curve25519: fiat-crypto field arithmetic.
Each operation was translated from fiat-crypto output using fiat-crypto
prettyprint.py. For example fe_mul is synthesized in
https://github.com/mit-plv/fiat-crypto/blob/master/src/Specific/X25519/C32/femul.v,
and shown in the last Coq-compatible form at
https://github.com/mit-plv/fiat-crypto/blob/master/src/Specific/X25519/C32/femulDisplay.log.
Benchmarks on Google Cloud's unidentified Intel Xeon with AVX2:
git checkout $VARIANT && ( cd build && rm -rf * && CC=clang CXX=clang++ cmake -GNinja -DCMAKE_TOOLCHAIN_FILE=../util/32-bit-toolchain.cmake -DCMAKE_BUILD_TYPE=Release .. && ninja && ./tool/bssl speed -filter 25519 )
this branch:
Did 11382 Ed25519 key generation operations in 1053046us (10808.6 ops/sec)
Did 11169 Ed25519 signing operations in 1038080us (10759.3 ops/sec)
Did 2925 Ed25519 verify operations in 1001346us (2921.1 ops/sec)
Did 12000 Curve25519 base-point multiplication operations in 1084851us (11061.4 ops/sec)
Did 3850 Curve25519 arbitrary point multiplication operations in 1085565us (3546.5 ops/sec)
Did 11466 Ed25519 key generation operations in 1049821us (10921.9 ops/sec)
Did 11000 Ed25519 signing operations in 1013317us (10855.4 ops/sec)
Did 3047 Ed25519 verify operations in 1043846us (2919.0 ops/sec)
Did 12000 Curve25519 base-point multiplication operations in 1068924us (11226.2 ops/sec)
Did 3850 Curve25519 arbitrary point multiplication operations in 1090598us (3530.2 ops/sec)
Did 10309 Ed25519 key generation operations in 1003320us (10274.9 ops/sec)
Did 11000 Ed25519 signing operations in 1017862us (10807.0 ops/sec)
Did 3135 Ed25519 verify operations in 1098624us (2853.6 ops/sec)
Did 9000 Curve25519 base-point multiplication operations in 1046608us (8599.2 ops/sec)
Did 3132 Curve25519 arbitrary point multiplication operations in 1038963us (3014.5 ops/sec)
master:
Did 11564 Ed25519 key generation operations in 1068762us (10820.0 ops/sec)
Did 11104 Ed25519 signing operations in 1024278us (10840.8 ops/sec)
Did 3206 Ed25519 verify operations in 1049179us (3055.7 ops/sec)
Did 12000 Curve25519 base-point multiplication operations in 1073619us (11177.1 ops/sec)
Did 3550 Curve25519 arbitrary point multiplication operations in 1000279us (3549.0 ops/sec)
andreser@linux-andreser:~/boringssl$ build/tool/bssl speed -filter 25519
Did 11760 Ed25519 key generation operations in 1072495us (10965.1 ops/sec)
Did 10800 Ed25519 signing operations in 1003486us (10762.5 ops/sec)
Did 3245 Ed25519 verify operations in 1080399us (3003.5 ops/sec)
Did 12000 Curve25519 base-point multiplication operations in 1076021us (11152.2 ops/sec)
Did 3570 Curve25519 arbitrary point multiplication operations in 1005087us (3551.9 ops/sec)
andreser@linux-andreser:~/boringssl$ build/tool/bssl speed -filter 25519
Did 11438 Ed25519 key generation operations in 1041115us (10986.3 ops/sec)
Did 11000 Ed25519 signing operations in 1012589us (10863.2 ops/sec)
Did 3312 Ed25519 verify operations in 1082834us (3058.6 ops/sec)
Did 12000 Curve25519 base-point multiplication operations in 1061318us (11306.7 ops/sec)
Did 3580 Curve25519 arbitrary point multiplication operations in 1004923us (3562.5 ops/sec)
squashed: curve25519: convert field constants to unsigned.
import re, sys, math
def weight(i):
return 2**int(math.ceil(25.5*i))
def convert(t):
limbs = [x for x in t.groups() if x.replace('-','').isdigit()]
v = sum(weight(i)*x for (i,x) in enumerate(map(int, limbs))) % (2**255-19)
limbs = [(v % weight(i+1)) // weight(i) for i in range(10)]
assert v == sum(weight(i)*x for (i,x) in enumerate(limbs))
i = 0
ret = ''
for s in t.groups():
if s.replace('-','').isdigit():
ret += str(limbs[i])
i += 1
else:
ret += s
return ret
fe_re = re.compile(r'(\s*,\s*)'.join(r'(-?\d+)' for i in range(10)))
print (re.sub(fe_re, convert, sys.stdin.read()))
Change-Id: Ibd4f7f5c38e5c4d61c9826afb406baebe2be5168
Reviewed-on: https://boringssl-review.googlesource.com/22385
Reviewed-by: Adam Langley <agl@google.com>
Commit-Queue: Adam Langley <agl@google.com>
CQ-Verified: CQ bot account: commit-bot@chromium.org <commit-bot@chromium.org>
diff --git a/LICENSE b/LICENSE
index 9eb5bb4..ff4116f 100644
--- a/LICENSE
+++ b/LICENSE
@@ -7,7 +7,8 @@
Some files from Intel are under yet another license, which is also included
underneath. Files in third_party/ have their own licenses, as described
-therein.
+therein. The MIT license, for third_party/fiat, which, unlike other third_party
+directories, is compiled into non-test libraries, is included below.
The OpenSSL toolkit stays under a dual license, i.e. both the conditions of the
OpenSSL License and the original SSLeay license apply to the toolkit. See below
@@ -191,3 +192,27 @@
# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+
+The code in third_party/fiat carries the MIT license:
+
+Copyright (c) 2015-2016 the fiat-crypto authors (see
+https://github.com/mit-plv/fiat-crypto/blob/master/AUTHORS).
+
+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.
diff --git a/third_party/fiat/LICENSE b/third_party/fiat/LICENSE
new file mode 100644
index 0000000..bd46c61
--- /dev/null
+++ b/third_party/fiat/LICENSE
@@ -0,0 +1,22 @@
+The MIT License (MIT)
+
+Copyright (c) 2015-2016 the fiat-crypto authors (see
+https://github.com/mit-plv/fiat-crypto/blob/master/AUTHORS).
+
+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.
diff --git a/third_party/fiat/METADATA b/third_party/fiat/METADATA
new file mode 100644
index 0000000..bae0285
--- /dev/null
+++ b/third_party/fiat/METADATA
@@ -0,0 +1,14 @@
+name: "fiat"
+description:
+ "Fiat-Crypto: Synthesizing Correct-by-Construction Code for Cryptographic Primitives".
+
+third_party {
+ url {
+ type: HOMEPAGE
+ value: "https://github.com/mit-plv/fiat-crypto"
+ }
+ version: "6c4d4afb26de639718fcac39094353ca7feec365"
+ last_upgrade_date { year: 2017 month: 11 day: 3 }
+
+ local_modifications: "Fiat-generated code has been integrated into existing BoringSSL code"
+}
diff --git a/third_party/fiat/README.md b/third_party/fiat/README.md
new file mode 100644
index 0000000..5512715
--- /dev/null
+++ b/third_party/fiat/README.md
@@ -0,0 +1,5 @@
+# Fiat
+
+Some of the code in this directory is generated by
+[Fiat](https://github.com/mit-plv/fiat-crypto) and thus these files are
+licensed under the MIT license. (See LICENSE file.)
diff --git a/third_party/fiat/curve25519.c b/third_party/fiat/curve25519.c
index b135481..d54aa83 100644
--- a/third_party/fiat/curve25519.c
+++ b/third_party/fiat/curve25519.c
@@ -1,21 +1,29 @@
-/* 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. */
+// The MIT License (MIT)
+//
+// Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file).
+//
+// 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.
-// This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
+// Some of this code is 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.
+// public domain but parts have been replaced with code generated by Fiat
+// (https://github.com/mit-plv/fiat-crypto), which is MIT licensed.
//
// The field functions are shared by Ed25519 and X25519 where possible.
@@ -35,8 +43,6 @@
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;
@@ -57,63 +63,36 @@
#define assert_fe(f) do { \
for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \
- assert(-1.1*(1<<(25-(_assert_fe_i&1))) < f[_assert_fe_i]); \
- assert(f[_assert_fe_i] < 1.1*(1<<(25-(_assert_fe_i&1)))); \
+ assert(f[_assert_fe_i] < 1.125*(1<<(26-(_assert_fe_i&1)))); \
} \
} while (0)
#define assert_fe_loose(f) do { \
for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \
- assert(-1.1*(1<<(26-(_assert_fe_i&1))) < f[_assert_fe_i]); \
- assert(f[_assert_fe_i] < 1.1*(1<<(26-(_assert_fe_i&1)))); \
+ assert(f[_assert_fe_i] < 3.375*(1<<(26-(_assert_fe_i&1)))); \
} \
} while (0)
-static void fe_frombytes_impl(int32_t h[10], 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;
+static void fe_frombytes_impl(uint32_t h[10], const uint8_t *s) {
+ // Ignores top bit of s.
+ uint32_t a0 = load_4(s);
+ uint32_t a1 = load_4(s+4);
+ uint32_t a2 = load_4(s+8);
+ uint32_t a3 = load_4(s+12);
+ uint32_t a4 = load_4(s+16);
+ uint32_t a5 = load_4(s+20);
+ uint32_t a6 = load_4(s+24);
+ uint32_t a7 = load_4(s+28);
+ h[0] = a0&((1<<26)-1); // 26 used, 32-26 left. 26
+ h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); // (32-26) + 19 = 6+19 = 25
+ h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); // (32-19) + 13 = 13+13 = 26
+ h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); // (32-13) + 6 = 19+ 6 = 25
+ h[4] = (a3>> 6); // (32- 6) = 26
+ h[5] = a4&((1<<25)-1); // 25
+ h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); // (32-25) + 19 = 7+19 = 26
+ h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); // (32-19) + 12 = 13+12 = 25
+ h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); // (32-12) + 6 = 20+ 6 = 26
+ h[9] = (a7>> 6)&((1<<25)-1); // 25
assert_fe(h);
}
@@ -143,7 +122,7 @@
//
// 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_impl(uint8_t *s, const int32_t h[10]) {
+static void fe_tobytes_impl(uint8_t *s, const uint32_t h[10]) {
assert_fe_loose(h);
int32_t h0 = h[0];
int32_t h1 = h[1];
@@ -234,38 +213,72 @@
// h = f
static void fe_copy(fe *h, const fe *f) {
- OPENSSL_memmove(h, f, sizeof(int32_t) * 10);
+ OPENSSL_memmove(h, f, sizeof(uint32_t) * 10);
}
static void fe_copy_lt(fe_loose *h, const fe *f) {
- OPENSSL_memmove(h, f, sizeof(int32_t) * 10);
+ OPENSSL_memmove(h, f, sizeof(uint32_t) * 10);
}
#if !defined(OPENSSL_SMALL)
static void fe_copy_ll(fe_loose *h, const fe_loose *f) {
- OPENSSL_memmove(h, f, sizeof(int32_t) * 10);
+ OPENSSL_memmove(h, f, sizeof(uint32_t) * 10);
}
#endif // !defined(OPENSSL_SMALL)
// h = 0
static void fe_0(fe *h) {
- OPENSSL_memset(h, 0, sizeof(int32_t) * 10);
+ OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
}
static void fe_loose_0(fe_loose *h) {
- OPENSSL_memset(h, 0, sizeof(int32_t) * 10);
+ OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
}
// h = 1
static void fe_1(fe *h) {
- OPENSSL_memset(h, 0, sizeof(int32_t) * 10);
+ OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
h->v[0] = 1;
}
static void fe_loose_1(fe_loose *h) {
- OPENSSL_memset(h, 0, sizeof(int32_t) * 10);
+ OPENSSL_memset(h, 0, sizeof(uint32_t) * 10);
h->v[0] = 1;
}
+static void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = in2[9];
+ { const uint32_t x39 = in2[8];
+ { const uint32_t x37 = in2[7];
+ { const uint32_t x35 = in2[6];
+ { const uint32_t x33 = in2[5];
+ { const uint32_t x31 = in2[4];
+ { const uint32_t x29 = in2[3];
+ { const uint32_t x27 = in2[2];
+ { const uint32_t x25 = in2[1];
+ { const uint32_t x23 = in2[0];
+ out[0] = (x5 + x23);
+ out[1] = (x7 + x25);
+ out[2] = (x9 + x27);
+ out[3] = (x11 + x29);
+ out[4] = (x13 + x31);
+ out[5] = (x15 + x33);
+ out[6] = (x17 + x35);
+ out[7] = (x19 + x37);
+ out[8] = (x21 + x39);
+ out[9] = (x20 + x38);
+ }}}}}}}}}}}}}}}}}}}}
+}
+
// h = f + g
// Can overlap h with f or g.
//
@@ -278,13 +291,44 @@
static void fe_add(fe_loose *h, const fe *f, const fe *g) {
assert_fe(f->v);
assert_fe(g->v);
- unsigned i;
- for (i = 0; i < 10; i++) {
- h->v[i] = f->v[i] + g->v[i];
- }
+ fe_add_impl(h->v, f->v, g->v);
assert_fe_loose(h->v);
}
+static void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = in2[9];
+ { const uint32_t x39 = in2[8];
+ { const uint32_t x37 = in2[7];
+ { const uint32_t x35 = in2[6];
+ { const uint32_t x33 = in2[5];
+ { const uint32_t x31 = in2[4];
+ { const uint32_t x29 = in2[3];
+ { const uint32_t x27 = in2[2];
+ { const uint32_t x25 = in2[1];
+ { const uint32_t x23 = in2[0];
+ out[0] = ((0x7ffffda + x5) - x23);
+ out[1] = ((0x3fffffe + x7) - x25);
+ out[2] = ((0x7fffffe + x9) - x27);
+ out[3] = ((0x3fffffe + x11) - x29);
+ out[4] = ((0x7fffffe + x13) - x31);
+ out[5] = ((0x3fffffe + x15) - x33);
+ out[6] = ((0x7fffffe + x17) - x35);
+ out[7] = ((0x3fffffe + x19) - x37);
+ out[8] = ((0x7fffffe + x21) - x39);
+ out[9] = ((0x3fffffe + x20) - x38);
+ }}}}}}}}}}}}}}}}}}}}
+}
+
// h = f - g
// Can overlap h with f or g.
//
@@ -297,305 +341,191 @@
static void fe_sub(fe_loose *h, const fe *f, const fe *g) {
assert_fe(f->v);
assert_fe(g->v);
- unsigned i;
- for (i = 0; i < 10; i++) {
- h->v[i] = f->v[i] - g->v[i];
- }
+ fe_sub_impl(h->v, f->v, g->v);
assert_fe_loose(h->v);
}
+static void fe_carry_impl(uint32_t out[10], const uint32_t in1[10]) {
+ { const uint32_t x17 = in1[9];
+ { const uint32_t x18 = in1[8];
+ { const uint32_t x16 = in1[7];
+ { const uint32_t x14 = in1[6];
+ { const uint32_t x12 = in1[5];
+ { const uint32_t x10 = in1[4];
+ { const uint32_t x8 = in1[3];
+ { const uint32_t x6 = in1[2];
+ { const uint32_t x4 = in1[1];
+ { const uint32_t x2 = in1[0];
+ { uint32_t x19 = (x2 >> 0x1a);
+ { uint32_t x20 = (x2 & 0x3ffffff);
+ { uint32_t x21 = (x19 + x4);
+ { uint32_t x22 = (x21 >> 0x19);
+ { uint32_t x23 = (x21 & 0x1ffffff);
+ { uint32_t x24 = (x22 + x6);
+ { uint32_t x25 = (x24 >> 0x1a);
+ { uint32_t x26 = (x24 & 0x3ffffff);
+ { uint32_t x27 = (x25 + x8);
+ { uint32_t x28 = (x27 >> 0x19);
+ { uint32_t x29 = (x27 & 0x1ffffff);
+ { uint32_t x30 = (x28 + x10);
+ { uint32_t x31 = (x30 >> 0x1a);
+ { uint32_t x32 = (x30 & 0x3ffffff);
+ { uint32_t x33 = (x31 + x12);
+ { uint32_t x34 = (x33 >> 0x19);
+ { uint32_t x35 = (x33 & 0x1ffffff);
+ { uint32_t x36 = (x34 + x14);
+ { uint32_t x37 = (x36 >> 0x1a);
+ { uint32_t x38 = (x36 & 0x3ffffff);
+ { uint32_t x39 = (x37 + x16);
+ { uint32_t x40 = (x39 >> 0x19);
+ { uint32_t x41 = (x39 & 0x1ffffff);
+ { uint32_t x42 = (x40 + x18);
+ { uint32_t x43 = (x42 >> 0x1a);
+ { uint32_t x44 = (x42 & 0x3ffffff);
+ { uint32_t x45 = (x43 + x17);
+ { uint32_t x46 = (x45 >> 0x19);
+ { uint32_t x47 = (x45 & 0x1ffffff);
+ { uint32_t x48 = (x20 + (0x13 * x46));
+ { uint32_t x49 = (x48 >> 0x1a);
+ { uint32_t x50 = (x48 & 0x3ffffff);
+ { uint32_t x51 = (x49 + x23);
+ { uint32_t x52 = (x51 >> 0x19);
+ { uint32_t x53 = (x51 & 0x1ffffff);
+ out[0] = x50;
+ out[1] = x53;
+ out[2] = (x52 + x26);
+ out[3] = x29;
+ out[4] = x32;
+ out[5] = x35;
+ out[6] = x38;
+ out[7] = x41;
+ out[8] = x44;
+ out[9] = x47;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+}
+
static void fe_carry(fe *h, const fe_loose* f) {
assert_fe_loose(f->v);
- int32_t h0 = f->v[0];
- int32_t h1 = f->v[1];
- int32_t h2 = f->v[2];
- int32_t h3 = f->v[3];
- int32_t h4 = f->v[4];
- int32_t h5 = f->v[5];
- int32_t h6 = f->v[6];
- int32_t h7 = f->v[7];
- int32_t h8 = f->v[8];
- int32_t h9 = f->v[9];
- 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->v[0] = h0;
- h->v[1] = h1;
- h->v[2] = h2;
- h->v[3] = h3;
- h->v[4] = h4;
- h->v[5] = h5;
- h->v[6] = h6;
- h->v[7] = h7;
- h->v[8] = h8;
- h->v[9] = h9;
+ fe_carry_impl(h->v, f->v);
assert_fe(h->v);
}
-// 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_impl(int32_t h[10], const int32_t f[10], const int32_t g[10]) {
- assert_fe_loose(f);
- assert_fe_loose(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;
- assert_fe(h);
+static void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) {
+ assert_fe_loose(in1);
+ assert_fe_loose(in2);
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = in2[9];
+ { const uint32_t x39 = in2[8];
+ { const uint32_t x37 = in2[7];
+ { const uint32_t x35 = in2[6];
+ { const uint32_t x33 = in2[5];
+ { const uint32_t x31 = in2[4];
+ { const uint32_t x29 = in2[3];
+ { const uint32_t x27 = in2[2];
+ { const uint32_t x25 = in2[1];
+ { const uint32_t x23 = in2[0];
+ { uint64_t x40 = ((uint64_t)x23 * x5);
+ { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
+ { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
+ { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
+ { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
+ { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
+ { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
+ { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
+ { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
+ { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
+ { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
+ { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
+ { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
+ { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
+ { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
+ { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
+ { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
+ { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
+ { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
+ { uint64_t x59 = (x48 + (x58 << 0x4));
+ { uint64_t x60 = (x59 + (x58 << 0x1));
+ { uint64_t x61 = (x60 + x58);
+ { uint64_t x62 = (x47 + (x57 << 0x4));
+ { uint64_t x63 = (x62 + (x57 << 0x1));
+ { uint64_t x64 = (x63 + x57);
+ { uint64_t x65 = (x46 + (x56 << 0x4));
+ { uint64_t x66 = (x65 + (x56 << 0x1));
+ { uint64_t x67 = (x66 + x56);
+ { uint64_t x68 = (x45 + (x55 << 0x4));
+ { uint64_t x69 = (x68 + (x55 << 0x1));
+ { uint64_t x70 = (x69 + x55);
+ { uint64_t x71 = (x44 + (x54 << 0x4));
+ { uint64_t x72 = (x71 + (x54 << 0x1));
+ { uint64_t x73 = (x72 + x54);
+ { uint64_t x74 = (x43 + (x53 << 0x4));
+ { uint64_t x75 = (x74 + (x53 << 0x1));
+ { uint64_t x76 = (x75 + x53);
+ { uint64_t x77 = (x42 + (x52 << 0x4));
+ { uint64_t x78 = (x77 + (x52 << 0x1));
+ { uint64_t x79 = (x78 + x52);
+ { uint64_t x80 = (x41 + (x51 << 0x4));
+ { uint64_t x81 = (x80 + (x51 << 0x1));
+ { uint64_t x82 = (x81 + x51);
+ { uint64_t x83 = (x40 + (x50 << 0x4));
+ { uint64_t x84 = (x83 + (x50 << 0x1));
+ { uint64_t x85 = (x84 + x50);
+ { uint64_t x86 = (x85 >> 0x1a);
+ { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
+ { uint64_t x88 = (x86 + x82);
+ { uint64_t x89 = (x88 >> 0x19);
+ { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
+ { uint64_t x91 = (x89 + x79);
+ { uint64_t x92 = (x91 >> 0x1a);
+ { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
+ { uint64_t x94 = (x92 + x76);
+ { uint64_t x95 = (x94 >> 0x19);
+ { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
+ { uint64_t x97 = (x95 + x73);
+ { uint64_t x98 = (x97 >> 0x1a);
+ { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
+ { uint64_t x100 = (x98 + x70);
+ { uint64_t x101 = (x100 >> 0x19);
+ { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
+ { uint64_t x103 = (x101 + x67);
+ { uint64_t x104 = (x103 >> 0x1a);
+ { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
+ { uint64_t x106 = (x104 + x64);
+ { uint64_t x107 = (x106 >> 0x19);
+ { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
+ { uint64_t x109 = (x107 + x61);
+ { uint64_t x110 = (x109 >> 0x1a);
+ { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
+ { uint64_t x112 = (x110 + x49);
+ { uint64_t x113 = (x112 >> 0x19);
+ { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
+ { uint64_t x115 = (x87 + (0x13 * x113));
+ { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
+ { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
+ { uint32_t x118 = (x116 + x90);
+ { uint32_t x119 = (x118 >> 0x19);
+ { uint32_t x120 = (x118 & 0x1ffffff);
+ out[0] = x117;
+ out[1] = x120;
+ out[2] = (x119 + x93);
+ out[3] = x96;
+ out[4] = x99;
+ out[5] = x102;
+ out[6] = x105;
+ out[7] = x108;
+ out[8] = x111;
+ out[9] = x114;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+ assert_fe(out);
}
static void fe_mul_ltt(fe_loose *h, const fe *f, const fe *g) {
@@ -622,155 +552,119 @@
fe_mul_impl(h->v, f->v, g->v);
}
-// 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_impl(int32_t h[10], const int32_t f[10]) {
- assert_fe_loose(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;
- assert_fe(h);
+static void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10]) {
+ assert_fe_loose(in1);
+ { const uint32_t x17 = in1[9];
+ { const uint32_t x18 = in1[8];
+ { const uint32_t x16 = in1[7];
+ { const uint32_t x14 = in1[6];
+ { const uint32_t x12 = in1[5];
+ { const uint32_t x10 = in1[4];
+ { const uint32_t x8 = in1[3];
+ { const uint32_t x6 = in1[2];
+ { const uint32_t x4 = in1[1];
+ { const uint32_t x2 = in1[0];
+ { uint64_t x19 = ((uint64_t)x2 * x2);
+ { uint64_t x20 = ((uint64_t)(0x2 * x2) * x4);
+ { uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6)));
+ { uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8)));
+ { uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10));
+ { uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12)));
+ { uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12)));
+ { uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16)));
+ { uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12))))));
+ { uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17)));
+ { uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17)))));
+ { uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17)));
+ { uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17))))));
+ { uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17)));
+ { uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17)));
+ { uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17)));
+ { uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17));
+ { uint64_t x36 = ((uint64_t)(0x2 * x18) * x17);
+ { uint64_t x37 = ((uint64_t)(0x2 * x17) * x17);
+ { uint64_t x38 = (x27 + (x37 << 0x4));
+ { uint64_t x39 = (x38 + (x37 << 0x1));
+ { uint64_t x40 = (x39 + x37);
+ { uint64_t x41 = (x26 + (x36 << 0x4));
+ { uint64_t x42 = (x41 + (x36 << 0x1));
+ { uint64_t x43 = (x42 + x36);
+ { uint64_t x44 = (x25 + (x35 << 0x4));
+ { uint64_t x45 = (x44 + (x35 << 0x1));
+ { uint64_t x46 = (x45 + x35);
+ { uint64_t x47 = (x24 + (x34 << 0x4));
+ { uint64_t x48 = (x47 + (x34 << 0x1));
+ { uint64_t x49 = (x48 + x34);
+ { uint64_t x50 = (x23 + (x33 << 0x4));
+ { uint64_t x51 = (x50 + (x33 << 0x1));
+ { uint64_t x52 = (x51 + x33);
+ { uint64_t x53 = (x22 + (x32 << 0x4));
+ { uint64_t x54 = (x53 + (x32 << 0x1));
+ { uint64_t x55 = (x54 + x32);
+ { uint64_t x56 = (x21 + (x31 << 0x4));
+ { uint64_t x57 = (x56 + (x31 << 0x1));
+ { uint64_t x58 = (x57 + x31);
+ { uint64_t x59 = (x20 + (x30 << 0x4));
+ { uint64_t x60 = (x59 + (x30 << 0x1));
+ { uint64_t x61 = (x60 + x30);
+ { uint64_t x62 = (x19 + (x29 << 0x4));
+ { uint64_t x63 = (x62 + (x29 << 0x1));
+ { uint64_t x64 = (x63 + x29);
+ { uint64_t x65 = (x64 >> 0x1a);
+ { uint32_t x66 = ((uint32_t)x64 & 0x3ffffff);
+ { uint64_t x67 = (x65 + x61);
+ { uint64_t x68 = (x67 >> 0x19);
+ { uint32_t x69 = ((uint32_t)x67 & 0x1ffffff);
+ { uint64_t x70 = (x68 + x58);
+ { uint64_t x71 = (x70 >> 0x1a);
+ { uint32_t x72 = ((uint32_t)x70 & 0x3ffffff);
+ { uint64_t x73 = (x71 + x55);
+ { uint64_t x74 = (x73 >> 0x19);
+ { uint32_t x75 = ((uint32_t)x73 & 0x1ffffff);
+ { uint64_t x76 = (x74 + x52);
+ { uint64_t x77 = (x76 >> 0x1a);
+ { uint32_t x78 = ((uint32_t)x76 & 0x3ffffff);
+ { uint64_t x79 = (x77 + x49);
+ { uint64_t x80 = (x79 >> 0x19);
+ { uint32_t x81 = ((uint32_t)x79 & 0x1ffffff);
+ { uint64_t x82 = (x80 + x46);
+ { uint64_t x83 = (x82 >> 0x1a);
+ { uint32_t x84 = ((uint32_t)x82 & 0x3ffffff);
+ { uint64_t x85 = (x83 + x43);
+ { uint64_t x86 = (x85 >> 0x19);
+ { uint32_t x87 = ((uint32_t)x85 & 0x1ffffff);
+ { uint64_t x88 = (x86 + x40);
+ { uint64_t x89 = (x88 >> 0x1a);
+ { uint32_t x90 = ((uint32_t)x88 & 0x3ffffff);
+ { uint64_t x91 = (x89 + x28);
+ { uint64_t x92 = (x91 >> 0x19);
+ { uint32_t x93 = ((uint32_t)x91 & 0x1ffffff);
+ { uint64_t x94 = (x66 + (0x13 * x92));
+ { uint32_t x95 = (uint32_t) (x94 >> 0x1a);
+ { uint32_t x96 = ((uint32_t)x94 & 0x3ffffff);
+ { uint32_t x97 = (x95 + x69);
+ { uint32_t x98 = (x97 >> 0x19);
+ { uint32_t x99 = (x97 & 0x1ffffff);
+ out[0] = x96;
+ out[1] = x99;
+ out[2] = (x98 + x72);
+ out[3] = x75;
+ out[4] = x78;
+ out[5] = x81;
+ out[6] = x84;
+ out[7] = x87;
+ out[8] = x90;
+ out[9] = x93;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+ assert_fe(out);
}
static void fe_sq_tl(fe *h, const fe_loose *f) {
- fe_sq_impl(h->v, f->v);
+ fe_sqr_impl(h->v, f->v);
}
static void fe_sq_tt(fe *h, const fe *f) {
- fe_sq_impl(h->v, f->v);
+ fe_sqr_impl(h->v, f->v);
}
static void fe_loose_invert(fe *out, const fe_loose *z) {
@@ -837,6 +731,40 @@
fe_loose_invert(out, &l);
}
+static void fe_neg_impl(uint32_t out[10], const uint32_t in2[10]) {
+ { const uint32_t x20 = 0;
+ { const uint32_t x21 = 0;
+ { const uint32_t x19 = 0;
+ { const uint32_t x17 = 0;
+ { const uint32_t x15 = 0;
+ { const uint32_t x13 = 0;
+ { const uint32_t x11 = 0;
+ { const uint32_t x9 = 0;
+ { const uint32_t x7 = 0;
+ { const uint32_t x5 = 0;
+ { const uint32_t x38 = in2[9];
+ { const uint32_t x39 = in2[8];
+ { const uint32_t x37 = in2[7];
+ { const uint32_t x35 = in2[6];
+ { const uint32_t x33 = in2[5];
+ { const uint32_t x31 = in2[4];
+ { const uint32_t x29 = in2[3];
+ { const uint32_t x27 = in2[2];
+ { const uint32_t x25 = in2[1];
+ { const uint32_t x23 = in2[0];
+ out[0] = ((0x7ffffda + x5) - x23);
+ out[1] = ((0x3fffffe + x7) - x25);
+ out[2] = ((0x7fffffe + x9) - x27);
+ out[3] = ((0x3fffffe + x11) - x29);
+ out[4] = ((0x7fffffe + x13) - x31);
+ out[5] = ((0x3fffffe + x15) - x33);
+ out[6] = ((0x7fffffe + x17) - x35);
+ out[7] = ((0x3fffffe + x19) - x37);
+ out[8] = ((0x7fffffe + x21) - x39);
+ out[9] = ((0x3fffffe + x20) - x38);
+ }}}}}}}}}}}}}}}}}}}}
+}
+
// h = -f
//
// Preconditions:
@@ -846,10 +774,7 @@
// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
static void fe_neg(fe_loose *h, const fe *f) {
assert_fe(f->v);
- unsigned i;
- for (i = 0; i < 10; i++) {
- h->v[i] = -f->v[i];
- }
+ fe_neg_impl(h->v, f->v);
assert_fe_loose(h->v);
}
@@ -861,7 +786,7 @@
b = 0-b;
unsigned i;
for (i = 0; i < 10; i++) {
- int32_t x = f->v[i] ^ g->v[i];
+ uint32_t x = f->v[i] ^ g->v[i];
x &= b;
f->v[i] ^= x;
}
@@ -891,158 +816,122 @@
return s[0] & 1;
}
-// h = 2 * f * f
-// 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.
-//
-// See fe_mul.c for discussion of implementation strategy.
-static void fe_sq2_impl(int32_t h[10], const int32_t f[10]) {
- assert_fe_loose(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;
-
- h0 += h0;
- h1 += h1;
- h2 += h2;
- h3 += h3;
- h4 += h4;
- h5 += h5;
- h6 += h6;
- h7 += h7;
- h8 += h8;
- h9 += h9;
-
- 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;
- assert_fe(h);
+// NOTE: based on fiat-crypto fe_mul, edited for in2=2*in1
+static void fe_sq2_impl(uint32_t out[10], const uint32_t in1[10]) {
+ assert_fe_loose(in1);
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = 2*in1[9];
+ { const uint32_t x39 = 2*in1[8];
+ { const uint32_t x37 = 2*in1[7];
+ { const uint32_t x35 = 2*in1[6];
+ { const uint32_t x33 = 2*in1[5];
+ { const uint32_t x31 = 2*in1[4];
+ { const uint32_t x29 = 2*in1[3];
+ { const uint32_t x27 = 2*in1[2];
+ { const uint32_t x25 = 2*in1[1];
+ { const uint32_t x23 = 2*in1[0];
+ { uint64_t x40 = ((uint64_t)x23 * x5);
+ { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
+ { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
+ { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
+ { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
+ { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
+ { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
+ { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
+ { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
+ { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
+ { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
+ { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
+ { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
+ { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
+ { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
+ { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
+ { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
+ { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
+ { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
+ { uint64_t x59 = (x48 + (x58 << 0x4));
+ { uint64_t x60 = (x59 + (x58 << 0x1));
+ { uint64_t x61 = (x60 + x58);
+ { uint64_t x62 = (x47 + (x57 << 0x4));
+ { uint64_t x63 = (x62 + (x57 << 0x1));
+ { uint64_t x64 = (x63 + x57);
+ { uint64_t x65 = (x46 + (x56 << 0x4));
+ { uint64_t x66 = (x65 + (x56 << 0x1));
+ { uint64_t x67 = (x66 + x56);
+ { uint64_t x68 = (x45 + (x55 << 0x4));
+ { uint64_t x69 = (x68 + (x55 << 0x1));
+ { uint64_t x70 = (x69 + x55);
+ { uint64_t x71 = (x44 + (x54 << 0x4));
+ { uint64_t x72 = (x71 + (x54 << 0x1));
+ { uint64_t x73 = (x72 + x54);
+ { uint64_t x74 = (x43 + (x53 << 0x4));
+ { uint64_t x75 = (x74 + (x53 << 0x1));
+ { uint64_t x76 = (x75 + x53);
+ { uint64_t x77 = (x42 + (x52 << 0x4));
+ { uint64_t x78 = (x77 + (x52 << 0x1));
+ { uint64_t x79 = (x78 + x52);
+ { uint64_t x80 = (x41 + (x51 << 0x4));
+ { uint64_t x81 = (x80 + (x51 << 0x1));
+ { uint64_t x82 = (x81 + x51);
+ { uint64_t x83 = (x40 + (x50 << 0x4));
+ { uint64_t x84 = (x83 + (x50 << 0x1));
+ { uint64_t x85 = (x84 + x50);
+ { uint64_t x86 = (x85 >> 0x1a);
+ { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
+ { uint64_t x88 = (x86 + x82);
+ { uint64_t x89 = (x88 >> 0x19);
+ { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
+ { uint64_t x91 = (x89 + x79);
+ { uint64_t x92 = (x91 >> 0x1a);
+ { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
+ { uint64_t x94 = (x92 + x76);
+ { uint64_t x95 = (x94 >> 0x19);
+ { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
+ { uint64_t x97 = (x95 + x73);
+ { uint64_t x98 = (x97 >> 0x1a);
+ { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
+ { uint64_t x100 = (x98 + x70);
+ { uint64_t x101 = (x100 >> 0x19);
+ { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
+ { uint64_t x103 = (x101 + x67);
+ { uint64_t x104 = (x103 >> 0x1a);
+ { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
+ { uint64_t x106 = (x104 + x64);
+ { uint64_t x107 = (x106 >> 0x19);
+ { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
+ { uint64_t x109 = (x107 + x61);
+ { uint64_t x110 = (x109 >> 0x1a);
+ { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
+ { uint64_t x112 = (x110 + x49);
+ { uint64_t x113 = (x112 >> 0x19);
+ { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
+ { uint64_t x115 = (x87 + (0x13 * x113));
+ { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
+ { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
+ { uint32_t x118 = (x116 + x90);
+ { uint32_t x119 = (x118 >> 0x19);
+ { uint32_t x120 = (x118 & 0x1ffffff);
+ out[0] = x117;
+ out[1] = x120;
+ out[2] = (x119 + x93);
+ out[3] = x96;
+ out[4] = x99;
+ out[5] = x102;
+ out[6] = x105;
+ out[7] = x108;
+ out[8] = x111;
+ out[9] = x114;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+ assert_fe(out);
}
static void fe_sq2_tt(fe *h, const fe *f) {
@@ -1130,11 +1019,11 @@
s[31] ^= fe_isnegative(&x) << 7;
}
-static const fe d = {{-10913610, 13857413, -15372611, 6949391, 114729,
- -8787816, -6275908, -3247719, -18696448, -12055116}};
+static const fe d = {{56195235, 13857412, 51736253, 6949390, 114729,
+ 24766616, 60832955, 30306712, 48412415, 21499315}};
-static const fe sqrtm1 = {{-32595792, -7943725, 9377950, 3500415, 12389472,
- -272473, -25146209, -2005654, 326686, 11406482}};
+static const fe sqrtm1 = {{34513072, 25610706, 9377949, 3500415, 12389472,
+ 33281959, 41962654, 31548777, 326685, 11406482}};
int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) {
fe u;
@@ -1215,8 +1104,8 @@
fe_copy(&r->Z, &p->Z);
}
-static const fe d2 = {{-21827239, -5839606, -30745221, 13898782, 229458,
- 15978800, -12551817, -6495438, 29715968, 9444199}};
+static const fe d2 = {{45281625, 27714825, 36363642, 13898781, 229458,
+ 15978800, 54557047, 27058993, 29715967, 9444199}};
// r = p
void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
@@ -1515,2114 +1404,2114 @@
static const ge_precomp k25519Precomp[32][8] = {
{
{
- {{25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
- 27544626, -11754271, -6079156, 2047605}},
- {{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
- 5043384, 19500929, -15469378}},
- {{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
- 29287919, 11864899, -24514362, -4438546}},
+ {{25967493, 19198397, 29566455, 3660896, 54414519, 4014786,
+ 27544626, 21800161, 61029707, 2047604}},
+ {{54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692,
+ 5043384, 19500929, 18085054}},
+ {{58370664, 4489569, 9688441, 18769238, 10184608, 21191052,
+ 29287918, 11864899, 42594502, 29115885}},
},
{
- {{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
- -11717903, -3814571, -358445, -10211303}},
- {{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
- -15616551, 11189268, -26829678, -5319081}},
- {{26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
- -3128826, -9541118, -15472047, -4166697}},
+ {{54292951, 20578084, 45527620, 11784319, 41753206, 30803714,
+ 55390960, 29739860, 66750418, 23343128}},
+ {{45405608, 6903824, 27185491, 6451973, 37531140, 24000426,
+ 51492312, 11189267, 40279186, 28235350}},
+ {{26966623, 11152617, 32442495, 15396054, 14353839, 20802097,
+ 63980037, 24013313, 51636816, 29387734}},
},
{
- {{15636291, -9688557, 24204773, -7912398, 616977, -16685262,
- 27787600, -14772189, 28944400, -1550024}},
- {{16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
- 16354577, -11775962, 7689662, 11199574}},
- {{30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
- 7512774, 10017326, -17749093, -9920357}},
+ {{15636272, 23865875, 24204772, 25642034, 616976, 16869170,
+ 27787599, 18782243, 28944399, 32004408}},
+ {{16568933, 4717097, 55552716, 32452109, 15682895, 21747389,
+ 16354576, 21778470, 7689661, 11199574}},
+ {{30464137, 27578307, 55329429, 17883566, 23220364, 15915852,
+ 7512774, 10017326, 49359771, 23634074}},
},
{
- {{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
- -28926210, 15006023, 3284568, -6276540}},
- {{23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
+ {{50071967, 13921891, 10945806, 27521001, 27105051, 17470053,
+ 38182653, 15006022, 3284568, 27277892}},
+ {{23599295, 25248385, 55915199, 25867015, 13236773, 10506355,
7464579, 9656445, 13059162, 10374397}},
- {{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
- -3839045, -641708, -101325}},
+ {{7798537, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
+ 29715387, 66467155, 33453106}},
},
{
- {{10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
- 32867885, 14515107, -15438304, 10819380}},
- {{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
- 12483688, -12668491, 5581306}},
- {{19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
- 28542350, 13850243, -23678021, -15815942}},
+ {{10861363, 11473154, 27284546, 1981175, 37044515, 12577860,
+ 32867885, 14515107, 51670560, 10819379}},
+ {{4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196,
+ 12483687, 54440373, 5581305}},
+ {{19563141, 16186464, 37722007, 4097518, 10237984, 29206317,
+ 28542349, 13850243, 43430843, 17738489}},
},
{
- {{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
- -19188627, -15224819, -9818940, -12085777}},
- {{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
- -15689887, 1762328, 14866737}},
- {{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
- -28236412, 3959421, 27914454, 4383652}},
+ {{51736881, 20691677, 32573249, 4720197, 40672342, 5875510,
+ 47920237, 18329612, 57289923, 21468654}},
+ {{58559652, 109982, 15149363, 2178705, 22900618, 4543417, 3044240,
+ 17864545, 1762327, 14866737}},
+ {{48909169, 17603008, 56635573, 1707277, 49922944, 3916100,
+ 38872452, 3959420, 27914454, 4383652}},
},
{
- {{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
- 5230134, -23952439, -15175766}},
- {{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
+ {{5153727, 9909285, 1723747, 30776558, 30523604, 5516873, 19480852,
+ 5230134, 43156425, 18378665}},
+ {{36839857, 30090922, 7665485, 10083793, 28475525, 1649722,
20654025, 16520125, 30598449, 7715701}},
- {{28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
- -31400660, 1370708, 29794553, -1409300}},
+ {{28881826, 14381568, 9657904, 3680757, 46927229, 7843315,
+ 35708204, 1370707, 29794553, 32145132}},
},
{
- {{14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
- 30290735, 10876454, -33154098, 2381726}},
- {{-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
- -6236617, 3696005, -32300832, 15351955}},
- {{27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
- -32961401, -2970515, 29551813, 10109425}},
+ {{14499471, 30824833, 33917750, 29299779, 28494861, 14271267,
+ 30290735, 10876454, 33954766, 2381725}},
+ {{59913433, 30899068, 52378708, 462250, 39384538, 3941371,
+ 60872247, 3696004, 34808032, 15351954}},
+ {{27431194, 8222322, 16448760, 29646437, 48401861, 11938354,
+ 34147463, 30583916, 29551812, 10109425}},
},
},
{
{
- {{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
- -2378284, -1627556, 10092783, -4764171}},
- {{27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
- -32508754, 12005538, -17810127, 12803510}},
- {{17228999, -15661624, -1233527, 300140, -1224870, -11714777,
- 30364213, -9038194, 18016357, 4397660}},
+ {{53451805, 20399000, 35825113, 11777097, 21447386, 6519384,
+ 64730580, 31926875, 10092782, 28790261}},
+ {{27939166, 14210322, 4677035, 16277044, 44144402, 21156292,
+ 34600109, 12005537, 49298737, 12803509}},
+ {{17228999, 17892808, 65875336, 300139, 65883994, 21839654,
+ 30364212, 24516238, 18016356, 4397660}},
},
{
- {{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
- -26619106, 14544525, -17477504, 982639}},
- {{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
- -4120128, -21047696, 9934963}},
- {{5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
- -14747930, 4559895, -30123922, -10897950}},
+ {{56150021, 25864224, 4776340, 18600194, 27850027, 17952220,
+ 40489757, 14544524, 49631360, 982638}},
+ {{29253598, 15796703, 64244882, 23645547, 10057022, 3163536, 7332899,
+ 29434304, 46061167, 9934962}},
+ {{5793284, 16271923, 42977250, 23438027, 29188559, 1206517,
+ 52360934, 4559894, 36984942, 22656481}},
},
{
- {{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
- 24191034, 4541697, -13338309, 5500568}},
- {{12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
- -17430592, 12264343, 10874051, 13524335}},
- {{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
- 5080568, -22528059, 5376628}},
+ {{39464912, 22061425, 16282656, 22517939, 28414020, 18542168,
+ 24191033, 4541697, 53770555, 5500567}},
+ {{12650548, 32057319, 9052870, 11355358, 49428827, 25154267,
+ 49678271, 12264342, 10874051, 13524335}},
+ {{25556948, 30508442, 714650, 2510400, 23394682, 23139102, 33119037,
+ 5080568, 44580805, 5376627}},
},
{
- {{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
- -22321305, -9447443, 4535768, 1569007}},
- {{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
- -30494562, 3044290, 31848280, 12543772}},
- {{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
- -27377195, -2062731, 7718482, 14474653}},
+ {{41020600, 29543379, 50095164, 30016803, 60382070, 1920896,
+ 44787559, 24106988, 4535767, 1569007}},
+ {{64853442, 14606629, 45416424, 25514613, 28430648, 8775819,
+ 36614302, 3044289, 31848280, 12543772}},
+ {{45080285, 2943892, 35251351, 6777305, 13784462, 29262229,
+ 39731668, 31491700, 7718481, 14474653}},
},
{
- {{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
- -7236665, 24316168, -5253567}},
- {{13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
- 33040651, -13424532, -20729456, 8321686}},
- {{21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
- 23845965, -11874838, -9984458, 608372}},
+ {{2385296, 2454213, 44477544, 46602, 62670929, 17874016, 656964,
+ 26317767, 24316167, 28300865}},
+ {{13741529, 10911568, 33875447, 24950694, 46931033, 32521134,
+ 33040650, 20129900, 46379407, 8321685}},
+ {{21060490, 31341688, 15712756, 29218333, 1639039, 10656336,
+ 23845965, 21679594, 57124405, 608371}},
},
{
- {{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
- 1123968, -6780577, 27229399, 23887}},
- {{-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
- 12797024, -6440308, -1633405, 16678954}},
- {{-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
- -1508144, -4795045, -17169265, 4904953}},
+ {{53436132, 18466845, 56219170, 25997372, 61071954, 11305546,
+ 1123968, 26773855, 27229398, 23887}},
+ {{43864724, 33260226, 55364135, 14712570, 37643165, 31524814,
+ 12797023, 27114124, 65475458, 16678953}},
+ {{37608244, 4770661, 51054477, 14001337, 7830047, 9564805,
+ 65600720, 28759386, 49939598, 4904952}},
},
{
- {{24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
- 5169211, 16191880, 2128236, -4326833}},
- {{-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
- -29806336, 916033, -6882542, -2986532}},
- {{-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
+ {{24059538, 14617003, 19037157, 18514524, 19766092, 18648003,
+ 5169210, 16191880, 2128236, 29227599}},
+ {{50127693, 4124965, 58568254, 22900634, 30336521, 19449185,
+ 37302527, 916032, 60226322, 30567899}},
+ {{44477957, 12419371, 59974635, 26081060, 50629959, 16739174,
285431, 2763829, 15736322, 4143876}},
},
{
- {{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
- -14594663, 23527084, -16458268}},
- {{33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
- -32625340, 4087881, -15188911, -14416214}},
- {{1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
- 4357868, -4774191, -16323038}},
+ {{2379333, 11839345, 62998462, 27565766, 11274297, 794957, 212801,
+ 18959769, 23527083, 17096164}},
+ {{33431108, 22423954, 49269897, 17927531, 8909498, 8376530,
+ 34483524, 4087880, 51919953, 19138217}},
+ {{1767664, 7197987, 53903638, 31531796, 54017513, 448825, 5799055,
+ 4357868, 62334673, 17231393}},
},
},
{
{
- {{6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
- 23365147, -3949732, 7390890, 2759800}},
- {{4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
- -4264057, 1244380, -12919645}},
- {{-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
+ {{6721966, 13833823, 43585476, 32003117, 26354292, 21691111,
+ 23365146, 29604700, 7390889, 2759800}},
+ {{4409022, 2052381, 23373853, 10530217, 7676779, 20668478, 21302352,
+ 29290375, 1244379, 20634787}},
+ {{62687625, 7169618, 4982368, 30596842, 30256824, 30776892, 14086412,
9208236, 15886429, 16489664}},
},
{
- {{1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
- -13693198, 398369, -30606455, -712933}},
- {{-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
- 13348553, 12076947, -30836462, 5113182}},
- {{-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
- -30341101, -7336386, 13847711, 5387222}},
+ {{1996056, 10375649, 14346367, 13311202, 60234729, 17116020,
+ 53415665, 398368, 36502409, 32841498}},
+ {{41801399, 9795879, 64331450, 14878808, 33577029, 14780362,
+ 13348553, 12076947, 36272402, 5113181}},
+ {{49338080, 11797795, 31950843, 13929123, 41220562, 12288343,
+ 36767763, 26218045, 13847710, 5387222}},
},
{
- {{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
- 8763061, 3617786, -19600662, 10370991}},
- {{20246567, -14369378, 22358229, -543712, 18507283, -10413996,
- 14554437, -8746092, 32232924, 16763880}},
- {{9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
- 11094161, 15689506, 3140038, -16510092}},
+ {{48526701, 30138214, 17824842, 31213466, 22744342, 23111821,
+ 8763060, 3617786, 47508202, 10370990}},
+ {{20246567, 19185054, 22358228, 33010720, 18507282, 23140436,
+ 14554436, 24808340, 32232923, 16763880}},
+ {{9648486, 10094563, 26416693, 14745928, 36734546, 27081810,
+ 11094160, 15689506, 3140038, 17044340}},
},
{
- {{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
- -27224800, 9448613, -28774454, 366295}},
- {{19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
+ {{50948792, 5472694, 31895588, 4744994, 8823515, 10365685,
+ 39884064, 9448612, 38334410, 366294}},
+ {{19153450, 11523972, 56012374, 27051289, 42461232, 5420646,
28344573, 8041113, 719605, 11671788}},
- {{8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
- -15266516, 27000813, -10195553}},
+ {{8678006, 2694440, 60300850, 2517371, 4964326, 11152271, 51675948,
+ 18287915, 27000812, 23358879}},
},
{
- {{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
- 5336097, 6750977, -14521026}},
- {{11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
- 1695823, -8819122, 8169720, 16220347}},
- {{-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
- -11144307, -2627664, -5990708, -14166033}},
+ {{51950941, 7134311, 8639287, 30739555, 59873175, 10421741, 564065,
+ 5336097, 6750977, 19033406}},
+ {{11836410, 29574944, 26297893, 16080799, 23455045, 15735944,
+ 1695823, 24735310, 8169719, 16220347}},
+ {{48993007, 8653646, 17578566, 27461813, 59083086, 17541668,
+ 55964556, 30926767, 61118155, 19388398}},
},
{
- {{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
- 27884329, 2847284, 2655861, 1738395}},
- {{-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
- 21651608, -3239336, -19087449, -11005278}},
+ {{43800366, 22586119, 15213227, 23473218, 36255258, 22504427,
+ 27884328, 2847284, 2655861, 1738395}},
+ {{39571412, 19301410, 41772562, 25551651, 57738101, 8129820,
+ 21651608, 30315096, 48021414, 22549153}},
{{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
5821408, 10478196, 8544890}},
},
{
- {{32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
- 19270449, 12217473, 17789017, -3395995}},
- {{-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
- 15479401, -3853233, 30460520, 1052596}},
- {{-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
- 27491595, -4612359, 3179268, -9478891}},
+ {{32173102, 17425121, 24896206, 3921497, 22579056, 30143578,
+ 19270448, 12217473, 17789017, 30158437}},
+ {{36555903, 31326030, 51530034, 23407230, 13243888, 517024,
+ 15479401, 29701199, 30460519, 1052596}},
+ {{55493970, 13323617, 32618793, 8175907, 51878691, 12596686,
+ 27491595, 28942073, 3179267, 24075541}},
},
{
- {{31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
- -14756777, -16411740, 19072640, -9511060}},
- {{11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
- 5977896, -5215017, 473099, 5040608}},
- {{-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
- 28326862, 1721092, -19558642, -3131606}},
+ {{31947050, 19187781, 62468280, 18214510, 51982886, 27514722,
+ 52352086, 17142691, 19072639, 24043372}},
+ {{11685058, 11822410, 3158003, 19601838, 33402193, 29389366,
+ 5977895, 28339415, 473098, 5040608}},
+ {{46817982, 8198641, 39698732, 11602122, 1290375, 30754672,
+ 28326861, 1721092, 47550222, 30422825}},
},
},
{
{
- {{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
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21382910, 11042292, 25838796, 4642684}},
- {{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
- 30468147, -13900640, 18423289, 4177476}},
+ {{46678630, 14955536, 42982517, 8124618, 61739576, 27563961,
+ 30468146, 19653792, 18423288, 4177476}},
},
},
};
@@ -3811,68 +3700,68 @@
static const ge_precomp Bi[8] = {
{
- {{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
- -11754271, -6079156, 2047605}},
- {{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
- 5043384, 19500929, -15469378}},
- {{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
- 11864899, -24514362, -4438546}},
+ {{25967493, 19198397, 29566455, 3660896, 54414519, 4014786, 27544626,
+ 21800161, 61029707, 2047604}},
+ {{54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692,
+ 5043384, 19500929, 18085054}},
+ {{58370664, 4489569, 9688441, 18769238, 10184608, 21191052, 29287918,
+ 11864899, 42594502, 29115885}},
},
{
- {{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
- -14772189, 28944400, -1550024}},
- {{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
- -11775962, 7689662, 11199574}},
- {{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
- 10017326, -17749093, -9920357}},
+ {{15636272, 23865875, 24204772, 25642034, 616976, 16869170, 27787599,
+ 18782243, 28944399, 32004408}},
+ {{16568933, 4717097, 55552716, 32452109, 15682895, 21747389, 16354576,
+ 21778470, 7689661, 11199574}},
+ {{30464137, 27578307, 55329429, 17883566, 23220364, 15915852, 7512774,
+ 10017326, 49359771, 23634074}},
},
{
- {{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
- 14515107, -15438304, 10819380}},
- {{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
- 12483688, -12668491, 5581306}},
- {{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
- 13850243, -23678021, -15815942}},
+ {{10861363, 11473154, 27284546, 1981175, 37044515, 12577860, 32867885,
+ 14515107, 51670560, 10819379}},
+ {{4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196,
+ 12483687, 54440373, 5581305}},
+ {{19563141, 16186464, 37722007, 4097518, 10237984, 29206317, 28542349,
+ 13850243, 43430843, 17738489}},
},
{
- {{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
- 5230134, -23952439, -15175766}},
- {{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
+ {{5153727, 9909285, 1723747, 30776558, 30523604, 5516873, 19480852,
+ 5230134, 43156425, 18378665}},
+ {{36839857, 30090922, 7665485, 10083793, 28475525, 1649722, 20654025,
16520125, 30598449, 7715701}},
- {{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
- 1370708, 29794553, -1409300}},
+ {{28881826, 14381568, 9657904, 3680757, 46927229, 7843315, 35708204,
+ 1370707, 29794553, 32145132}},
},
{
- {{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
- -1361450, -13062696, 13821877}},
- {{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
- -7212327, 18853322, -14220951}},
- {{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
- -10431137, 2207753, -3209784}},
+ {{44589871, 26862249, 14201701, 24808930, 43598457, 8844725, 18474211,
+ 32192982, 54046167, 13821876}},
+ {{60653668, 25714560, 3374701, 28813570, 40010246, 22982724, 31655027,
+ 26342105, 18853321, 19333481}},
+ {{4566811, 20590564, 38133974, 21313742, 59506191, 30723862, 58594505,
+ 23123294, 2207752, 30344648}},
},
{
- {{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
- -663000, -31111463, -16132436}},
- {{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
+ {{41954014, 29368610, 29681143, 7868801, 60254203, 24130566, 54671499,
+ 32891431, 35997400, 17421995}},
+ {{25576264, 30851218, 7349803, 21739588, 16472781, 9300885, 3844789,
15725684, 171356, 6466918}},
- {{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
- -14088058, -30714912, 16193877}},
+ {{23103977, 13316479, 9739013, 17404951, 817874, 18515490, 8965338,
+ 19466374, 36393951, 16193876}},
},
{
- {{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
- 4729455, -18074513, 9256800}},
- {{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
- 9761698, -19827198, 630305}},
- {{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
- -15960994, -2449256, -14291300}},
+ {{33587053, 3180712, 64714734, 14003686, 50205390, 17283591, 17238397,
+ 4729455, 49034351, 9256799}},
+ {{41926547, 29380300, 32336397, 5036987, 45872047, 11360616, 22616405,
+ 9761698, 47281666, 630304}},
+ {{53388152, 2639452, 42871404, 26147950, 9494426, 27780403, 60554312,
+ 17593437, 64659607, 19263131}},
},
{
- {{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
- 15033784, 25105118, -7894876}},
- {{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
- 1573892, -2625887, 2198790, -15804619}},
- {{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
- -16236442, -32461234, -12290683}},
+ {{63957664, 28508356, 9282713, 6866145, 35201802, 32691408, 48168288,
+ 15033783, 25105118, 25659556}},
+ {{42782475, 15950225, 35307649, 18961608, 55446126, 28463506,
+ 1573891, 30928545, 2198789, 17749813}},
+ {{64009494, 10324966, 64867251, 7453182, 61661885, 30818928, 53296841,
+ 17317989, 34647629, 21263748}},
},
};
@@ -4897,76 +4786,134 @@
b = 0-b;
unsigned i;
for (i = 0; i < 10; i++) {
- int32_t x = f->v[i] ^ g->v[i];
+ uint32_t x = f->v[i] ^ g->v[i];
x &= b;
f->v[i] ^= x;
g->v[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.
+// NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0..
+static void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10]) {
+ assert_fe_loose(in1);
+ { const uint32_t x20 = in1[9];
+ { const uint32_t x21 = in1[8];
+ { const uint32_t x19 = in1[7];
+ { const uint32_t x17 = in1[6];
+ { const uint32_t x15 = in1[5];
+ { const uint32_t x13 = in1[4];
+ { const uint32_t x11 = in1[3];
+ { const uint32_t x9 = in1[2];
+ { const uint32_t x7 = in1[1];
+ { const uint32_t x5 = in1[0];
+ { const uint32_t x38 = 0;
+ { const uint32_t x39 = 0;
+ { const uint32_t x37 = 0;
+ { const uint32_t x35 = 0;
+ { const uint32_t x33 = 0;
+ { const uint32_t x31 = 0;
+ { const uint32_t x29 = 0;
+ { const uint32_t x27 = 0;
+ { const uint32_t x25 = 0;
+ { const uint32_t x23 = 121666;
+ { uint64_t x40 = ((uint64_t)x23 * x5);
+ { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
+ { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
+ { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
+ { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
+ { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
+ { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
+ { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
+ { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
+ { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
+ { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
+ { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
+ { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
+ { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
+ { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
+ { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
+ { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
+ { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
+ { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
+ { uint64_t x59 = (x48 + (x58 << 0x4));
+ { uint64_t x60 = (x59 + (x58 << 0x1));
+ { uint64_t x61 = (x60 + x58);
+ { uint64_t x62 = (x47 + (x57 << 0x4));
+ { uint64_t x63 = (x62 + (x57 << 0x1));
+ { uint64_t x64 = (x63 + x57);
+ { uint64_t x65 = (x46 + (x56 << 0x4));
+ { uint64_t x66 = (x65 + (x56 << 0x1));
+ { uint64_t x67 = (x66 + x56);
+ { uint64_t x68 = (x45 + (x55 << 0x4));
+ { uint64_t x69 = (x68 + (x55 << 0x1));
+ { uint64_t x70 = (x69 + x55);
+ { uint64_t x71 = (x44 + (x54 << 0x4));
+ { uint64_t x72 = (x71 + (x54 << 0x1));
+ { uint64_t x73 = (x72 + x54);
+ { uint64_t x74 = (x43 + (x53 << 0x4));
+ { uint64_t x75 = (x74 + (x53 << 0x1));
+ { uint64_t x76 = (x75 + x53);
+ { uint64_t x77 = (x42 + (x52 << 0x4));
+ { uint64_t x78 = (x77 + (x52 << 0x1));
+ { uint64_t x79 = (x78 + x52);
+ { uint64_t x80 = (x41 + (x51 << 0x4));
+ { uint64_t x81 = (x80 + (x51 << 0x1));
+ { uint64_t x82 = (x81 + x51);
+ { uint64_t x83 = (x40 + (x50 << 0x4));
+ { uint64_t x84 = (x83 + (x50 << 0x1));
+ { uint64_t x85 = (x84 + x50);
+ { uint64_t x86 = (x85 >> 0x1a);
+ { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
+ { uint64_t x88 = (x86 + x82);
+ { uint64_t x89 = (x88 >> 0x19);
+ { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
+ { uint64_t x91 = (x89 + x79);
+ { uint64_t x92 = (x91 >> 0x1a);
+ { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
+ { uint64_t x94 = (x92 + x76);
+ { uint64_t x95 = (x94 >> 0x19);
+ { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
+ { uint64_t x97 = (x95 + x73);
+ { uint64_t x98 = (x97 >> 0x1a);
+ { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
+ { uint64_t x100 = (x98 + x70);
+ { uint64_t x101 = (x100 >> 0x19);
+ { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
+ { uint64_t x103 = (x101 + x67);
+ { uint64_t x104 = (x103 >> 0x1a);
+ { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
+ { uint64_t x106 = (x104 + x64);
+ { uint64_t x107 = (x106 >> 0x19);
+ { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
+ { uint64_t x109 = (x107 + x61);
+ { uint64_t x110 = (x109 >> 0x1a);
+ { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
+ { uint64_t x112 = (x110 + x49);
+ { uint64_t x113 = (x112 >> 0x19);
+ { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
+ { uint64_t x115 = (x87 + (0x13 * x113));
+ { uint32_t x116 = (uint32_t) (x115 >> 0x1a);
+ { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
+ { uint32_t x118 = (x116 + x90);
+ { uint32_t x119 = (x118 >> 0x19);
+ { uint32_t x120 = (x118 & 0x1ffffff);
+ out[0] = x117;
+ out[1] = x120;
+ out[2] = (x119 + x93);
+ out[3] = x96;
+ out[4] = x99;
+ out[5] = x102;
+ out[6] = x105;
+ out[7] = x108;
+ out[8] = x111;
+ out[9] = x114;
+ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+ assert_fe(out);
+}
+
static void fe_mul121666(fe *h, const fe_loose *f) {
assert_fe_loose(f->v);
- int32_t f0 = f->v[0];
- int32_t f1 = f->v[1];
- int32_t f2 = f->v[2];
- int32_t f3 = f->v[3];
- int32_t f4 = f->v[4];
- int32_t f5 = f->v[5];
- int32_t f6 = f->v[6];
- int32_t f7 = f->v[7];
- int32_t f8 = f->v[8];
- int32_t f9 = f->v[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->v[0] = h0;
- h->v[1] = h1;
- h->v[2] = h2;
- h->v[3] = h3;
- h->v[4] = h4;
- h->v[5] = h5;
- h->v[6] = h6;
- h->v[7] = h7;
- h->v[8] = h8;
- h->v[9] = h9;
+ fe_mul_121666_impl(h->v, f->v);
assert_fe(h->v);
}
diff --git a/third_party/fiat/internal.h b/third_party/fiat/internal.h
index 68de500..10218e0 100644
--- a/third_party/fiat/internal.h
+++ b/third_party/fiat/internal.h
@@ -1,16 +1,24 @@
-/* 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. */
+// The MIT License (MIT)
+//
+// Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file).
+//
+// 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.
#ifndef OPENSSL_HEADER_CURVE25519_INTERNAL_H
#define OPENSSL_HEADER_CURVE25519_INTERNAL_H
@@ -40,13 +48,13 @@
// 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].
-// fe limbs are bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+// fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc.
// Multiplication and carrying produce fe from fe_loose.
-typedef struct fe { int32_t v[10]; } fe;
+typedef struct fe { uint32_t v[10]; } fe;
-// fe_loose limbs are bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+// fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc.
// Addition and subtraction produce fe_loose from (fe, fe).
-typedef struct fe_loose { int32_t v[10]; } fe_loose;
+typedef struct fe_loose { uint32_t v[10]; } fe_loose;
/* ge means group element.
