curve25519: adhere to preconditions of fe_*.
Previously, the ed25519 and SPAKE implementations called field element
operations in ways that did not satisfy the preconditions about ranges
of limbs. Furthermore, replacing signed field arithmetic with unsigned field
arithmetic with similar specifications caused tests to fail. This commit
addresses this in three steps:
(1) Split fe into fe and fe_loose, tracking the bounds
(2) Insert carry operations before uses of fe_add/fe_sub/fe_neg whose
input is already within only the loose bounds
(3) Assert that each field element is within the appropriate bounds at
the beginning and end of every field operation.
Throughput diff:
Ed25519 key generation: -2%
Ed25519 signing: -2%
Ed25519 verify: -2%
X25519: roughly unchanged
Detailed 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 11206 Ed25519 key generation operations in 1029462us (10885.3 ops/sec)
Did 11104 Ed25519 signing operations in 1035735us (10720.9 ops/sec)
Did 3278 Ed25519 verify operations in 1087969us (3013.0 ops/sec)
Did 12000 Curve25519 base-point multiplication operations in 1078962us (11121.8 ops/sec)
Did 3610 Curve25519 arbitrary point multiplication operations in 1002767us (3600.0 ops/sec)
Did 11662 Ed25519 key generation operations in 1077690us (10821.3 ops/sec)
Did 10780 Ed25519 signing operations in 1011474us (10657.7 ops/sec)
Did 3289 Ed25519 verify operations in 1083638us (3035.1 ops/sec)
Did 12000 Curve25519 base-point multiplication operations in 1087477us (11034.7 ops/sec)
Did 3610 Curve25519 arbitrary point multiplication operations in 1017023us (3549.6 ops/sec)
Did 11018 Ed25519 key generation operations in 1011606us (10891.6 ops/sec)
Did 11000 Ed25519 signing operations in 1029961us (10680.0 ops/sec)
Did 3124 Ed25519 verify operations in 1045163us (2989.0 ops/sec)
Did 12000 Curve25519 base-point multiplication operations in 1081770us (11092.9 ops/sec)
Did 3610 Curve25519 arbitrary point multiplication operations in 1014503us (3558.4 ops/sec)
master:
Did 11662 Ed25519 key generation operations in 1059449us (11007.6 ops/sec)
Did 10908 Ed25519 signing operations in 1000081us (10907.1 ops/sec)
Did 3333 Ed25519 verify operations in 1078798us (3089.5 ops/sec)
Did 12000 Curve25519 base-point multiplication operations in 1072831us (11185.4 ops/sec)
Did 3850 Curve25519 arbitrary point multiplication operations in 1075821us (3578.7 ops/sec)
Did 11102 Ed25519 key generation operations in 1017540us (10910.6 ops/sec)
Did 11000 Ed25519 signing operations in 1013279us (10855.8 ops/sec)
Did 3311 Ed25519 verify operations in 1066866us (3103.5 ops/sec)
Did 12000 Curve25519 base-point multiplication operations in 1069668us (11218.4 ops/sec)
Did 3905 Curve25519 arbitrary point multiplication operations in 1095501us (3564.6 ops/sec)
Did 11206 Ed25519 key generation operations in 1014127us (11049.9 ops/sec)
Did 10908 Ed25519 signing operations in 1015821us (10738.1 ops/sec)
Did 3344 Ed25519 verify operations in 1100592us (3038.4 ops/sec)
Did 12000 Curve25519 base-point multiplication operations in 1072847us (11185.2 ops/sec)
Did 3570 Curve25519 arbitrary point multiplication operations in 1009373us (3536.8 ops/sec)
Change-Id: Ia014386daf36c913f3ea44c5f9a420b98670e465
Reviewed-on: https://boringssl-review.googlesource.com/22104
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/crypto/curve25519/curve25519.c b/crypto/curve25519/curve25519.c
index e49a8b3..1496134 100644
--- a/crypto/curve25519/curve25519.c
+++ b/crypto/curve25519/curve25519.c
@@ -21,6 +21,7 @@
#include <openssl/curve25519.h>
+#include <assert.h>
#include <string.h>
#include <openssl/cpu.h>
@@ -54,7 +55,21 @@
return result;
}
-static void fe_frombytes(fe h, const uint8_t *s) {
+#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)))); \
+ } \
+} 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)))); \
+ } \
+} 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;
@@ -99,6 +114,11 @@
h[7] = h7;
h[8] = h8;
h[9] = h9;
+ assert_fe(h);
+}
+
+static void fe_frombytes(fe *h, const uint8_t *s) {
+ fe_frombytes_impl(h->v, s);
}
// Preconditions:
@@ -123,7 +143,8 @@
//
// Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
// so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
-static void fe_tobytes(uint8_t *s, const fe h) {
+static void fe_tobytes_impl(uint8_t *s, const int32_t h[10]) {
+ assert_fe_loose(h);
int32_t h0 = h[0];
int32_t h1 = h[1];
int32_t h2 = h[2];
@@ -203,18 +224,46 @@
s[31] = h9 >> 18;
}
+static void fe_tobytes(uint8_t *s, const fe *h) {
+ fe_tobytes_impl(s, h->v);
+}
+
+static void fe_loose_tobytes(uint8_t *s, const fe_loose *h) {
+ fe_tobytes_impl(s, h->v);
+}
+
// h = f
-static void fe_copy(fe h, const fe f) {
+static void fe_copy(fe *h, const fe *f) {
OPENSSL_memmove(h, f, sizeof(int32_t) * 10);
}
+static void fe_copy_lt(fe_loose *h, const fe *f) {
+ OPENSSL_memmove(h, f, sizeof(int32_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);
+}
+#endif // !defined(OPENSSL_SMALL)
+
// h = 0
-static void fe_0(fe h) { OPENSSL_memset(h, 0, sizeof(int32_t) * 10); }
+static void fe_0(fe *h) {
+ OPENSSL_memset(h, 0, sizeof(int32_t) * 10);
+}
+
+static void fe_loose_0(fe_loose *h) {
+ OPENSSL_memset(h, 0, sizeof(int32_t) * 10);
+}
// h = 1
-static void fe_1(fe h) {
+static void fe_1(fe *h) {
OPENSSL_memset(h, 0, sizeof(int32_t) * 10);
- h[0] = 1;
+ h->v[0] = 1;
+}
+
+static void fe_loose_1(fe_loose *h) {
+ OPENSSL_memset(h, 0, sizeof(int32_t) * 10);
+ h->v[0] = 1;
}
// h = f + g
@@ -226,11 +275,14 @@
//
// Postconditions:
// |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-static void fe_add(fe h, const fe f, const fe g) {
+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[i] = f[i] + g[i];
+ h->v[i] = f->v[i] + g->v[i];
}
+ assert_fe_loose(h->v);
}
// h = f - g
@@ -242,11 +294,62 @@
//
// Postconditions:
// |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-static void fe_sub(fe h, const fe f, const fe g) {
+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[i] = f[i] - g[i];
+ h->v[i] = f->v[i] - g->v[i];
}
+ assert_fe_loose(h->v);
+}
+
+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;
+ assert_fe(h->v);
}
// h = f * g
@@ -276,7 +379,9 @@
// Can get away with 11 carries, but then data flow is much deeper.
//
// With tighter constraints on inputs can squeeze carries into int32.
-static void fe_mul(fe h, const fe f, const fe g) {
+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];
@@ -490,6 +595,31 @@
h[7] = h7;
h[8] = h8;
h[9] = h9;
+ assert_fe(h);
+}
+
+static void fe_mul_ltt(fe_loose *h, const fe *f, const fe *g) {
+ fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_llt(fe_loose *h, const fe_loose *f, const fe *g) {
+ fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_ttt(fe *h, const fe *f, const fe *g) {
+ fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) {
+ fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_ttl(fe *h, const fe *f, const fe_loose *g) {
+ fe_mul_impl(h->v, f->v, g->v);
+}
+
+static void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) {
+ fe_mul_impl(h->v, f->v, g->v);
}
// h = f * f
@@ -502,7 +632,8 @@
// |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
//
// See fe_mul.c for discussion of implementation strategy.
-static void fe_sq(fe h, const fe f) {
+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];
@@ -631,64 +762,79 @@
h[7] = h7;
h[8] = h8;
h[9] = h9;
+ assert_fe(h);
}
-static void fe_invert(fe out, const fe z) {
+static void fe_sq_tl(fe *h, const fe_loose *f) {
+ fe_sq_impl(h->v, f->v);
+}
+
+static void fe_sq_tt(fe *h, const fe *f) {
+ fe_sq_impl(h->v, f->v);
+}
+
+static void fe_loose_invert(fe *out, const fe_loose *z) {
fe t0;
fe t1;
fe t2;
fe t3;
int i;
- fe_sq(t0, z);
- fe_sq(t1, t0);
+ fe_sq_tl(&t0, z);
+ fe_sq_tt(&t1, &t0);
for (i = 1; i < 2; ++i) {
- fe_sq(t1, t1);
+ fe_sq_tt(&t1, &t1);
}
- fe_mul(t1, z, t1);
- fe_mul(t0, t0, t1);
- fe_sq(t2, t0);
- fe_mul(t1, t1, t2);
- fe_sq(t2, t1);
+ fe_mul_tlt(&t1, z, &t1);
+ fe_mul_ttt(&t0, &t0, &t1);
+ fe_sq_tt(&t2, &t0);
+ fe_mul_ttt(&t1, &t1, &t2);
+ fe_sq_tt(&t2, &t1);
for (i = 1; i < 5; ++i) {
- fe_sq(t2, t2);
+ fe_sq_tt(&t2, &t2);
}
- fe_mul(t1, t2, t1);
- fe_sq(t2, t1);
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t2, &t1);
for (i = 1; i < 10; ++i) {
- fe_sq(t2, t2);
+ fe_sq_tt(&t2, &t2);
}
- fe_mul(t2, t2, t1);
- fe_sq(t3, t2);
+ fe_mul_ttt(&t2, &t2, &t1);
+ fe_sq_tt(&t3, &t2);
for (i = 1; i < 20; ++i) {
- fe_sq(t3, t3);
+ fe_sq_tt(&t3, &t3);
}
- fe_mul(t2, t3, t2);
- fe_sq(t2, t2);
+ fe_mul_ttt(&t2, &t3, &t2);
+ fe_sq_tt(&t2, &t2);
for (i = 1; i < 10; ++i) {
- fe_sq(t2, t2);
+ fe_sq_tt(&t2, &t2);
}
- fe_mul(t1, t2, t1);
- fe_sq(t2, t1);
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t2, &t1);
for (i = 1; i < 50; ++i) {
- fe_sq(t2, t2);
+ fe_sq_tt(&t2, &t2);
}
- fe_mul(t2, t2, t1);
- fe_sq(t3, t2);
+ fe_mul_ttt(&t2, &t2, &t1);
+ fe_sq_tt(&t3, &t2);
for (i = 1; i < 100; ++i) {
- fe_sq(t3, t3);
+ fe_sq_tt(&t3, &t3);
}
- fe_mul(t2, t3, t2);
- fe_sq(t2, t2);
+ fe_mul_ttt(&t2, &t3, &t2);
+ fe_sq_tt(&t2, &t2);
for (i = 1; i < 50; ++i) {
- fe_sq(t2, t2);
+ fe_sq_tt(&t2, &t2);
}
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t1, &t1);
for (i = 1; i < 5; ++i) {
- fe_sq(t1, t1);
+ fe_sq_tt(&t1, &t1);
}
- fe_mul(out, t1, t0);
+ fe_mul_ttt(out, &t1, &t0);
+}
+
+static void fe_invert(fe *out, const fe *z) {
+ fe_loose l;
+ fe_copy_lt(&l, z);
+ fe_loose_invert(out, &l);
}
// h = -f
@@ -698,24 +844,26 @@
//
// Postconditions:
// |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 h, const fe f) {
+static void fe_neg(fe_loose *h, const fe *f) {
+ assert_fe(f->v);
unsigned i;
for (i = 0; i < 10; i++) {
- h[i] = -f[i];
+ h->v[i] = -f->v[i];
}
+ assert_fe_loose(h->v);
}
// Replace (f,g) with (g,g) if b == 1;
// replace (f,g) with (f,g) if b == 0.
//
// Preconditions: b in {0,1}.
-static void fe_cmov(fe f, const fe g, unsigned b) {
+static void fe_cmov(fe_loose *f, const fe_loose *g, unsigned b) {
b = 0-b;
unsigned i;
for (i = 0; i < 10; i++) {
- int32_t x = f[i] ^ g[i];
+ int32_t x = f->v[i] ^ g->v[i];
x &= b;
- f[i] ^= x;
+ f->v[i] ^= x;
}
}
@@ -724,9 +872,9 @@
//
// Preconditions:
// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-static int fe_isnonzero(const fe f) {
+static int fe_isnonzero(const fe_loose *f) {
uint8_t s[32];
- fe_tobytes(s, f);
+ fe_loose_tobytes(s, f);
static const uint8_t zero[32] = {0};
return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
@@ -737,7 +885,7 @@
//
// Preconditions:
// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-static int fe_isnegative(const fe f) {
+static int fe_isnegative(const fe *f) {
uint8_t s[32];
fe_tobytes(s, f);
return s[0] & 1;
@@ -747,13 +895,14 @@
// 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.
+// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
//
// Postconditions:
-// |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+// |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(fe h, const fe f) {
+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];
@@ -893,63 +1042,68 @@
h[7] = h7;
h[8] = h8;
h[9] = h9;
+ assert_fe(h);
}
-static void fe_pow22523(fe out, const fe z) {
+static void fe_sq2_tt(fe *h, const fe *f) {
+ fe_sq2_impl(h->v, f->v);
+}
+
+static void fe_pow22523(fe *out, const fe *z) {
fe t0;
fe t1;
fe t2;
int i;
- fe_sq(t0, z);
- fe_sq(t1, t0);
+ fe_sq_tt(&t0, z);
+ fe_sq_tt(&t1, &t0);
for (i = 1; i < 2; ++i) {
- fe_sq(t1, t1);
+ fe_sq_tt(&t1, &t1);
}
- fe_mul(t1, z, t1);
- fe_mul(t0, t0, t1);
- fe_sq(t0, t0);
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
+ fe_mul_ttt(&t1, z, &t1);
+ fe_mul_ttt(&t0, &t0, &t1);
+ fe_sq_tt(&t0, &t0);
+ fe_mul_ttt(&t0, &t1, &t0);
+ fe_sq_tt(&t1, &t0);
for (i = 1; i < 5; ++i) {
- fe_sq(t1, t1);
+ fe_sq_tt(&t1, &t1);
}
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
+ fe_mul_ttt(&t0, &t1, &t0);
+ fe_sq_tt(&t1, &t0);
for (i = 1; i < 10; ++i) {
- fe_sq(t1, t1);
+ fe_sq_tt(&t1, &t1);
}
- fe_mul(t1, t1, t0);
- fe_sq(t2, t1);
+ fe_mul_ttt(&t1, &t1, &t0);
+ fe_sq_tt(&t2, &t1);
for (i = 1; i < 20; ++i) {
- fe_sq(t2, t2);
+ fe_sq_tt(&t2, &t2);
}
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t1, &t1);
for (i = 1; i < 10; ++i) {
- fe_sq(t1, t1);
+ fe_sq_tt(&t1, &t1);
}
- fe_mul(t0, t1, t0);
- fe_sq(t1, t0);
+ fe_mul_ttt(&t0, &t1, &t0);
+ fe_sq_tt(&t1, &t0);
for (i = 1; i < 50; ++i) {
- fe_sq(t1, t1);
+ fe_sq_tt(&t1, &t1);
}
- fe_mul(t1, t1, t0);
- fe_sq(t2, t1);
+ fe_mul_ttt(&t1, &t1, &t0);
+ fe_sq_tt(&t2, &t1);
for (i = 1; i < 100; ++i) {
- fe_sq(t2, t2);
+ fe_sq_tt(&t2, &t2);
}
- fe_mul(t1, t2, t1);
- fe_sq(t1, t1);
+ fe_mul_ttt(&t1, &t2, &t1);
+ fe_sq_tt(&t1, &t1);
for (i = 1; i < 50; ++i) {
- fe_sq(t1, t1);
+ fe_sq_tt(&t1, &t1);
}
- fe_mul(t0, t1, t0);
- fe_sq(t0, t0);
+ fe_mul_ttt(&t0, &t1, &t0);
+ fe_sq_tt(&t0, &t0);
for (i = 1; i < 2; ++i) {
- fe_sq(t0, t0);
+ fe_sq_tt(&t0, &t0);
}
- fe_mul(out, t0, z);
+ fe_mul_ttt(out, &t0, z);
}
void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h) {
@@ -957,11 +1111,11 @@
fe x;
fe y;
- fe_invert(recip, h->Z);
- fe_mul(x, h->X, recip);
- fe_mul(y, h->Y, recip);
- fe_tobytes(s, y);
- s[31] ^= fe_isnegative(x) << 7;
+ fe_invert(&recip, &h->Z);
+ fe_mul_ttt(&x, &h->X, &recip);
+ fe_mul_ttt(&y, &h->Y, &recip);
+ fe_tobytes(s, &y);
+ s[31] ^= fe_isnegative(&x) << 7;
}
static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) {
@@ -969,119 +1123,122 @@
fe x;
fe y;
- fe_invert(recip, h->Z);
- fe_mul(x, h->X, recip);
- fe_mul(y, h->Y, recip);
- fe_tobytes(s, y);
- s[31] ^= fe_isnegative(x) << 7;
+ fe_invert(&recip, &h->Z);
+ fe_mul_ttt(&x, &h->X, &recip);
+ fe_mul_ttt(&y, &h->Y, &recip);
+ fe_tobytes(s, &y);
+ s[31] ^= fe_isnegative(&x) << 7;
}
-static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729,
- -8787816, -6275908, -3247719, -18696448, -12055116};
+static const fe d = {{-10913610, 13857413, -15372611, 6949391, 114729,
+ -8787816, -6275908, -3247719, -18696448, -12055116}};
-static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472,
- -272473, -25146209, -2005654, 326686, 11406482};
+static const fe sqrtm1 = {{-32595792, -7943725, 9377950, 3500415, 12389472,
+ -272473, -25146209, -2005654, 326686, 11406482}};
int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) {
fe u;
- fe v;
+ fe_loose v;
fe v3;
fe vxx;
- fe check;
+ fe_loose check;
- fe_frombytes(h->Y, s);
- fe_1(h->Z);
- fe_sq(u, h->Y);
- fe_mul(v, u, d);
- fe_sub(u, u, h->Z); // u = y^2-1
- fe_add(v, v, h->Z); // v = dy^2+1
+ fe_frombytes(&h->Y, s);
+ fe_1(&h->Z);
+ fe_sq_tt(&v3, &h->Y);
+ fe_mul_ttt(&vxx, &v3, &d);
+ fe_sub(&v, &v3, &h->Z); // u = y^2-1
+ fe_carry(&u, &v);
+ fe_add(&v, &vxx, &h->Z); // v = dy^2+1
- fe_sq(v3, v);
- fe_mul(v3, v3, v); // v3 = v^3
- fe_sq(h->X, v3);
- fe_mul(h->X, h->X, v);
- fe_mul(h->X, h->X, u); // x = uv^7
+ fe_sq_tl(&v3, &v);
+ fe_mul_ttl(&v3, &v3, &v); // v3 = v^3
+ fe_sq_tt(&h->X, &v3);
+ fe_mul_ttl(&h->X, &h->X, &v);
+ fe_mul_ttt(&h->X, &h->X, &u); // x = uv^7
- fe_pow22523(h->X, h->X); // x = (uv^7)^((q-5)/8)
- fe_mul(h->X, h->X, v3);
- fe_mul(h->X, h->X, u); // x = uv^3(uv^7)^((q-5)/8)
+ fe_pow22523(&h->X, &h->X); // x = (uv^7)^((q-5)/8)
+ fe_mul_ttt(&h->X, &h->X, &v3);
+ fe_mul_ttt(&h->X, &h->X, &u); // x = uv^3(uv^7)^((q-5)/8)
- fe_sq(vxx, h->X);
- fe_mul(vxx, vxx, v);
- fe_sub(check, vxx, u); // vx^2-u
- if (fe_isnonzero(check)) {
- fe_add(check, vxx, u); // vx^2+u
- if (fe_isnonzero(check)) {
+ fe_sq_tt(&vxx, &h->X);
+ fe_mul_ttl(&vxx, &vxx, &v);
+ fe_sub(&check, &vxx, &u);
+ if (fe_isnonzero(&check)) {
+ fe_add(&check, &vxx, &u);
+ if (fe_isnonzero(&check)) {
return -1;
}
- fe_mul(h->X, h->X, sqrtm1);
+ fe_mul_ttt(&h->X, &h->X, &sqrtm1);
}
- if (fe_isnegative(h->X) != (s[31] >> 7)) {
- fe_neg(h->X, h->X);
+ if (fe_isnegative(&h->X) != (s[31] >> 7)) {
+ fe_loose t;
+ fe_neg(&t, &h->X);
+ fe_carry(&h->X, &t);
}
- fe_mul(h->T, h->X, h->Y);
+ fe_mul_ttt(&h->T, &h->X, &h->Y);
return 0;
}
static void ge_p2_0(ge_p2 *h) {
- fe_0(h->X);
- fe_1(h->Y);
- fe_1(h->Z);
+ fe_0(&h->X);
+ fe_1(&h->Y);
+ fe_1(&h->Z);
}
static void ge_p3_0(ge_p3 *h) {
- fe_0(h->X);
- fe_1(h->Y);
- fe_1(h->Z);
- fe_0(h->T);
+ fe_0(&h->X);
+ fe_1(&h->Y);
+ fe_1(&h->Z);
+ fe_0(&h->T);
}
static void ge_cached_0(ge_cached *h) {
- fe_1(h->YplusX);
- fe_1(h->YminusX);
- fe_1(h->Z);
- fe_0(h->T2d);
+ fe_loose_1(&h->YplusX);
+ fe_loose_1(&h->YminusX);
+ fe_loose_1(&h->Z);
+ fe_loose_0(&h->T2d);
}
static void ge_precomp_0(ge_precomp *h) {
- fe_1(h->yplusx);
- fe_1(h->yminusx);
- fe_0(h->xy2d);
+ fe_loose_1(&h->yplusx);
+ fe_loose_1(&h->yminusx);
+ fe_loose_0(&h->xy2d);
}
// r = p
static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
- fe_copy(r->X, p->X);
- fe_copy(r->Y, p->Y);
- fe_copy(r->Z, p->Z);
+ fe_copy(&r->X, &p->X);
+ fe_copy(&r->Y, &p->Y);
+ fe_copy(&r->Z, &p->Z);
}
-static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458,
- 15978800, -12551817, -6495438, 29715968, 9444199};
+static const fe d2 = {{-21827239, -5839606, -30745221, 13898782, 229458,
+ 15978800, -12551817, -6495438, 29715968, 9444199}};
// r = p
void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
- fe_add(r->YplusX, p->Y, p->X);
- fe_sub(r->YminusX, p->Y, p->X);
- fe_copy(r->Z, p->Z);
- fe_mul(r->T2d, p->T, d2);
+ fe_add(&r->YplusX, &p->Y, &p->X);
+ fe_sub(&r->YminusX, &p->Y, &p->X);
+ fe_copy_lt(&r->Z, &p->Z);
+ fe_mul_ltt(&r->T2d, &p->T, &d2);
}
// r = p
void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
- fe_mul(r->X, p->X, p->T);
- fe_mul(r->Y, p->Y, p->Z);
- fe_mul(r->Z, p->Z, p->T);
+ fe_mul_tll(&r->X, &p->X, &p->T);
+ fe_mul_tll(&r->Y, &p->Y, &p->Z);
+ fe_mul_tll(&r->Z, &p->Z, &p->T);
}
// r = p
void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
- fe_mul(r->X, p->X, p->T);
- fe_mul(r->Y, p->Y, p->Z);
- fe_mul(r->Z, p->Z, p->T);
- fe_mul(r->T, p->X, p->Y);
+ fe_mul_tll(&r->X, &p->X, &p->T);
+ fe_mul_tll(&r->Y, &p->Y, &p->Z);
+ fe_mul_tll(&r->Z, &p->Z, &p->T);
+ fe_mul_tll(&r->T, &p->X, &p->Y);
}
// r = p
@@ -1093,17 +1250,21 @@
// r = 2 * p
static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
+ fe trX, trZ, trT;
fe t0;
- fe_sq(r->X, p->X);
- fe_sq(r->Z, p->Y);
- fe_sq2(r->T, p->Z);
- fe_add(r->Y, p->X, p->Y);
- fe_sq(t0, r->Y);
- fe_add(r->Y, r->Z, r->X);
- fe_sub(r->Z, r->Z, r->X);
- fe_sub(r->X, t0, r->Y);
- fe_sub(r->T, r->T, r->Z);
+ fe_sq_tt(&trX, &p->X);
+ fe_sq_tt(&trZ, &p->Y);
+ fe_sq2_tt(&trT, &p->Z);
+ fe_add(&r->Y, &p->X, &p->Y);
+ fe_sq_tl(&t0, &r->Y);
+
+ fe_add(&r->Y, &trZ, &trX);
+ fe_sub(&r->Z, &trZ, &trX);
+ fe_carry(&trZ, &r->Y);
+ fe_sub(&r->X, &t0, &trZ);
+ fe_carry(&trZ, &r->Z);
+ fe_sub(&r->T, &trT, &trZ);
}
// r = 2 * p
@@ -1115,68 +1276,72 @@
// r = p + q
static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
- fe t0;
+ fe trY, trZ, trT;
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->yplusx);
- fe_mul(r->Y, r->Y, q->yminusx);
- fe_mul(r->T, q->xy2d, p->T);
- fe_add(t0, p->Z, p->Z);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_add(r->Z, t0, r->T);
- fe_sub(r->T, t0, r->T);
+ fe_add(&r->X, &p->Y, &p->X);
+ fe_sub(&r->Y, &p->Y, &p->X);
+ fe_mul_tll(&trZ, &r->X, &q->yplusx);
+ fe_mul_tll(&trY, &r->Y, &q->yminusx);
+ fe_mul_tlt(&trT, &q->xy2d, &p->T);
+ fe_add(&r->T, &p->Z, &p->Z);
+ fe_sub(&r->X, &trZ, &trY);
+ fe_add(&r->Y, &trZ, &trY);
+ fe_carry(&trZ, &r->T);
+ fe_add(&r->Z, &trZ, &trT);
+ fe_sub(&r->T, &trZ, &trT);
}
// r = p - q
static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
- fe t0;
+ fe trY, trZ, trT;
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->yminusx);
- fe_mul(r->Y, r->Y, q->yplusx);
- fe_mul(r->T, q->xy2d, p->T);
- fe_add(t0, p->Z, p->Z);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_sub(r->Z, t0, r->T);
- fe_add(r->T, t0, r->T);
+ fe_add(&r->X, &p->Y, &p->X);
+ fe_sub(&r->Y, &p->Y, &p->X);
+ fe_mul_tll(&trZ, &r->X, &q->yminusx);
+ fe_mul_tll(&trY, &r->Y, &q->yplusx);
+ fe_mul_tlt(&trT, &q->xy2d, &p->T);
+ fe_add(&r->T, &p->Z, &p->Z);
+ fe_sub(&r->X, &trZ, &trY);
+ fe_add(&r->Y, &trZ, &trY);
+ fe_carry(&trZ, &r->T);
+ fe_sub(&r->Z, &trZ, &trT);
+ fe_add(&r->T, &trZ, &trT);
}
// r = p + q
void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
- fe t0;
+ fe trX, trY, trZ, trT;
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->YplusX);
- fe_mul(r->Y, r->Y, q->YminusX);
- fe_mul(r->T, q->T2d, p->T);
- fe_mul(r->X, p->Z, q->Z);
- fe_add(t0, r->X, r->X);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_add(r->Z, t0, r->T);
- fe_sub(r->T, t0, r->T);
+ fe_add(&r->X, &p->Y, &p->X);
+ fe_sub(&r->Y, &p->Y, &p->X);
+ fe_mul_tll(&trZ, &r->X, &q->YplusX);
+ fe_mul_tll(&trY, &r->Y, &q->YminusX);
+ fe_mul_tlt(&trT, &q->T2d, &p->T);
+ fe_mul_ttl(&trX, &p->Z, &q->Z);
+ fe_add(&r->T, &trX, &trX);
+ fe_sub(&r->X, &trZ, &trY);
+ fe_add(&r->Y, &trZ, &trY);
+ fe_carry(&trZ, &r->T);
+ fe_add(&r->Z, &trZ, &trT);
+ fe_sub(&r->T, &trZ, &trT);
}
// r = p - q
void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
- fe t0;
+ fe trX, trY, trZ, trT;
- fe_add(r->X, p->Y, p->X);
- fe_sub(r->Y, p->Y, p->X);
- fe_mul(r->Z, r->X, q->YminusX);
- fe_mul(r->Y, r->Y, q->YplusX);
- fe_mul(r->T, q->T2d, p->T);
- fe_mul(r->X, p->Z, q->Z);
- fe_add(t0, r->X, r->X);
- fe_sub(r->X, r->Z, r->Y);
- fe_add(r->Y, r->Z, r->Y);
- fe_sub(r->Z, t0, r->T);
- fe_add(r->T, t0, r->T);
+ fe_add(&r->X, &p->Y, &p->X);
+ fe_sub(&r->Y, &p->Y, &p->X);
+ fe_mul_tll(&trZ, &r->X, &q->YminusX);
+ fe_mul_tll(&trY, &r->Y, &q->YplusX);
+ fe_mul_tlt(&trT, &q->T2d, &p->T);
+ fe_mul_ttl(&trX, &p->Z, &q->Z);
+ fe_add(&r->T, &trX, &trX);
+ fe_sub(&r->X, &trZ, &trY);
+ fe_add(&r->Y, &trZ, &trY);
+ fe_carry(&trZ, &r->T);
+ fe_sub(&r->Z, &trZ, &trT);
+ fe_add(&r->T, &trZ, &trT);
}
static uint8_t equal(signed char b, signed char c) {
@@ -1190,9 +1355,9 @@
}
static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) {
- fe_cmov(t->yplusx, u->yplusx, b);
- fe_cmov(t->yminusx, u->yminusx, b);
- fe_cmov(t->xy2d, u->xy2d, b);
+ fe_cmov(&t->yplusx, &u->yplusx, b);
+ fe_cmov(&t->yminusx, &u->yminusx, b);
+ fe_cmov(&t->xy2d, &u->xy2d, b);
}
void x25519_ge_scalarmult_small_precomp(
@@ -1205,14 +1370,14 @@
for (i = 0; i < 15; i++) {
const uint8_t *bytes = &precomp_table[i*(2 * 32)];
fe x, y;
- fe_frombytes(x, bytes);
- fe_frombytes(y, bytes + 32);
+ fe_frombytes(&x, bytes);
+ fe_frombytes(&y, bytes + 32);
ge_precomp *out = &multiples[i];
- fe_add(out->yplusx, y, x);
- fe_sub(out->yminusx, y, x);
- fe_mul(out->xy2d, x, y);
- fe_mul(out->xy2d, out->xy2d, d2);
+ fe_add(&out->yplusx, &y, &x);
+ fe_sub(&out->yminusx, &y, &x);
+ fe_mul_ltt(&out->xy2d, &x, &y);
+ fe_mul_llt(&out->xy2d, &out->xy2d, &d2);
}
// See the comment above |k25519SmallPrecomp| about the structure of the
@@ -1350,2114 +1515,2114 @@
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, -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}},
},
{
- {-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},
+ {{-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}},
},
{
- {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},
+ {{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}},
},
{
- {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
- -28926210, 15006023, 3284568, -6276540},
- {23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
- 7464579, 9656445, 13059162, 10374397},
- {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
- -3839045, -641708, -101325},
+ {{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
+ -28926210, 15006023, 3284568, -6276540}},
+ {{23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
+ 7464579, 9656445, 13059162, 10374397}},
+ {{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
+ -3839045, -641708, -101325}},
},
{
- {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, -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}},
},
{
- {-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},
+ {{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
+ -19188627, -15224819, -9818940, -12085777}},
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- -19690631, 2355319, -19284671, -6114373},
- {15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
- 18952177, 15496498, -29380133, 11754228},
- {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
- 7141596, 11724556, 22761615, -10134141},
+ {{-14467279, -683715, -33374107, 7448552, 19294360, 14334329,
+ -19690631, 2355319, -19284671, -6114373}},
+ {{15121312, -15796162, 6377020, -6031361, -10798111, -12957845,
+ 18952177, 15496498, -29380133, 11754228}},
+ {{-2637277, -13483075, 8488727, -14303896, 12728761, -1622493,
+ 7141596, 11724556, 22761615, -10134141}},
},
{
- {16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
- -28741185, -12227393, 32851222, 11717399},
- {11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
- 31474879, 3483633, -1193175, -4030831},
- {-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
- 33142652, 6546660, -19985279, -3948376},
+ {{16918416, 11729663, -18083579, 3022987, -31015732, -13339659,
+ -28741185, -12227393, 32851222, 11717399}},
+ {{11166634, 7338049, -6722523, 4531520, -29468672, -7302055,
+ 31474879, 3483633, -1193175, -4030831}},
+ {{-185635, 9921305, 31456609, -13536438, -12013818, 13348923,
+ 33142652, 6546660, -19985279, -3948376}},
},
{
- {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
- -8537131, -12833048, -30772034, -15486313},
- {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
- -31135347, -16049879, 10928917, 3011958},
- {-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
- -30831056, -12805180, 18008031, 10258577},
+ {{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903,
+ -8537131, -12833048, -30772034, -15486313}},
+ {{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425,
+ -31135347, -16049879, 10928917, 3011958}},
+ {{-6957757, -15594337, 31696059, 334240, 29576716, 14796075,
+ -30831056, -12805180, 18008031, 10258577}},
},
{
- {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
- -1853465, 1367120, 25127874, 6671743},
- {29701166, -14373934, -10878120, 9279288, -17568, 13127210,
- 21382910, 11042292, 25838796, 4642684},
- {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
- 30468147, -13900640, 18423289, 4177476},
+ {{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
+ -1853465, 1367120, 25127874, 6671743}},
+ {{29701166, -14373934, -10878120, 9279288, -17568, 13127210,
+ 21382910, 11042292, 25838796, 4642684}},
+ {{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
+ 30468147, -13900640, 18423289, 4177476}},
},
},
};
@@ -3482,9 +3647,14 @@
cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
- fe_copy(minust.yplusx, t->yminusx);
- fe_copy(minust.yminusx, t->yplusx);
- fe_neg(minust.xy2d, t->xy2d);
+ fe_copy_ll(&minust.yplusx, &t->yminusx);
+ fe_copy_ll(&minust.yminusx, &t->yplusx);
+
+ // NOTE: the input table is canonical, but types don't encode it
+ fe tmp;
+ fe_carry(&tmp, &t->xy2d);
+ fe_neg(&minust.xy2d, &tmp);
+
cmov(t, &minust, bnegative);
}
@@ -3545,10 +3715,10 @@
#endif
static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) {
- fe_cmov(t->YplusX, u->YplusX, b);
- fe_cmov(t->YminusX, u->YminusX, b);
- fe_cmov(t->Z, u->Z, b);
- fe_cmov(t->T2d, u->T2d, b);
+ fe_cmov(&t->YplusX, &u->YplusX, b);
+ fe_cmov(&t->YminusX, &u->YminusX, b);
+ fe_cmov(&t->Z, &u->Z, b);
+ fe_cmov(&t->T2d, &u->T2d, b);
}
// r = scalar * A.
@@ -3641,68 +3811,68 @@
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, -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}},
},
{
- {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},
+ {{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}},
},
{
- {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, -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}},
},
{
- {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
- 5230134, -23952439, -15175766},
- {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
- 16520125, 30598449, 7715701},
- {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
- 1370708, 29794553, -1409300},
+ {{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
+ 5230134, -23952439, -15175766}},
+ {{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
+ 16520125, 30598449, 7715701}},
+ {{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
+ 1370708, 29794553, -1409300}},
},
{
- {-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},
+ {{-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}},
},
{
- {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
- -663000, -31111463, -16132436},
- {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
- 15725684, 171356, 6466918},
- {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
- -14088058, -30714912, 16193877},
+ {{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
+ -663000, -31111463, -16132436}},
+ {{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
+ 15725684, 171356, 6466918}},
+ {{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
+ -14088058, -30714912, 16193877}},
},
{
- {-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},
+ {{-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}},
},
{
- {-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},
+ {{-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}},
},
};
@@ -4659,8 +4829,11 @@
return 0;
}
- fe_neg(A.X, A.X);
- fe_neg(A.T, A.T);
+ fe_loose t;
+ fe_neg(&t, &A.X);
+ fe_carry(&A.X, &t);
+ fe_neg(&t, &A.T);
+ fe_carry(&A.T, &t);
uint8_t pkcopy[32];
OPENSSL_memcpy(pkcopy, public_key, 32);
@@ -4720,14 +4893,14 @@
// replace (f,g) with (f,g) if b == 0.
//
// Preconditions: b in {0,1}.
-static void fe_cswap(fe f, fe g, unsigned int b) {
+static void fe_cswap(fe *f, fe *g, unsigned int b) {
b = 0-b;
unsigned i;
for (i = 0; i < 10; i++) {
- int32_t x = f[i] ^ g[i];
+ int32_t x = f->v[i] ^ g->v[i];
x &= b;
- f[i] ^= x;
- g[i] ^= x;
+ f->v[i] ^= x;
+ g->v[i] ^= x;
}
}
@@ -4739,17 +4912,18 @@
//
// Postconditions:
// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-static void fe_mul121666(fe h, fe f) {
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
+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;
@@ -4783,67 +4957,69 @@
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;
+ 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;
+ assert_fe(h->v);
}
static void x25519_scalar_mult_generic(uint8_t out[32],
const uint8_t scalar[32],
const uint8_t point[32]) {
fe x1, x2, z2, x3, z3, tmp0, tmp1;
+ fe_loose x2l, z2l, x3l, tmp0l, tmp1l;
uint8_t e[32];
OPENSSL_memcpy(e, scalar, 32);
e[0] &= 248;
e[31] &= 127;
e[31] |= 64;
- fe_frombytes(x1, point);
- fe_1(x2);
- fe_0(z2);
- fe_copy(x3, x1);
- fe_1(z3);
+ fe_frombytes(&x1, point);
+ fe_1(&x2);
+ fe_0(&z2);
+ fe_copy(&x3, &x1);
+ fe_1(&z3);
unsigned swap = 0;
int pos;
for (pos = 254; pos >= 0; --pos) {
unsigned b = 1 & (e[pos / 8] >> (pos & 7));
swap ^= b;
- fe_cswap(x2, x3, swap);
- fe_cswap(z2, z3, swap);
+ fe_cswap(&x2, &x3, swap);
+ fe_cswap(&z2, &z3, swap);
swap = b;
- fe_sub(tmp0, x3, z3);
- fe_sub(tmp1, x2, z2);
- fe_add(x2, x2, z2);
- fe_add(z2, x3, z3);
- fe_mul(z3, tmp0, x2);
- fe_mul(z2, z2, tmp1);
- fe_sq(tmp0, tmp1);
- fe_sq(tmp1, x2);
- fe_add(x3, z3, z2);
- fe_sub(z2, z3, z2);
- fe_mul(x2, tmp1, tmp0);
- fe_sub(tmp1, tmp1, tmp0);
- fe_sq(z2, z2);
- fe_mul121666(z3, tmp1);
- fe_sq(x3, x3);
- fe_add(tmp0, tmp0, z3);
- fe_mul(z3, x1, z2);
- fe_mul(z2, tmp1, tmp0);
+ fe_sub(&tmp0l, &x3, &z3);
+ fe_sub(&tmp1l, &x2, &z2);
+ fe_add(&x2l, &x2, &z2);
+ fe_add(&z2l, &x3, &z3);
+ fe_mul_tll(&z3, &tmp0l, &x2l);
+ fe_mul_tll(&z2, &z2l, &tmp1l);
+ fe_sq_tl(&tmp0, &tmp1l);
+ fe_sq_tl(&tmp1, &x2l);
+ fe_add(&x3l, &z3, &z2);
+ fe_sub(&z2l, &z3, &z2);
+ fe_mul_ttt(&x2, &tmp1, &tmp0);
+ fe_sub(&tmp1l, &tmp1, &tmp0);
+ fe_sq_tl(&z2, &z2l);
+ fe_mul121666(&z3, &tmp1l);
+ fe_sq_tl(&x3, &x3l);
+ fe_add(&tmp0l, &tmp0, &z3);
+ fe_mul_ttt(&z3, &x1, &z2);
+ fe_mul_tll(&z2, &tmp1l, &tmp0l);
}
- fe_cswap(x2, x3, swap);
- fe_cswap(z2, z3, swap);
+ fe_cswap(&x2, &x3, swap);
+ fe_cswap(&z2, &z3, swap);
- fe_invert(z2, z2);
- fe_mul(x2, x2, z2);
- fe_tobytes(out, x2);
+ fe_invert(&z2, &z2);
+ fe_mul_ttt(&x2, &x2, &z2);
+ fe_tobytes(out, &x2);
}
static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
@@ -4927,12 +5103,13 @@
// We only need the u-coordinate of the curve25519 point. The map is
// u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y).
- fe zplusy, zminusy, zminusy_inv;
- fe_add(zplusy, A.Z, A.Y);
- fe_sub(zminusy, A.Z, A.Y);
- fe_invert(zminusy_inv, zminusy);
- fe_mul(zplusy, zplusy, zminusy_inv);
- fe_tobytes(out_public_value, zplusy);
+ fe_loose zplusy, zminusy;
+ fe zminusy_inv;
+ fe_add(&zplusy, &A.Z, &A.Y);
+ fe_sub(&zminusy, &A.Z, &A.Y);
+ fe_loose_invert(&zminusy_inv, &zminusy);
+ fe_mul_tlt(&zminusy_inv, &zplusy, &zminusy_inv);
+ fe_tobytes(out_public_value, &zminusy_inv);
}
#endif // BORINGSSL_X25519_X86_64
diff --git a/crypto/curve25519/internal.h b/crypto/curve25519/internal.h
index 4d79cb9..68de500 100644
--- a/crypto/curve25519/internal.h
+++ b/crypto/curve25519/internal.h
@@ -39,9 +39,14 @@
// fe means field element. Here the field is \Z/(2^255-19). An element t,
// entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
-// t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
-// context.
-typedef int32_t fe[10];
+// 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.
+// Multiplication and carrying produce fe from fe_loose.
+typedef struct fe { int32_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.
+// Addition and subtraction produce fe_loose from (fe, fe).
+typedef struct fe_loose { int32_t v[10]; } fe_loose;
/* ge means group element.
@@ -69,23 +74,23 @@
} ge_p3;
typedef struct {
- fe X;
- fe Y;
- fe Z;
- fe T;
+ fe_loose X;
+ fe_loose Y;
+ fe_loose Z;
+ fe_loose T;
} ge_p1p1;
typedef struct {
- fe yplusx;
- fe yminusx;
- fe xy2d;
+ fe_loose yplusx;
+ fe_loose yminusx;
+ fe_loose xy2d;
} ge_precomp;
typedef struct {
- fe YplusX;
- fe YminusX;
- fe Z;
- fe T2d;
+ fe_loose YplusX;
+ fe_loose YminusX;
+ fe_loose Z;
+ fe_loose T2d;
} ge_cached;
void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h);
diff --git a/crypto/curve25519/x25519_test.cc b/crypto/curve25519/x25519_test.cc
index 903892f..3e0a27e 100644
--- a/crypto/curve25519/x25519_test.cc
+++ b/crypto/curve25519/x25519_test.cc
@@ -105,3 +105,22 @@
EXPECT_EQ(Bytes(kExpected), Bytes(scalar));
}
+
+TEST(X25519Test, DISABLED_IteratedLarge) {
+ // Taken from https://tools.ietf.org/html/rfc7748#section-5.2.
+ uint8_t scalar[32] = {9}, point[32] = {9}, out[32];
+
+ for (unsigned i = 0; i < 1000000; i++) {
+ EXPECT_TRUE(X25519(out, scalar, point));
+ OPENSSL_memcpy(point, scalar, sizeof(point));
+ OPENSSL_memcpy(scalar, out, sizeof(scalar));
+ }
+
+ static const uint8_t kExpected[32] = {
+ 0x7c, 0x39, 0x11, 0xe0, 0xab, 0x25, 0x86, 0xfd, 0x86, 0x44, 0x97,
+ 0x29, 0x7e, 0x57, 0x5e, 0x6f, 0x3b, 0xc6, 0x01, 0xc0, 0x88, 0x3c,
+ 0x30, 0xdf, 0x5f, 0x4d, 0xd2, 0xd2, 0x4f, 0x66, 0x54, 0x24,
+ };
+
+ EXPECT_EQ(Bytes(kExpected), Bytes(scalar));
+}
