7 = f7 * (int64_t) 121666; + int64_t h8 = f8 * (int64_t) 121666; + int64_t h9 = f9 * (int64_t) 121666; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +void x25519_scalar_mult(uint8_t out[32], + const uint8_t scalar[32], + const uint8_t point[32]) { + fe x1, x2, z2, x3, z3, tmp0, tmp1; + unsigned swap; + int pos; + + uint8_t e[32]; + memcpy(e, scalar, 32); + e[0] &= 248; + e[31] &= 127; + e[31] |= 64; + fe_frombytes(x1, point); + fe_1(x2); + fe_0(z2); + fe_copy(x3, x1); + fe_1(z3); + + swap = 0; + for (pos = 254; pos >= 0; --pos) { + unsigned b = 1 & (e[pos / 8] >> (pos & 7)); + swap ^= b; + fe_cswap(x2, x3, swap); + fe_cswap(z2, z3, swap); + swap = b; + fe_sub(tmp0, x3, z3); + fe_sub(tmp1, x2, z2); + fe_add(x2, x2, z2); + fe_add(z2, x3, z3); + fe_mul(z3, tmp0, x2); + fe_mul(z2, z2, tmp1); + fe_sq(tmp0, tmp1); + fe_sq(tmp1, x2); + fe_add(x3, z3, z2); + fe_sub(z2, z3, z2); + fe_mul(x2, tmp1, tmp0); + fe_sub(tmp1, tmp1, tmp0); + fe_sq(z2, z2); + fe_mul121666(z3, tmp1); + fe_sq(x3, x3); + fe_add(tmp0, tmp0, z3); + fe_mul(z3, x1, z2); + fe_mul(z2, tmp1, tmp0); + } + fe_cswap(x2, x3, swap); + fe_cswap(z2, z3, swap); + + fe_invert(z2, z2); + fe_mul(x2, x2, z2); + fe_tobytes(out, x2); +} diff --git a/common/curve25519.c b/common/curve25519.c index 5faa53dc11..5e3a8b81f6 100644 --- a/common/curve25519.c +++ b/common/curve25519.c @@ -19,815 +19,12 @@ * * The field functions are shared by Ed25519 and X25519 where possible. */ +#include "common.h" #include "curve25519.h" #include "trng.h" #include "util.h" #define CRYPTO_memcmp safe_memcmp - -/* - * fe means field element. Here the field is \Z/(2^255-19). An element t, - * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 - * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on - * context. - */ -typedef int32_t fe[10]; - -static const int64_t kBottom25Bits = INT64_C(0x1ffffff); -static const int64_t kBottom26Bits = INT64_C(0x3ffffff); -static const int64_t kTop39Bits = INT64_C(0xfffffffffe000000); -static const int64_t kTop38Bits = INT64_C(0xfffffffffc000000); - -static uint64_t load_3(const uint8_t *in) { - uint64_t result; - result = (uint64_t)in[0]; - result |= ((uint64_t)in[1]) << 8; - result |= ((uint64_t)in[2]) << 16; - return result; -} - -static uint64_t load_4(const uint8_t *in) { - uint64_t result; - result = (uint64_t)in[0]; - result |= ((uint64_t)in[1]) << 8; - result |= ((uint64_t)in[2]) << 16; - result |= ((uint64_t)in[3]) << 24; - return result; -} - -static void fe_frombytes(fe h, const uint8_t *s) { - /* Ignores top bit of h. */ - int64_t h0 = load_4(s); - int64_t h1 = load_3(s + 4) << 6; - int64_t h2 = load_3(s + 7) << 5; - int64_t h3 = load_3(s + 10) << 3; - int64_t h4 = load_3(s + 13) << 2; - int64_t h5 = load_4(s + 16); - int64_t h6 = load_3(s + 20) << 7; - int64_t h7 = load_3(s + 23) << 5; - int64_t h8 = load_3(s + 26) << 4; - int64_t h9 = (load_3(s + 29) & 8388607) << 2; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - - carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; - carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; - carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; - carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; - carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; - - carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; - carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; - - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} - -/* Preconditions: - * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. - * - * Write p=2^255-19; q=floor(h/p). - * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). - * - * Proof: - * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. - * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. - * - * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). - * Then 0<y<1. - * - * Write r=h-pq. - * Have 0<=r<=p-1=2^255-20. - * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. - * - * Write x=r+19(2^-255)r+y. - * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. - * - * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) - * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */ -static void fe_tobytes(uint8_t *s, const fe h) { - int32_t h0 = h[0]; - int32_t h1 = h[1]; - int32_t h2 = h[2]; - int32_t h3 = h[3]; - int32_t h4 = h[4]; - int32_t h5 = h[5]; - int32_t h6 = h[6]; - int32_t h7 = h[7]; - int32_t h8 = h[8]; - int32_t h9 = h[9]; - int32_t q; - - q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; - q = (h0 + q) >> 26; - q = (h1 + q) >> 25; - q = (h2 + q) >> 26; - q = (h3 + q) >> 25; - q = (h4 + q) >> 26; - q = (h5 + q) >> 25; - q = (h6 + q) >> 26; - q = (h7 + q) >> 25; - q = (h8 + q) >> 26; - q = (h9 + q) >> 25; - - /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ - h0 += 19 * q; - /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ - - h1 += h0 >> 26; h0 &= kBottom26Bits; - h2 += h1 >> 25; h1 &= kBottom25Bits; - h3 += h2 >> 26; h2 &= kBottom26Bits; - h4 += h3 >> 25; h3 &= kBottom25Bits; - h5 += h4 >> 26; h4 &= kBottom26Bits; - h6 += h5 >> 25; h5 &= kBottom25Bits; - h7 += h6 >> 26; h6 &= kBottom26Bits; - h8 += h7 >> 25; h7 &= kBottom25Bits; - h9 += h8 >> 26; h8 &= kBottom26Bits; - h9 &= kBottom25Bits; - /* h10 = carry9 */ - - /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. - * Have h0+...+2^230 h9 between 0 and 2^255-1; - * evidently 2^255 h10-2^255 q = 0. - * Goal: Output h0+...+2^230 h9. */ - - s[0] = h0 >> 0; - s[1] = h0 >> 8; - s[2] = h0 >> 16; - s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2); - s[4] = h1 >> 6; - s[5] = h1 >> 14; - s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3); - s[7] = h2 >> 5; - s[8] = h2 >> 13; - s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5); - s[10] = h3 >> 3; - s[11] = h3 >> 11; - s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6); - s[13] = h4 >> 2; - s[14] = h4 >> 10; - s[15] = h4 >> 18; - s[16] = h5 >> 0; - s[17] = h5 >> 8; - s[18] = h5 >> 16; - s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1); - s[20] = h6 >> 7; - s[21] = h6 >> 15; - s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3); - s[23] = h7 >> 5; - s[24] = h7 >> 13; - s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4); - s[26] = h8 >> 4; - s[27] = h8 >> 12; - s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6); - s[29] = h9 >> 2; - s[30] = h9 >> 10; - s[31] = h9 >> 18; -} - -/* h = f */ -static void fe_copy(fe h, const fe f) { - memmove(h, f, sizeof(int32_t) * 10); -} - -/* h = 0 */ -static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); } - -/* h = 1 */ -static void fe_1(fe h) { - memset(h, 0, sizeof(int32_t) * 10); - h[0] = 1; -} - -/* h = f + g - * Can overlap h with f or g. - * - * Preconditions: - * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - * - * Postconditions: - * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ -static void fe_add(fe h, const fe f, const fe g) { - unsigned i; - for (i = 0; i < 10; i++) { - h[i] = f[i] + g[i]; - } -} - -/* h = f - g - * Can overlap h with f or g. - * - * Preconditions: - * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - * - * Postconditions: - * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ -static void fe_sub(fe h, const fe f, const fe g) { - unsigned i; - for (i = 0; i < 10; i++) { - h[i] = f[i] - g[i]; - } -} - -/* h = f * g - * Can overlap h with f or g. - * - * Preconditions: - * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. - * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. - * - * Postconditions: - * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. - * - * Notes on implementation strategy: - * - * Using schoolbook multiplication. - * Karatsuba would save a little in some cost models. - * - * Most multiplications by 2 and 19 are 32-bit precomputations; - * cheaper than 64-bit postcomputations. - * - * There is one remaining multiplication by 19 in the carry chain; - * one *19 precomputation can be merged into this, - * but the resulting data flow is considerably less clean. - * - * There are 12 carries below. - * 10 of them are 2-way parallelizable and vectorizable. - * Can get away with 11 carries, but then data flow is much deeper. - * - * With tighter constraints on inputs can squeeze carries into int32. */ -static void fe_mul(fe h, const fe f, const fe g) { - int32_t f0 = f[0]; - int32_t f1 = f[1]; - int32_t f2 = f[2]; - int32_t f3 = f[3]; - int32_t f4 = f[4]; - int32_t f5 = f[5]; - int32_t f6 = f[6]; - int32_t f7 = f[7]; - int32_t f8 = f[8]; - int32_t f9 = f[9]; - int32_t g0 = g[0]; - int32_t g1 = g[1]; - int32_t g2 = g[2]; - int32_t g3 = g[3]; - int32_t g4 = g[4]; - int32_t g5 = g[5]; - int32_t g6 = g[6]; - int32_t g7 = g[7]; - int32_t g8 = g[8]; - int32_t g9 = g[9]; - int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ - int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ - int32_t g3_19 = 19 * g3; - int32_t g4_19 = 19 * g4; - int32_t g5_19 = 19 * g5; - int32_t g6_19 = 19 * g6; - int32_t g7_19 = 19 * g7; - int32_t g8_19 = 19 * g8; - int32_t g9_19 = 19 * g9; - int32_t f1_2 = 2 * f1; - int32_t f3_2 = 2 * f3; - int32_t f5_2 = 2 * f5; - int32_t f7_2 = 2 * f7; - int32_t f9_2 = 2 * f9; - int64_t f0g0 = f0 * (int64_t) g0; - int64_t f0g1 = f0 * (int64_t) g1; - int64_t f0g2 = f0 * (int64_t) g2; - int64_t f0g3 = f0 * (int64_t) g3; - int64_t f0g4 = f0 * (int64_t) g4; - int64_t f0g5 = f0 * (int64_t) g5; - int64_t f0g6 = f0 * (int64_t) g6; - int64_t f0g7 = f0 * (int64_t) g7; - int64_t f0g8 = f0 * (int64_t) g8; - int64_t f0g9 = f0 * (int64_t) g9; - int64_t f1g0 = f1 * (int64_t) g0; - int64_t f1g1_2 = f1_2 * (int64_t) g1; - int64_t f1g2 = f1 * (int64_t) g2; - int64_t f1g3_2 = f1_2 * (int64_t) g3; - int64_t f1g4 = f1 * (int64_t) g4; - int64_t f1g5_2 = f1_2 * (int64_t) g5; - int64_t f1g6 = f1 * (int64_t) g6; - int64_t f1g7_2 = f1_2 * (int64_t) g7; - int64_t f1g8 = f1 * (int64_t) g8; - int64_t f1g9_38 = f1_2 * (int64_t) g9_19; - int64_t f2g0 = f2 * (int64_t) g0; - int64_t f2g1 = f2 * (int64_t) g1; - int64_t f2g2 = f2 * (int64_t) g2; - int64_t f2g3 = f2 * (int64_t) g3; - int64_t f2g4 = f2 * (int64_t) g4; - int64_t f2g5 = f2 * (int64_t) g5; - int64_t f2g6 = f2 * (int64_t) g6; - int64_t f2g7 = f2 * (int64_t) g7; - int64_t f2g8_19 = f2 * (int64_t) g8_19; - int64_t f2g9_19 = f2 * (int64_t) g9_19; - int64_t f3g0 = f3 * (int64_t) g0; - int64_t f3g1_2 = f3_2 * (int64_t) g1; - int64_t f3g2 = f3 * (int64_t) g2; - int64_t f3g3_2 = f3_2 * (int64_t) g3; - int64_t f3g4 = f3 * (int64_t) g4; - int64_t f3g5_2 = f3_2 * (int64_t) g5; - int64_t f3g6 = f3 * (int64_t) g6; - int64_t f3g7_38 = f3_2 * (int64_t) g7_19; - int64_t f3g8_19 = f3 * (int64_t) g8_19; - int64_t f3g9_38 = f3_2 * (int64_t) g9_19; - int64_t f4g0 = f4 * (int64_t) g0; - int64_t f4g1 = f4 * (int64_t) g1; - int64_t f4g2 = f4 * (int64_t) g2; - int64_t f4g3 = f4 * (int64_t) g3; - int64_t f4g4 = f4 * (int64_t) g4; - int64_t f4g5 = f4 * (int64_t) g5; - int64_t f4g6_19 = f4 * (int64_t) g6_19; - int64_t f4g7_19 = f4 * (int64_t) g7_19; - int64_t f4g8_19 = f4 * (int64_t) g8_19; - int64_t f4g9_19 = f4 * (int64_t) g9_19; - int64_t f5g0 = f5 * (int64_t) g0; - int64_t f5g1_2 = f5_2 * (int64_t) g1; - int64_t f5g2 = f5 * (int64_t) g2; - int64_t f5g3_2 = f5_2 * (int64_t) g3; - int64_t f5g4 = f5 * (int64_t) g4; - int64_t f5g5_38 = f5_2 * (int64_t) g5_19; - int64_t f5g6_19 = f5 * (int64_t) g6_19; - int64_t f5g7_38 = f5_2 * (int64_t) g7_19; - int64_t f5g8_19 = f5 * (int64_t) g8_19; - int64_t f5g9_38 = f5_2 * (int64_t) g9_19; - int64_t f6g0 = f6 * (int64_t) g0; - int64_t f6g1 = f6 * (int64_t) g1; - int64_t f6g2 = f6 * (int64_t) g2; - int64_t f6g3 = f6 * (int64_t) g3; - int64_t f6g4_19 = f6 * (int64_t) g4_19; - int64_t f6g5_19 = f6 * (int64_t) g5_19; - int64_t f6g6_19 = f6 * (int64_t) g6_19; - int64_t f6g7_19 = f6 * (int64_t) g7_19; - int64_t f6g8_19 = f6 * (int64_t) g8_19; - int64_t f6g9_19 = f6 * (int64_t) g9_19; - int64_t f7g0 = f7 * (int64_t) g0; - int64_t f7g1_2 = f7_2 * (int64_t) g1; - int64_t f7g2 = f7 * (int64_t) g2; - int64_t f7g3_38 = f7_2 * (int64_t) g3_19; - int64_t f7g4_19 = f7 * (int64_t) g4_19; - int64_t f7g5_38 = f7_2 * (int64_t) g5_19; - int64_t f7g6_19 = f7 * (int64_t) g6_19; - int64_t f7g7_38 = f7_2 * (int64_t) g7_19; - int64_t f7g8_19 = f7 * (int64_t) g8_19; - int64_t f7g9_38 = f7_2 * (int64_t) g9_19; - int64_t f8g0 = f8 * (int64_t) g0; - int64_t f8g1 = f8 * (int64_t) g1; - int64_t f8g2_19 = f8 * (int64_t) g2_19; - int64_t f8g3_19 = f8 * (int64_t) g3_19; - int64_t f8g4_19 = f8 * (int64_t) g4_19; - int64_t f8g5_19 = f8 * (int64_t) g5_19; - int64_t f8g6_19 = f8 * (int64_t) g6_19; - int64_t f8g7_19 = f8 * (int64_t) g7_19; - int64_t f8g8_19 = f8 * (int64_t) g8_19; - int64_t f8g9_19 = f8 * (int64_t) g9_19; - int64_t f9g0 = f9 * (int64_t) g0; - int64_t f9g1_38 = f9_2 * (int64_t) g1_19; - int64_t f9g2_19 = f9 * (int64_t) g2_19; - int64_t f9g3_38 = f9_2 * (int64_t) g3_19; - int64_t f9g4_19 = f9 * (int64_t) g4_19; - int64_t f9g5_38 = f9_2 * (int64_t) g5_19; - int64_t f9g6_19 = f9 * (int64_t) g6_19; - int64_t f9g7_38 = f9_2 * (int64_t) g7_19; - int64_t f9g8_19 = f9 * (int64_t) g8_19; - int64_t f9g9_38 = f9_2 * (int64_t) g9_19; - int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; - int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; - int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; - int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; - int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; - int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; - int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; - int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; - int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; - int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - - /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) - * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 - * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) - * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ - - carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - /* |h0| <= 2^25 */ - /* |h4| <= 2^25 */ - /* |h1| <= 1.71*2^59 */ - /* |h5| <= 1.71*2^59 */ - - carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; - carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; - /* |h1| <= 2^24; from now on fits into int32 */ - /* |h5| <= 2^24; from now on fits into int32 */ - /* |h2| <= 1.41*2^60 */ - /* |h6| <= 1.41*2^60 */ - - carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; - carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; - /* |h2| <= 2^25; from now on fits into int32 unchanged */ - /* |h6| <= 2^25; from now on fits into int32 unchanged */ - /* |h3| <= 1.71*2^59 */ - /* |h7| <= 1.71*2^59 */ - - carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; - carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; - /* |h3| <= 2^24; from now on fits into int32 unchanged */ - /* |h7| <= 2^24; from now on fits into int32 unchanged */ - /* |h4| <= 1.72*2^34 */ - /* |h8| <= 1.41*2^60 */ - - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; - /* |h4| <= 2^25; from now on fits into int32 unchanged */ - /* |h8| <= 2^25; from now on fits into int32 unchanged */ - /* |h5| <= 1.01*2^24 */ - /* |h9| <= 1.71*2^59 */ - - carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; - /* |h9| <= 2^24; from now on fits into int32 unchanged */ - /* |h0| <= 1.1*2^39 */ - - carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - /* |h0| <= 2^25; from now on fits into int32 unchanged */ - /* |h1| <= 1.01*2^24 */ - - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} - -/* h = f * f - * Can overlap h with f. - * - * Preconditions: - * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. - * - * Postconditions: - * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. - * - * See fe_mul.c for discussion of implementation strategy. */ -static void fe_sq(fe h, const fe f) { - int32_t f0 = f[0]; - int32_t f1 = f[1]; - int32_t f2 = f[2]; - int32_t f3 = f[3]; - int32_t f4 = f[4]; - int32_t f5 = f[5]; - int32_t f6 = f[6]; - int32_t f7 = f[7]; - int32_t f8 = f[8]; - int32_t f9 = f[9]; - int32_t f0_2 = 2 * f0; - int32_t f1_2 = 2 * f1; - int32_t f2_2 = 2 * f2; - int32_t f3_2 = 2 * f3; - int32_t f4_2 = 2 * f4; - int32_t f5_2 = 2 * f5; - int32_t f6_2 = 2 * f6; - int32_t f7_2 = 2 * f7; - int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ - int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ - int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ - int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ - int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ - int64_t f0f0 = f0 * (int64_t) f0; - int64_t f0f1_2 = f0_2 * (int64_t) f1; - int64_t f0f2_2 = f0_2 * (int64_t) f2; - int64_t f0f3_2 = f0_2 * (int64_t) f3; - int64_t f0f4_2 = f0_2 * (int64_t) f4; - int64_t f0f5_2 = f0_2 * (int64_t) f5; - int64_t f0f6_2 = f0_2 * (int64_t) f6; - int64_t f0f7_2 = f0_2 * (int64_t) f7; - int64_t f0f8_2 = f0_2 * (int64_t) f8; - int64_t f0f9_2 = f0_2 * (int64_t) f9; - int64_t f1f1_2 = f1_2 * (int64_t) f1; - int64_t f1f2_2 = f1_2 * (int64_t) f2; - int64_t f1f3_4 = f1_2 * (int64_t) f3_2; - int64_t f1f4_2 = f1_2 * (int64_t) f4; - int64_t f1f5_4 = f1_2 * (int64_t) f5_2; - int64_t f1f6_2 = f1_2 * (int64_t) f6; - int64_t f1f7_4 = f1_2 * (int64_t) f7_2; - int64_t f1f8_2 = f1_2 * (int64_t) f8; - int64_t f1f9_76 = f1_2 * (int64_t) f9_38; - int64_t f2f2 = f2 * (int64_t) f2; - int64_t f2f3_2 = f2_2 * (int64_t) f3; - int64_t f2f4_2 = f2_2 * (int64_t) f4; - int64_t f2f5_2 = f2_2 * (int64_t) f5; - int64_t f2f6_2 = f2_2 * (int64_t) f6; - int64_t f2f7_2 = f2_2 * (int64_t) f7; - int64_t f2f8_38 = f2_2 * (int64_t) f8_19; - int64_t f2f9_38 = f2 * (int64_t) f9_38; - int64_t f3f3_2 = f3_2 * (int64_t) f3; - int64_t f3f4_2 = f3_2 * (int64_t) f4; - int64_t f3f5_4 = f3_2 * (int64_t) f5_2; - int64_t f3f6_2 = f3_2 * (int64_t) f6; - int64_t f3f7_76 = f3_2 * (int64_t) f7_38; - int64_t f3f8_38 = f3_2 * (int64_t) f8_19; - int64_t f3f9_76 = f3_2 * (int64_t) f9_38; - int64_t f4f4 = f4 * (int64_t) f4; - int64_t f4f5_2 = f4_2 * (int64_t) f5; - int64_t f4f6_38 = f4_2 * (int64_t) f6_19; - int64_t f4f7_38 = f4 * (int64_t) f7_38; - int64_t f4f8_38 = f4_2 * (int64_t) f8_19; - int64_t f4f9_38 = f4 * (int64_t) f9_38; - int64_t f5f5_38 = f5 * (int64_t) f5_38; - int64_t f5f6_38 = f5_2 * (int64_t) f6_19; - int64_t f5f7_76 = f5_2 * (int64_t) f7_38; - int64_t f5f8_38 = f5_2 * (int64_t) f8_19; - int64_t f5f9_76 = f5_2 * (int64_t) f9_38; - int64_t f6f6_19 = f6 * (int64_t) f6_19; - int64_t f6f7_38 = f6 * (int64_t) f7_38; - int64_t f6f8_38 = f6_2 * (int64_t) f8_19; - int64_t f6f9_38 = f6 * (int64_t) f9_38; - int64_t f7f7_38 = f7 * (int64_t) f7_38; - int64_t f7f8_38 = f7_2 * (int64_t) f8_19; - int64_t f7f9_76 = f7_2 * (int64_t) f9_38; - int64_t f8f8_19 = f8 * (int64_t) f8_19; - int64_t f8f9_38 = f8 * (int64_t) f9_38; - int64_t f9f9_38 = f9 * (int64_t) f9_38; - int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; - int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; - int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; - int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; - int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; - int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; - int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; - int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; - int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; - int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - - carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - - carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; - carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; - - carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; - carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; - - carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; - carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; - - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; - - carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; - - carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} - -static void fe_invert(fe out, const fe z) { - fe t0; - fe t1; - fe t2; - fe t3; - int i; - - fe_sq(t0, z); - fe_sq(t1, t0); - for (i = 1; i < 2; ++i) { - fe_sq(t1, t1); - } - fe_mul(t1, z, t1); - fe_mul(t0, t0, t1); - fe_sq(t2, t0); - fe_mul(t1, t1, t2); - fe_sq(t2, t1); - for (i = 1; i < 5; ++i) { - fe_sq(t2, t2); - } - fe_mul(t1, t2, t1); - fe_sq(t2, t1); - for (i = 1; i < 10; ++i) { - fe_sq(t2, t2); - } - fe_mul(t2, t2, t1); - fe_sq(t3, t2); - for (i = 1; i < 20; ++i) { - fe_sq(t3, t3); - } - fe_mul(t2, t3, t2); - fe_sq(t2, t2); - for (i = 1; i < 10; ++i) { - fe_sq(t2, t2); - } - fe_mul(t1, t2, t1); - fe_sq(t2, t1); - for (i = 1; i < 50; ++i) { - fe_sq(t2, t2); - } - fe_mul(t2, t2, t1); - fe_sq(t3, t2); - for (i = 1; i < 100; ++i) { - fe_sq(t3, t3); - } - fe_mul(t2, t3, t2); - fe_sq(t2, t2); - for (i = 1; i < 50; ++i) { - fe_sq(t2, t2); - } - fe_mul(t1, t2, t1); - fe_sq(t1, t1); - for (i = 1; i < 5; ++i) { - fe_sq(t1, t1); - } - fe_mul(out, t1, t0); -} - -/* Replace (f,g) with (g,f) if b == 1; - * replace (f,g) with (f,g) if b == 0. - * - * Preconditions: b in {0,1}. */ -static void fe_cswap(fe f, fe g, unsigned int b) { - unsigned i; - b = 0-b; - for (i = 0; i < 10; i++) { - int32_t x = f[i] ^ g[i]; - x &= b; - f[i] ^= x; - g[i] ^= x; - } -} - -/* h = f * 121666 - * Can overlap h with f. - * - * Preconditions: - * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. - * - * Postconditions: - * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ -static void fe_mul121666(fe h, fe f) { - int32_t f0 = f[0]; - int32_t f1 = f[1]; - int32_t f2 = f[2]; - int32_t f3 = f[3]; - int32_t f4 = f[4]; - int32_t f5 = f[5]; - int32_t f6 = f[6]; - int32_t f7 = f[7]; - int32_t f8 = f[8]; - int32_t f9 = f[9]; - int64_t h0 = f0 * (int64_t) 121666; - int64_t h1 = f1 * (int64_t) 121666; - int64_t h2 = f2 * (int64_t) 121666; - int64_t h3 = f3 * (int64_t) 121666; - int64_t h4 = f4 * (int64_t) 121666; - int64_t h5 = f5 * (int64_t) 121666; - int64_t h6 = f6 * (int64_t) 121666; - int64_t h7 = f7 * (int64_t) 121666; - int64_t h8 = f8 * (int64_t) 121666; - int64_t h9 = f9 * (int64_t) 121666; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - - carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; - carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; - carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; - carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; - carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; - - carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; - carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; - carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; - carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; - carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; - - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} - -static void x25519_scalar_mult_generic(uint8_t out[32], - const uint8_t scalar[32], - const uint8_t point[32]) { - fe x1, x2, z2, x3, z3, tmp0, tmp1; - unsigned swap; - int pos; - - uint8_t e[32]; - memcpy(e, scalar, 32); - e[0] &= 248; - e[31] &= 127; - e[31] |= 64; - fe_frombytes(x1, point); - fe_1(x2); - fe_0(z2); - fe_copy(x3, x1); - fe_1(z3); - - swap = 0; - for (pos = 254; pos >= 0; --pos) { - unsigned b = 1 & (e[pos / 8] >> (pos & 7)); - swap ^= b; - fe_cswap(x2, x3, swap); - fe_cswap(z2, z3, swap); - swap = b; - fe_sub(tmp0, x3, z3); - fe_sub(tmp1, x2, z2); - fe_add(x2, x2, z2); - fe_add(z2, x3, z3); - fe_mul(z3, tmp0, x2); - fe_mul(z2, z2, tmp1); - fe_sq(tmp0, tmp1); - fe_sq(tmp1, x2); - fe_add(x3, z3, z2); - fe_sub(z2, z3, z2); - fe_mul(x2, tmp1, tmp0); - fe_sub(tmp1, tmp1, tmp0); - fe_sq(z2, z2); - fe_mul121666(z3, tmp1); - fe_sq(x3, x3); - fe_add(tmp0, tmp0, z3); - fe_mul(z3, x1, z2); - fe_mul(z2, tmp1, tmp0); - } - fe_cswap(x2, x3, swap); - fe_cswap(z2, z3, swap); - - fe_invert(z2, z2); - fe_mul(x2, x2, z2); - fe_tobytes(out, x2); -} - -static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], - const uint8_t point[32]) { - x25519_scalar_mult_generic(out, scalar, point); -} - #ifdef CONFIG_RNG void X25519_keypair(uint8_t out_public_value[32], uint8_t out_private_key[32]) { rand_bytes(out_private_key, 32); |