[git commit] tls: replace "26-bit" P256 code with 32-bit one.
Denys Vlasenko
vda.linux at googlemail.com
Tue Oct 5 18:01:38 UTC 2021
commit: https://git.busybox.net/busybox/commit/?id=3b411ebbfc749f9f12b0eb739cb5ba3ec052197e
branch: https://git.busybox.net/busybox/commit/?id=refs/heads/master
function old new delta
sp_256_ecc_mulmod_8 - 1171 +1171
sp_256_mod_mul_norm_8 - 834 +834
sp_256_proj_point_dbl_8 - 374 +374
sp_256_mont_reduce_8 - 268 +268
sp_256_mont_mul_8 - 151 +151
sp_256_sub_8 - 76 +76
sp_256_add_8 - 76 +76
sp_256_cmp_8 - 38 +38
static.sp_256_mont_dbl_8 - 31 +31
static.sp_256_mont_sub_8 - 29 +29
sp_256_to_bin_8 - 28 +28
sp_256_point_from_bin2x32 50 73 +23
sp_256_mont_sqr_8 - 7 +7
sp_256_mont_sqr_10 7 - -7
p256_mod 40 32 -8
curve_P256_compute_pubkey_and_premaster 186 167 -19
sp_256_sub_10 22 - -22
sp_256_add_10 22 - -22
sp_256_cmp_10 24 - -24
sp_256_norm_10 31 - -31
static.sp_256_mont_sub_10 49 - -49
static.sp_256_mont_dbl_10 52 - -52
static.sp_256_mul_add_10 82 - -82
sp_256_from_bin_10 119 - -119
sp_256_to_bin_10 120 - -120
sp_256_mont_reduce_10 178 - -178
sp_256_mont_mul_10 214 - -214
sp_256_proj_point_dbl_10 451 - -451
sp_256_ecc_mulmod_10 1216 - -1216
sp_256_mod_mul_norm_10 1305 - -1305
------------------------------------------------------------------------------
(add/remove: 12/15 grow/shrink: 1/2 up/down: 3106/-3919) Total: -813 bytes
Signed-off-by: Denys Vlasenko <vda.linux at googlemail.com>
---
networking/tls.c | 15 +-
networking/tls_sp_c32.c | 1071 +++++++++++++++++++++++++----------------------
2 files changed, 588 insertions(+), 498 deletions(-)
diff --git a/networking/tls.c b/networking/tls.c
index 4f0e2b6eb..675ef4b3a 100644
--- a/networking/tls.c
+++ b/networking/tls.c
@@ -2334,7 +2334,6 @@ void FAST_FUNC tls_run_copy_loop(tls_state_t *tls, unsigned flags)
// e.g. at the very beginning of wget_main()
//
{
-//kbuild:lib-$(CONFIG_TLS) += tls_sp_c32_new.o
uint8_t ecc_pub_key32[2 * 32];
uint8_t pubkey2x32[2 * 32];
uint8_t premaster32[32];
@@ -2345,14 +2344,14 @@ void FAST_FUNC tls_run_copy_loop(tls_state_t *tls, unsigned flags)
// memset(ecc_pub_key32, 0x00, sizeof(ecc_pub_key32));
// ecc_pub_key32[18] = 0xab;
//Random key:
- tls_get_random(ecc_pub_key32, sizeof(ecc_pub_key32));
+// tls_get_random(ecc_pub_key32, sizeof(ecc_pub_key32));
//Biased random (almost all zeros or almost all ones):
-// srand(time(NULL) ^ getpid());
-// if (rand() & 1)
-// memset(ecc_pub_key32, 0x00, sizeof(ecc_pub_key32));
-// else
-// memset(ecc_pub_key32, 0xff, sizeof(ecc_pub_key32));
-// ecc_pub_key32[rand() & 0x3f] = rand();
+ srand(time(NULL) ^ getpid());
+ if (rand() & 1)
+ memset(ecc_pub_key32, 0x00, sizeof(ecc_pub_key32));
+ else
+ memset(ecc_pub_key32, 0xff, sizeof(ecc_pub_key32));
+ ecc_pub_key32[rand() & 0x3f] = rand();
xmove_fd(xopen("p256.OLD", O_WRONLY | O_CREAT | O_TRUNC), 2);
curve_P256_compute_pubkey_and_premaster(
diff --git a/networking/tls_sp_c32.c b/networking/tls_sp_c32.c
index bba22dee3..b99951890 100644
--- a/networking/tls_sp_c32.c
+++ b/networking/tls_sp_c32.c
@@ -9,6 +9,8 @@
#define FIXED_SECRET 0
#define FIXED_PEER_PUBKEY 0
+#define ALLOW_ASM 1
+
#if SP_DEBUG
# define dbg(...) fprintf(stderr, __VA_ARGS__)
static void dump_hex(const char *fmt, const void *vp, int len)
@@ -24,7 +26,8 @@ static void dump_hex(const char *fmt, const void *vp, int len)
# define dump_hex(...) ((void)0)
#endif
-typedef int32_t sp_digit;
+typedef uint32_t sp_digit;
+typedef int32_t signed_sp_digit;
/* The code below is taken from parts of
* wolfssl-3.15.3/wolfcrypt/src/sp_c32.c
@@ -32,53 +35,23 @@ typedef int32_t sp_digit;
* Header comment is kept intact:
*/
-/* sp.c
- *
- * Copyright (C) 2006-2018 wolfSSL Inc.
- *
- * This file is part of wolfSSL.
- *
- * wolfSSL is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License as published by
- * the Free Software Foundation; either version 2 of the License, or
- * (at your option) any later version.
- *
- * wolfSSL is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
- */
-
-/* Implementation by Sean Parkinson. */
-
typedef struct sp_point {
- sp_digit x[2 * 10];
- sp_digit y[2 * 10];
- sp_digit z[2 * 10];
+ sp_digit x[2 * 8];
+ sp_digit y[2 * 8];
+ sp_digit z[2 * 8];
int infinity;
} sp_point;
/* The modulus (prime) of the curve P256. */
-static const sp_digit p256_mod[10] = {
- 0x3ffffff,0x3ffffff,0x3ffffff,0x003ffff,0x0000000,
- 0x0000000,0x0000000,0x0000400,0x3ff0000,0x03fffff,
+static const sp_digit p256_mod[8] = {
+ 0xffffffff,0xffffffff,0xffffffff,0x00000000,
+ 0x00000000,0x00000000,0x00000001,0xffffffff,
};
#define p256_mp_mod ((sp_digit)0x000001)
-/* Normalize the values in each word to 26 bits. */
-static void sp_256_norm_10(sp_digit* a)
-{
- int i;
- for (i = 0; i < 9; i++) {
- a[i+1] += a[i] >> 26;
- a[i] &= 0x3ffffff;
- }
-}
+/* Normalize the values in each word to 32 bits - NOP */
+#define sp_256_norm_8(a) ((void)0)
/* Write r as big endian to byte array.
* Fixed length number of bytes written: 32
@@ -86,31 +59,17 @@ static void sp_256_norm_10(sp_digit* a)
* r A single precision integer.
* a Byte array.
*/
-static void sp_256_to_bin_10(sp_digit* r, uint8_t* a)
-{
- int i, j, s = 0, b;
-
- sp_256_norm_10(r);
-
- j = 256 / 8 - 1;
- a[j] = 0;
- for (i = 0; i < 10 && j >= 0; i++) {
- b = 0;
- a[j--] |= r[i] << s;
- b += 8 - s;
- if (j < 0)
- break;
- while (b < 26) {
- a[j--] = r[i] >> b;
- b += 8;
- if (j < 0)
- break;
- }
- s = 8 - (b - 26);
- if (j >= 0)
- a[j] = 0;
- if (s != 0)
- j++;
+static void sp_256_to_bin_8(const sp_digit* r, uint8_t* a)
+{
+ int i;
+
+ sp_256_norm_8(r);
+
+ r += 8;
+ for (i = 0; i < 8; i++) {
+ r--;
+ move_to_unaligned32(a, SWAP_BE32(*r));
+ a += 4;
}
}
@@ -120,67 +79,32 @@ static void sp_256_to_bin_10(sp_digit* r, uint8_t* a)
* a Byte array.
* n Number of bytes in array to read.
*/
-static void sp_256_from_bin_10(sp_digit* r, const uint8_t* a)
-{
- int i, j = 0, s = 0;
-
- r[0] = 0;
- for (i = 32 - 1; i >= 0; i--) {
- r[j] |= ((sp_digit)a[i]) << s;
- if (s >= 18) {
- r[j] &= 0x3ffffff;
- s = 26 - s;
- r[++j] = a[i] >> s;
- s = 8 - s;
- }
- else
- s += 8;
+static void sp_256_from_bin_8(sp_digit* r, const uint8_t* a)
+{
+ int i;
+
+ r += 8;
+ for (i = 0; i < 8; i++) {
+ sp_digit v;
+ move_from_unaligned32(v, a);
+ *--r = SWAP_BE32(v);
+ a += 4;
}
}
#if SP_DEBUG
-static void dump_256(const char *fmt, const sp_digit* cr)
+static void dump_256(const char *fmt, const sp_digit* r)
{
- sp_digit* r = (sp_digit*)cr;
uint8_t b32[32];
- sp_256_to_bin_10(r, b32);
+ sp_256_to_bin_8(r, b32);
dump_hex(fmt, b32, 32);
}
-static void dump_512(const char *fmt, const sp_digit* cr)
+static void dump_512(const char *fmt, const sp_digit* r)
{
- sp_digit* r = (sp_digit*)cr;
- uint8_t a[64];
- int i, j, s, b;
-
- /* sp_512_norm_10: */
- for (i = 0; i < 19; i++) {
- r[i+1] += r[i] >> 26;
- r[i] &= 0x3ffffff;
- }
- /* sp_512_to_bin_10: */
- s = 0;
- j = 512 / 8 - 1;
- a[j] = 0;
- for (i = 0; i < 20 && j >= 0; i++) {
- b = 0;
- a[j--] |= r[i] << s;
- b += 8 - s;
- if (j < 0)
- break;
- while (b < 26) {
- a[j--] = r[i] >> b;
- b += 8;
- if (j < 0)
- break;
- }
- s = 8 - (b - 26);
- if (j >= 0)
- a[j] = 0;
- if (s != 0)
- j++;
- }
-
- dump_hex(fmt, a, 64);
+ uint8_t b64[64];
+ sp_256_to_bin_8(r, b64 + 32);
+ sp_256_to_bin_8(r+8, b64);
+ dump_hex(fmt, b64, 64);
}
#else
# define dump_256(...) ((void)0)
@@ -192,8 +116,8 @@ static void sp_256_point_from_bin2x32(sp_point* p, const uint8_t *bin2x32)
{
memset(p, 0, sizeof(*p));
/*p->infinity = 0;*/
- sp_256_from_bin_10(p->x, bin2x32);
- sp_256_from_bin_10(p->y, bin2x32 + 32);
+ sp_256_from_bin_8(p->x, bin2x32);
+ sp_256_from_bin_8(p->y, bin2x32 + 32);
p->z[0] = 1; /* p->z = 1 */
}
@@ -202,170 +126,303 @@ static void sp_256_point_from_bin2x32(sp_point* p, const uint8_t *bin2x32)
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
-static sp_digit sp_256_cmp_10(const sp_digit* a, const sp_digit* b)
+static signed_sp_digit sp_256_cmp_8(const sp_digit* a, const sp_digit* b)
{
- sp_digit r;
int i;
- for (i = 9; i >= 0; i--) {
- r = a[i] - b[i];
- if (r != 0)
- break;
+ for (i = 7; i >= 0; i--) {
+/* signed_sp_digit r = a[i] - b[i];
+ * if (r != 0)
+ * return r;
+ * does not work: think about a[i]=0, b[i]=0xffffffff
+ */
+ if (a[i] == b[i])
+ continue;
+ return (a[i] > b[i]) * 2 - 1;
}
- return r;
+ return 0;
}
/* Compare two numbers to determine if they are equal.
*
* return 1 when equal and 0 otherwise.
*/
-static int sp_256_cmp_equal_10(const sp_digit* a, const sp_digit* b)
+static int sp_256_cmp_equal_8(const sp_digit* a, const sp_digit* b)
{
- return sp_256_cmp_10(a, b) == 0;
+ return sp_256_cmp_8(a, b) == 0;
}
-/* Add b to a into r. (r = a + b) */
-static void sp_256_add_10(sp_digit* r, const sp_digit* a, const sp_digit* b)
+/* Add b to a into r. (r = a + b). Return !0 on overflow */
+static int sp_256_add_8(sp_digit* r, const sp_digit* a, const sp_digit* b)
{
+#if ALLOW_ASM && defined(__GNUC__) && defined(__i386__)
+ sp_digit reg;
+ asm volatile (
+"\n movl (%0), %3"
+"\n addl (%1), %3"
+"\n movl %3, (%2)"
+"\n"
+"\n movl 1*4(%0), %3"
+"\n adcl 1*4(%1), %3"
+"\n movl %3, 1*4(%2)"
+"\n"
+"\n movl 2*4(%0), %3"
+"\n adcl 2*4(%1), %3"
+"\n movl %3, 2*4(%2)"
+"\n"
+"\n movl 3*4(%0), %3"
+"\n adcl 3*4(%1), %3"
+"\n movl %3, 3*4(%2)"
+"\n"
+"\n movl 4*4(%0), %3"
+"\n adcl 4*4(%1), %3"
+"\n movl %3, 4*4(%2)"
+"\n"
+"\n movl 5*4(%0), %3"
+"\n adcl 5*4(%1), %3"
+"\n movl %3, 5*4(%2)"
+"\n"
+"\n movl 6*4(%0), %3"
+"\n adcl 6*4(%1), %3"
+"\n movl %3, 6*4(%2)"
+"\n"
+"\n movl 7*4(%0), %3"
+"\n adcl 7*4(%1), %3"
+"\n movl %3, 7*4(%2)"
+"\n"
+"\n sbbl %3, %3"
+"\n"
+ : "=r" (a), "=r" (b), "=r" (r), "=r" (reg)
+ : "0" (a), "1" (b), "2" (r)
+ : "memory"
+ );
+ return reg;
+#else
int i;
- for (i = 0; i < 10; i++)
- r[i] = a[i] + b[i];
+ sp_digit carry;
+
+ carry = 0;
+ for (i = 0; i < 8; i++) {
+ sp_digit w, v;
+ w = b[i] + carry;
+ v = a[i];
+ if (w != 0) {
+ v = a[i] + w;
+ carry = (v < a[i]);
+ /* hope compiler detects above as "carry flag set" */
+ }
+ /* else: b + carry == 0, two cases:
+ * b:ffffffff, carry:1
+ * b:00000000, carry:0
+ * in either case, r[i] = a[i] and carry remains unchanged
+ */
+ r[i] = v;
+ }
+ return carry;
+#endif
}
-/* Sub b from a into r. (r = a - b) */
-static void sp_256_sub_10(sp_digit* r, const sp_digit* a, const sp_digit* b)
+/* Sub b from a into r. (r = a - b). Return !0 on underflow */
+static int sp_256_sub_8(sp_digit* r, const sp_digit* a, const sp_digit* b)
{
+#if ALLOW_ASM && defined(__GNUC__) && defined(__i386__)
+ sp_digit reg;
+ asm volatile (
+"\n movl (%0), %3"
+"\n subl (%1), %3"
+"\n movl %3, (%2)"
+"\n"
+"\n movl 1*4(%0), %3"
+"\n sbbl 1*4(%1), %3"
+"\n movl %3, 1*4(%2)"
+"\n"
+"\n movl 2*4(%0), %3"
+"\n sbbl 2*4(%1), %3"
+"\n movl %3, 2*4(%2)"
+"\n"
+"\n movl 3*4(%0), %3"
+"\n sbbl 3*4(%1), %3"
+"\n movl %3, 3*4(%2)"
+"\n"
+"\n movl 4*4(%0), %3"
+"\n sbbl 4*4(%1), %3"
+"\n movl %3, 4*4(%2)"
+"\n"
+"\n movl 5*4(%0), %3"
+"\n sbbl 5*4(%1), %3"
+"\n movl %3, 5*4(%2)"
+"\n"
+"\n movl 6*4(%0), %3"
+"\n sbbl 6*4(%1), %3"
+"\n movl %3, 6*4(%2)"
+"\n"
+"\n movl 7*4(%0), %3"
+"\n sbbl 7*4(%1), %3"
+"\n movl %3, 7*4(%2)"
+"\n"
+"\n sbbl %3, %3"
+"\n"
+ : "=r" (a), "=r" (b), "=r" (r), "=r" (reg)
+ : "0" (a), "1" (b), "2" (r)
+ : "memory"
+ );
+ return reg;
+#else
int i;
- for (i = 0; i < 10; i++)
- r[i] = a[i] - b[i];
+ sp_digit borrow;
+
+ borrow = 0;
+ for (i = 0; i < 8; i++) {
+ sp_digit w, v;
+ w = b[i] + borrow;
+ v = a[i];
+ if (w != 0) {
+ v = a[i] - w;
+ borrow = (v > a[i]);
+ /* hope compiler detects above as "carry flag set" */
+ }
+ /* else: b + borrow == 0, two cases:
+ * b:ffffffff, borrow:1
+ * b:00000000, borrow:0
+ * in either case, r[i] = a[i] and borrow remains unchanged
+ */
+ r[i] = v;
+ }
+ return borrow;
+#endif
}
/* Multiply a and b into r. (r = a * b) */
-static void sp_256_mul_10(sp_digit* r, const sp_digit* a, const sp_digit* b)
+static void sp_256_mul_8(sp_digit* r, const sp_digit* a, const sp_digit* b)
{
+ sp_digit rr[15]; /* in case r coincides with a or b */
int i, j, k;
- int64_t c;
-
- c = ((int64_t)a[9]) * b[9];
- r[19] = (sp_digit)(c >> 26);
- c = (c & 0x3ffffff) << 26;
- for (k = 17; k >= 0; k--) {
- for (i = 9; i >= 0; i--) {
- j = k - i;
- if (j >= 10)
- break;
- if (j < 0)
- continue;
- c += ((int64_t)a[i]) * b[j];
+ uint64_t acc;
+
+ acc = 0;
+ for (k = 0; k < 15; k++) {
+ uint32_t acc_hi;
+ i = k - 7;
+ if (i < 0)
+ i = 0;
+ j = k - i;
+ acc_hi = 0;
+ while (i != 8 && i <= k) {
+ uint64_t m = ((uint64_t)a[i]) * b[j];
+ acc += m;
+ if (acc < m)
+ acc_hi++;
+ j--;
+ i++;
}
- r[k + 2] += c >> 52;
- r[k + 1] = (c >> 26) & 0x3ffffff;
- c = (c & 0x3ffffff) << 26;
+ rr[k] = acc;
+ acc = (acc >> 32) | ((uint64_t)acc_hi << 32);
}
- r[0] = (sp_digit)(c >> 26);
+ r[15] = acc;
+ memcpy(r, rr, sizeof(rr));
}
/* Shift number right one bit. Bottom bit is lost. */
-static void sp_256_rshift1_10(sp_digit* r, sp_digit* a)
+static void sp_256_rshift1_8(sp_digit* r, sp_digit* a, sp_digit carry)
{
int i;
- for (i = 0; i < 9; i++)
- r[i] = ((a[i] >> 1) | (a[i + 1] << 25)) & 0x3ffffff;
- r[9] = a[9] >> 1;
+
+ carry = (!!carry << 31);
+ for (i = 7; i >= 0; i--) {
+ sp_digit c = a[i] << 31;
+ r[i] = (a[i] >> 1) | carry;
+ carry = c;
+ }
}
/* Divide the number by 2 mod the modulus (prime). (r = a / 2 % m) */
-static void sp_256_div2_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
+static void sp_256_div2_8(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
+ int carry = 0;
if (a[0] & 1)
- sp_256_add_10(r, a, m);
- sp_256_norm_10(r);
- sp_256_rshift1_10(r, r);
+ carry = sp_256_add_8(r, a, m);
+ sp_256_norm_8(r);
+ sp_256_rshift1_8(r, r, carry);
}
/* Add two Montgomery form numbers (r = a + b % m) */
-static void sp_256_mont_add_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
+static void sp_256_mont_add_8(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m)
{
- sp_256_add_10(r, a, b);
- sp_256_norm_10(r);
- if ((r[9] >> 22) > 0) {
- sp_256_sub_10(r, r, m);
- sp_256_norm_10(r);
+ int carry = sp_256_add_8(r, a, b);
+ sp_256_norm_8(r);
+ if (carry) {
+ sp_256_sub_8(r, r, m);
+ sp_256_norm_8(r);
}
}
/* Subtract two Montgomery form numbers (r = a - b % m) */
-static void sp_256_mont_sub_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
+static void sp_256_mont_sub_8(sp_digit* r, const sp_digit* a, const sp_digit* b,
const sp_digit* m)
{
- sp_256_sub_10(r, a, b);
- sp_256_norm_10(r);
- if (r[9] >> 22) {
- sp_256_add_10(r, r, m);
- sp_256_norm_10(r);
- r[9] &= 0x03fffff; /* truncate to 22 bits */
+ int borrow;
+ borrow = sp_256_sub_8(r, a, b);
+ sp_256_norm_8(r);
+ if (borrow) {
+ sp_256_add_8(r, r, m);
+ sp_256_norm_8(r);
}
}
/* Double a Montgomery form number (r = a + a % m) */
-static void sp_256_mont_dbl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
+static void sp_256_mont_dbl_8(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
- sp_256_add_10(r, a, a);
- sp_256_norm_10(r);
- if ((r[9] >> 22) > 0)
- sp_256_sub_10(r, r, m);
- sp_256_norm_10(r);
+ int carry = sp_256_add_8(r, a, a);
+ sp_256_norm_8(r);
+ if (carry)
+ sp_256_sub_8(r, r, m);
+ sp_256_norm_8(r);
}
/* Triple a Montgomery form number (r = a + a + a % m) */
-static void sp_256_mont_tpl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
+static void sp_256_mont_tpl_8(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
- sp_256_add_10(r, a, a);
- sp_256_norm_10(r);
- if ((r[9] >> 22) > 0) {
- sp_256_sub_10(r, r, m);
- sp_256_norm_10(r);
+ int carry = sp_256_add_8(r, a, a);
+ sp_256_norm_8(r);
+ if (carry) {
+ sp_256_sub_8(r, r, m);
+ sp_256_norm_8(r);
}
- sp_256_add_10(r, r, a);
- sp_256_norm_10(r);
- if ((r[9] >> 22) > 0) {
- sp_256_sub_10(r, r, m);
- sp_256_norm_10(r);
+ carry = sp_256_add_8(r, r, a);
+ sp_256_norm_8(r);
+ if (carry) {
+ sp_256_sub_8(r, r, m);
+ sp_256_norm_8(r);
}
- r[9] &= 0x03fffff; /* truncate to 22 bits */
}
/* Shift the result in the high 256 bits down to the bottom. */
-static void sp_256_mont_shift_10(sp_digit* r, const sp_digit* a)
+static void sp_256_mont_shift_8(sp_digit* r, const sp_digit* a)
{
int i;
- sp_digit n, s;
-
- s = a[10];
- n = a[9] >> 22;
- for (i = 0; i < 9; i++) {
- n += (s & 0x3ffffff) << 4;
- r[i] = n & 0x3ffffff;
- n >>= 26;
- s = a[11 + i] + (s >> 26);
+
+ for (i = 0; i < 8; i++) {
+ r[i] = a[i+8];
+ r[i+8] = 0;
}
- n += s << 4;
- r[9] = n;
- memset(&r[10], 0, sizeof(*r) * 10);
}
/* Mul a by scalar b and add into r. (r += a * b) */
-static void sp_256_mul_add_10(sp_digit* r, const sp_digit* a, sp_digit b)
+static int sp_256_mul_add_8(sp_digit* r, const sp_digit* a, sp_digit b)
{
- int64_t t = 0;
+ uint64_t t = 0;
int i;
- for (i = 0; i < 10; i++) {
- t += ((int64_t)b * a[i]) + r[i];
- r[i] = t & 0x3ffffff;
- t >>= 26;
+ for (i = 0; i < 8; i++) {
+ uint32_t t_hi;
+ uint64_t m = ((uint64_t)b * a[i]) + r[i];
+ t += m;
+ t_hi = (t < m);
+ r[i] = (sp_digit)t;
+ t = (t >> 32) | ((uint64_t)t_hi << 32);
}
- r[10] += t;
+ r[8] += (sp_digit)t;
+ return (r[8] < (sp_digit)t); /* 1 if addition overflowed */
}
/* Reduce the number back to 256 bits using Montgomery reduction.
@@ -374,7 +431,7 @@ static void sp_256_mul_add_10(sp_digit* r, const sp_digit* a, sp_digit b)
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
-static void sp_256_mont_reduce_10(sp_digit* a /*, const sp_digit* m, sp_digit mp*/)
+static void sp_256_mont_reduce_8(sp_digit* a/*, const sp_digit* m, sp_digit mp*/)
{
const sp_digit* m = p256_mod;
sp_digit mp = p256_mp_mod;
@@ -383,33 +440,144 @@ static void sp_256_mont_reduce_10(sp_digit* a /*, const sp_digit* m, sp_digit mp
sp_digit mu;
if (mp != 1) {
- for (i = 0; i < 9; i++) {
- mu = (a[i] * mp) & 0x3ffffff;
- sp_256_mul_add_10(a+i, m, mu);
- a[i+1] += a[i] >> 26;
+ int too_wide;
+ for (i = 0; i < 7; i++) {
+ mu = (sp_digit)(a[i] * mp);
+ if (sp_256_mul_add_8(a+i, m, mu))
+ (a+i)[9]++;
}
- mu = (a[i] * mp) & 0x03fffff;
- sp_256_mul_add_10(a+i, m, mu);
- a[i+1] += a[i] >> 26;
- a[i] &= 0x3ffffff;
+ mu = (sp_digit)(a[7] * mp);
+ too_wide = sp_256_mul_add_8(a+7, m, mu);
+ sp_256_mont_shift_8(a, a);
+ if (too_wide)
+ sp_256_sub_8(a, a, m);
+ sp_256_norm_8(a);
}
else { /* Same code for explicit mp == 1 (which is always the case for P256) */
- for (i = 0; i < 9; i++) {
- mu = a[i] & 0x3ffffff;
- sp_256_mul_add_10(a+i, m, mu);
- a[i+1] += a[i] >> 26;
+ sp_digit word16th = 0;
+ for (i = 0; i < 8; i++) {
+ mu = a[i];
+//m = ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff
+ if (sp_256_mul_add_8(a+i, m, mu)) {
+ int j = i + 8;
+ inc_next_word:
+ if (++j > 15) { /* a[16] array has no more words? */
+ word16th++;
+ continue;
+ }
+ if (++a[j] == 0) /* did this overflow too? */
+ goto inc_next_word;
+ }
}
- mu = a[i] & 0x03fffff;
- sp_256_mul_add_10(a+i, m, mu);
- a[i+1] += a[i] >> 26;
- a[i] &= 0x3ffffff;
+ sp_256_mont_shift_8(a, a);
+ if (word16th != 0)
+ sp_256_sub_8(a, a, m);
+ sp_256_norm_8(a);
}
-
- sp_256_mont_shift_10(a, a);
- if ((a[9] >> 22) > 0)
- sp_256_sub_10(a, a, m);
- sp_256_norm_10(a);
}
+#if 0
+//TODO: arm32 asm (also adapt for x86?)
+static void sp_256_mont_reduce_8(sp_digit* a, sp_digit* m, sp_digit mp)
+{
+ sp_digit ca = 0;
+
+ asm volatile (
+ # i = 0
+ mov r12, #0 # i = 0
+ ldr r10, [%[a], #0] # r10 = a[0]
+ ldr r14, [%[a], #4] # r14 = a[1]
+1:
+ # mu = a[i] * mp #
+ mul r8, %[mp], r10 # mu = a[i] * mp
+ # a[i+0] += m[0] * mu #
+ ldr r7, [%[m], #0] # a[i+0] += m[0] * mu
+ ldr r9, [%[a], #0] #
+ umull r6, r7, r8, r7 # r7:r6 = mu * m[0]
+ adds r10, r10, r6 # r5:r10 += r7:r6
+ adc r5, r7, #0 #
+ # a[i+1] += m[1] * mu #
+ ldr r7, [%[m], #4] # a[i+1] += m[1] * mu
+ ldr r9, [%[a], #4] #
+ umull r6, r7, r8, r7 # r7:r6 = mu * m[1]
+ adds r10, r14, r6 # r4:r10 = r7:r14 + r7:r6
+ adc r4, r7, #0 #
+ adds r10, r10, r5 # r4:r10 += r5
+ adc r4, r4, #0 #
+ # a[i+2] += m[2] * mu #
+ ldr r7, [%[m], #8] # a[i+2] += m[2] * mu
+ ldr r14, [%[a], #8] #
+ umull r6, r7, r8, r7 #
+ adds r14, r14, r6 #
+ adc r5, r7, #0 #
+ adds r14, r14, r4 #
+ adc r5, r5, #0 #
+ # a[i+3] += m[3] * mu #
+ ldr r7, [%[m], #12] # a[i+3] += m[3] * mu
+ ldr r9, [%[a], #12] #
+ umull r6, r7, r8, r7 #
+ adds r9, r9, r6 #
+ adc r4, r7, #0 #
+ adds r9, r9, r5 #
+ str r9, [%[a], #12] # a[3] = r9
+ adc r4, r4, #0 #
+ # a[i+4] += m[4] * mu #
+ ldr r7, [%[m], #16] # a[i+4] += m[4] * mu
+ ldr r9, [%[a], #16] #
+ umull r6, r7, r8, r7 #
+ adds r9, r9, r6 #
+ adc r5, r7, #0 #
+ adds r9, r9, r4 #
+ str r9, [%[a], #16] # a[4] = r9
+ adc r5, r5, #0 #
+ # a[i+5] += m[5] * mu #
+ ldr r7, [%[m], #20] # a[i+5] += m[5] * mu
+ ldr r9, [%[a], #20] #
+ umull r6, r7, r8, r7 #
+ adds r9, r9, r6 #
+ adc r4, r7, #0 #
+ adds r9, r9, r5 #
+ str r9, [%[a], #20] # a[5] = r9
+ adc r4, r4, #0 #
+ # a[i+6] += m[6] * mu #
+ ldr r7, [%[m], #24] # a[i+6] += m[6] * mu
+ ldr r9, [%[a], #24] #
+ umull r6, r7, r8, r7 #
+ adds r9, r9, r6 #
+ adc r5, r7, #0 #
+ adds r9, r9, r4 #
+ str r9, [%[a], #24] # a[6] = r9
+ adc r5, r5, #0 #
+ # a[i+7] += m[7] * mu #
+ ldr r7, [%[m], #28] # a[i+7] += m[7] * mu
+ ldr r9, [%[a], #28] #
+ umull r6, r7, r8, r7 #
+ adds r5, r5, r6 #
+ adcs r7, r7, %[ca] #
+ mov %[ca], #0 #
+ adc %[ca], %[ca], %[ca] # ca = CF
+ adds r9, r9, r5 #
+ str r9, [%[a], #28] # a[7] = r9
+ ldr r9, [%[a], #32] # r9 = a[8]
+ adcs r9, r9, r7 #
+ str r9, [%[a], #32] # a[8] = r9
+ adc %[ca], %[ca], #0 # ca += CF
+ # i += 1 # i++
+ add %[a], %[a], #4 # a++
+ add r12, r12, #4 # i += 4
+ cmp r12, #32 # if (i < 32)
+ blt 1b # goto 1
+
+ str r10, [%[a], #0] # a[0] = r10
+ str r14, [%[a], #4] # a[1] = r14
+ : [ca] "+r" (ca), [a] "+r" (a)
+ : [m] "r" (m), [mp] "r" (mp)
+ : "memory", "r4", "r5", "r6", "r7", "r8", "r9", "r10", "r14", "r12"
+ );
+
+ if (ca)
+ a -= m;
+}
+#endif
/* Multiply two Montogmery form numbers mod the modulus (prime).
* (r = a * b mod m)
@@ -420,14 +588,13 @@ static void sp_256_mont_reduce_10(sp_digit* a /*, const sp_digit* m, sp_digit mp
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
-static void sp_256_mont_mul_10(sp_digit* r, const sp_digit* a, const sp_digit* b
+static void sp_256_mont_mul_8(sp_digit* r, const sp_digit* a, const sp_digit* b
/*, const sp_digit* m, sp_digit mp*/)
{
//const sp_digit* m = p256_mod;
//sp_digit mp = p256_mp_mod;
-
- sp_256_mul_10(r, a, b);
- sp_256_mont_reduce_10(r /*, m, mp*/);
+ sp_256_mul_8(r, a, b);
+ sp_256_mont_reduce_8(r /*, m, mp*/);
}
/* Square the Montgomery form number. (r = a * a mod m)
@@ -437,13 +604,12 @@ static void sp_256_mont_mul_10(sp_digit* r, const sp_digit* a, const sp_digit* b
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
-static void sp_256_mont_sqr_10(sp_digit* r, const sp_digit* a
+static void sp_256_mont_sqr_8(sp_digit* r, const sp_digit* a
/*, const sp_digit* m, sp_digit mp*/)
{
//const sp_digit* m = p256_mod;
//sp_digit mp = p256_mp_mod;
-
- sp_256_mont_mul_10(r, a, a /*, m, mp*/);
+ sp_256_mont_mul_8(r, a, a /*, m, mp*/);
}
/* Invert the number, in Montgomery form, modulo the modulus (prime) of the
@@ -464,19 +630,19 @@ static const uint32_t p256_mod_2[8] = {
//543210987654321098765432109876543210987654321098765432109876543210...09876543210...09876543210
//111111111111111111111111111111110000000000000000000000000000000100...00000111111...11111111101
#endif
-static void sp_256_mont_inv_10(sp_digit* r, sp_digit* a)
+static void sp_256_mont_inv_8(sp_digit* r, sp_digit* a)
{
- sp_digit t[2*10]; //can be just [10]?
+ sp_digit t[2*8]; //can be just [8]?
int i;
- memcpy(t, a, sizeof(sp_digit) * 10);
+ memcpy(t, a, sizeof(sp_digit) * 8);
for (i = 254; i >= 0; i--) {
- sp_256_mont_sqr_10(t, t /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_sqr_8(t, t /*, p256_mod, p256_mp_mod*/);
/*if (p256_mod_2[i / 32] & ((sp_digit)1 << (i % 32)))*/
if (i >= 224 || i == 192 || (i <= 95 && i != 1))
- sp_256_mont_mul_10(t, t, a /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(t, t, a /*, p256_mod, p256_mp_mod*/);
}
- memcpy(r, t, sizeof(sp_digit) * 10);
+ memcpy(r, t, sizeof(sp_digit) * 8);
}
/* Multiply a number by Montogmery normalizer mod modulus (prime).
@@ -484,93 +650,29 @@ static void sp_256_mont_inv_10(sp_digit* r, sp_digit* a)
* r The resulting Montgomery form number.
* a The number to convert.
*/
-static void sp_256_mod_mul_norm_10(sp_digit* r, const sp_digit* a)
+static void sp_256_mod_mul_norm_8(sp_digit* r, const sp_digit* a)
{
int64_t t[8];
- int64_t o;
- uint32_t a32;
+ int32_t o;
+#define A(n) ((uint64_t)a[n])
/* 1 1 0 -1 -1 -1 -1 0 */
+ t[0] = 0 + A(0) + A(1) - A(3) - A(4) - A(5) - A(6);
/* 0 1 1 0 -1 -1 -1 -1 */
+ t[1] = 0 + A(1) + A(2) - A(4) - A(5) - A(6) - A(7);
/* 0 0 1 1 0 -1 -1 -1 */
+ t[2] = 0 + A(2) + A(3) - A(5) - A(6) - A(7);
/* -1 -1 0 2 2 1 0 -1 */
+ t[3] = 0 - A(0) - A(1) + 2 * A(3) + 2 * A(4) + A(5) - A(7);
/* 0 -1 -1 0 2 2 1 0 */
+ t[4] = 0 - A(1) - A(2) + 2 * A(4) + 2 * A(5) + A(6);
/* 0 0 -1 -1 0 2 2 1 */
+ t[5] = 0 - A(2) - A(3) + 2 * A(5) + 2 * A(6) + A(7);
/* -1 -1 0 0 0 1 3 2 */
+ t[6] = 0 - A(0) - A(1) + A(5) + 3 * A(6) + 2 * A(7);
/* 1 0 -1 -1 -1 -1 0 3 */
- // t[] should be calculated from "a" (converted from 26-bit to 32-bit vector a32[8])
- // according to the above matrix:
- //t[0] = 0 + a32[0] + a32[1] - a32[3] - a32[4] - a32[5] - a32[6] ;
- //t[1] = 0 + a32[1] + a32[2] - a32[4] - a32[5] - a32[6] - a32[7] ;
- //t[2] = 0 + a32[2] + a32[3] - a32[5] - a32[6] - a32[7] ;
- //t[3] = 0 - a32[0] - a32[1] + 2*a32[3] + 2*a32[4] + a32[5] - a32[7] ;
- //t[4] = 0 - a32[1] - a32[2] + 2*a32[4] + 2*a32[5] + a32[6] ;
- //t[5] = 0 - a32[2] - a32[3] + 2*a32[5] + 2*a32[6] + a32[7] ;
- //t[6] = 0 - a32[0] - a32[1] + a32[5] + 3*a32[6] + 2*a32[7];
- //t[7] = 0 + a32[0] - a32[2] - a32[3] - a32[4] - a32[5] + 3*a32[7];
- // We can do it "piecemeal" after each a32[i] is known, no need to store entire a32[8] vector:
-
-#define A32 (int64_t)a32
- a32 = a[0] | (a[1] << 26);
- t[0] = 0 + A32;
- t[3] = 0 - A32;
- t[6] = 0 - A32;
- t[7] = 0 + A32;
-
- a32 = (a[1] >> 6) | (a[2] << 20);
- t[0] += A32 ;
- t[1] = 0 + A32;
- t[3] -= A32 ;
- t[4] = 0 - A32;
- t[6] -= A32 ;
-
- a32 = (a[2] >> 12) | (a[3] << 14);
- t[1] += A32 ;
- t[2] = 0 + A32;
- t[4] -= A32 ;
- t[5] = 0 - A32;
- t[7] -= A32 ;
-
- a32 = (a[3] >> 18) | (a[4] << 8);
- t[0] -= A32 ;
- t[2] += A32 ;
- t[3] += 2*A32;
- t[5] -= A32 ;
- t[7] -= A32 ;
-
- a32 = (a[4] >> 24) | (a[5] << 2) | (a[6] << 28);
- t[0] -= A32 ;
- t[1] -= A32 ;
- t[3] += 2*A32;
- t[4] += 2*A32;
- t[7] -= A32 ;
-
- a32 = (a[6] >> 4) | (a[7] << 22);
- t[0] -= A32 ;
- t[1] -= A32 ;
- t[2] -= A32 ;
- t[3] += A32 ;
- t[4] += 2*A32;
- t[5] += 2*A32;
- t[6] += A32 ;
- t[7] -= A32 ;
-
- a32 = (a[7] >> 10) | (a[8] << 16);
- t[0] -= A32 ;
- t[1] -= A32 ;
- t[2] -= A32 ;
- t[4] += A32 ;
- t[5] += 2*A32;
- t[6] += 3*A32;
-
- a32 = (a[8] >> 16) | (a[9] << 10);
- t[1] -= A32 ;
- t[2] -= A32 ;
- t[3] -= A32 ;
- t[5] += A32 ;
- t[6] += 2*A32;
- t[7] += 3*A32;
-#undef A32
+ t[7] = 0 + A(0) - A(2) - A(3) - A(4) - A(5) + 3 * A(7);
+#undef A
t[1] += t[0] >> 32; t[0] &= 0xffffffff;
t[2] += t[1] >> 32; t[1] &= 0xffffffff;
@@ -579,29 +681,27 @@ static void sp_256_mod_mul_norm_10(sp_digit* r, const sp_digit* a)
t[5] += t[4] >> 32; t[4] &= 0xffffffff;
t[6] += t[5] >> 32; t[5] &= 0xffffffff;
t[7] += t[6] >> 32; t[6] &= 0xffffffff;
- o = t[7] >> 32; t[7] &= 0xffffffff;
+ o = t[7] >> 32; //t[7] &= 0xffffffff;
t[0] += o;
t[3] -= o;
t[6] -= o;
t[7] += o;
- t[1] += t[0] >> 32; //t[0] &= 0xffffffff;
- t[2] += t[1] >> 32; //t[1] &= 0xffffffff;
- t[3] += t[2] >> 32; //t[2] &= 0xffffffff;
- t[4] += t[3] >> 32; //t[3] &= 0xffffffff;
- t[5] += t[4] >> 32; //t[4] &= 0xffffffff;
- t[6] += t[5] >> 32; //t[5] &= 0xffffffff;
- t[7] += t[6] >> 32; //t[6] &= 0xffffffff; - (uint32_t)t[i] casts below accomplish masking
-
- r[0] = 0x3ffffff & ((sp_digit)((uint32_t)t[0]));
- r[1] = 0x3ffffff & ((sp_digit)((uint32_t)t[0] >> 26) | ((sp_digit)t[1] << 6));
- r[2] = 0x3ffffff & ((sp_digit)((uint32_t)t[1] >> 20) | ((sp_digit)t[2] << 12));
- r[3] = 0x3ffffff & ((sp_digit)((uint32_t)t[2] >> 14) | ((sp_digit)t[3] << 18));
- r[4] = 0x3ffffff & ((sp_digit)((uint32_t)t[3] >> 8) | ((sp_digit)t[4] << 24));
- r[5] = 0x3ffffff & ((sp_digit)((uint32_t)t[4] >> 2));
- r[6] = 0x3ffffff & ((sp_digit)((uint32_t)t[4] >> 28) | ((sp_digit)t[5] << 4));
- r[7] = 0x3ffffff & ((sp_digit)((uint32_t)t[5] >> 22) | ((sp_digit)t[6] << 10));
- r[8] = 0x3ffffff & ((sp_digit)((uint32_t)t[6] >> 16) | ((sp_digit)t[7] << 16));
- r[9] = ((sp_digit)((uint32_t)t[7] >> 10));
+ r[0] = (sp_digit)t[0];
+ t[1] += t[0] >> 32;
+ r[1] = (sp_digit)t[1];
+ t[2] += t[1] >> 32;
+ r[2] = (sp_digit)t[2];
+ t[3] += t[2] >> 32;
+ r[3] = (sp_digit)t[3];
+ t[4] += t[3] >> 32;
+ r[4] = (sp_digit)t[4];
+ t[5] += t[4] >> 32;
+ r[5] = (sp_digit)t[5];
+ t[6] += t[5] >> 32;
+ r[6] = (sp_digit)t[6];
+// t[7] += t[6] >> 32;
+// r[7] = (sp_digit)t[7];
+ r[7] = (sp_digit)t[7] + (sp_digit)(t[6] >> 32);
}
/* Map the Montgomery form projective co-ordinate point to an affine point.
@@ -609,33 +709,33 @@ static void sp_256_mod_mul_norm_10(sp_digit* r, const sp_digit* a)
* r Resulting affine co-ordinate point.
* p Montgomery form projective co-ordinate point.
*/
-static void sp_256_map_10(sp_point* r, sp_point* p)
+static void sp_256_map_8(sp_point* r, sp_point* p)
{
- sp_digit t1[2*10];
- sp_digit t2[2*10];
+ sp_digit t1[2*8];
+ sp_digit t2[2*8];
- sp_256_mont_inv_10(t1, p->z);
+ sp_256_mont_inv_8(t1, p->z);
- sp_256_mont_sqr_10(t2, t1 /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_mul_10(t1, t2, t1 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_sqr_8(t2, t1 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(t1, t2, t1 /*, p256_mod, p256_mp_mod*/);
/* x /= z^2 */
- sp_256_mont_mul_10(r->x, p->x, t2 /*, p256_mod, p256_mp_mod*/);
- memset(r->x + 10, 0, sizeof(r->x) / 2);
- sp_256_mont_reduce_10(r->x /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(r->x, p->x, t2 /*, p256_mod, p256_mp_mod*/);
+ memset(r->x + 8, 0, sizeof(r->x) / 2);
+ sp_256_mont_reduce_8(r->x /*, p256_mod, p256_mp_mod*/);
/* Reduce x to less than modulus */
- if (sp_256_cmp_10(r->x, p256_mod) >= 0)
- sp_256_sub_10(r->x, r->x, p256_mod);
- sp_256_norm_10(r->x);
+ if (sp_256_cmp_8(r->x, p256_mod) >= 0)
+ sp_256_sub_8(r->x, r->x, p256_mod);
+ sp_256_norm_8(r->x);
/* y /= z^3 */
- sp_256_mont_mul_10(r->y, p->y, t1 /*, p256_mod, p256_mp_mod*/);
- memset(r->y + 10, 0, sizeof(r->y) / 2);
- sp_256_mont_reduce_10(r->y /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(r->y, p->y, t1 /*, p256_mod, p256_mp_mod*/);
+ memset(r->y + 8, 0, sizeof(r->y) / 2);
+ sp_256_mont_reduce_8(r->y /*, p256_mod, p256_mp_mod*/);
/* Reduce y to less than modulus */
- if (sp_256_cmp_10(r->y, p256_mod) >= 0)
- sp_256_sub_10(r->y, r->y, p256_mod);
- sp_256_norm_10(r->y);
+ if (sp_256_cmp_8(r->y, p256_mod) >= 0)
+ sp_256_sub_8(r->y, r->y, p256_mod);
+ sp_256_norm_8(r->y);
memset(r->z, 0, sizeof(r->z));
r->z[0] = 1;
@@ -646,16 +746,16 @@ static void sp_256_map_10(sp_point* r, sp_point* p)
* r Result of doubling point.
* p Point to double.
*/
-static void sp_256_proj_point_dbl_10(sp_point* r, sp_point* p)
+static void sp_256_proj_point_dbl_8(sp_point* r, sp_point* p)
{
- sp_digit t1[2*10];
- sp_digit t2[2*10];
+ sp_digit t1[2*8];
+ sp_digit t2[2*8];
/* Put point to double into result */
if (r != p)
*r = *p; /* struct copy */
- if (r->infinity) /* If infinity, don't double */
+ if (r->infinity)
return;
if (SP_DEBUG) {
@@ -666,41 +766,42 @@ static void sp_256_proj_point_dbl_10(sp_point* r, sp_point* p)
}
/* T1 = Z * Z */
- sp_256_mont_sqr_10(t1, r->z /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_sqr_8(t1, r->z /*, p256_mod, p256_mp_mod*/);
/* Z = Y * Z */
- sp_256_mont_mul_10(r->z, r->y, r->z /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(r->z, r->y, r->z /*, p256_mod, p256_mp_mod*/);
/* Z = 2Z */
- sp_256_mont_dbl_10(r->z, r->z, p256_mod);
+ sp_256_mont_dbl_8(r->z, r->z, p256_mod);
/* T2 = X - T1 */
- sp_256_mont_sub_10(t2, r->x, t1, p256_mod);
+ sp_256_mont_sub_8(t2, r->x, t1, p256_mod);
/* T1 = X + T1 */
- sp_256_mont_add_10(t1, r->x, t1, p256_mod);
+ sp_256_mont_add_8(t1, r->x, t1, p256_mod);
/* T2 = T1 * T2 */
- sp_256_mont_mul_10(t2, t1, t2 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(t2, t1, t2 /*, p256_mod, p256_mp_mod*/);
/* T1 = 3T2 */
- sp_256_mont_tpl_10(t1, t2, p256_mod);
+ sp_256_mont_tpl_8(t1, t2, p256_mod);
/* Y = 2Y */
- sp_256_mont_dbl_10(r->y, r->y, p256_mod);
+ sp_256_mont_dbl_8(r->y, r->y, p256_mod);
/* Y = Y * Y */
- sp_256_mont_sqr_10(r->y, r->y /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_sqr_8(r->y, r->y /*, p256_mod, p256_mp_mod*/);
/* T2 = Y * Y */
- sp_256_mont_sqr_10(t2, r->y /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_sqr_8(t2, r->y /*, p256_mod, p256_mp_mod*/);
/* T2 = T2/2 */
- sp_256_div2_10(t2, t2, p256_mod);
+ sp_256_div2_8(t2, t2, p256_mod);
/* Y = Y * X */
- sp_256_mont_mul_10(r->y, r->y, r->x /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(r->y, r->y, r->x /*, p256_mod, p256_mp_mod*/);
/* X = T1 * T1 */
- sp_256_mont_mul_10(r->x, t1, t1 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(r->x, t1, t1 /*, p256_mod, p256_mp_mod*/);
/* X = X - Y */
- sp_256_mont_sub_10(r->x, r->x, r->y, p256_mod);
+ sp_256_mont_sub_8(r->x, r->x, r->y, p256_mod);
/* X = X - Y */
- sp_256_mont_sub_10(r->x, r->x, r->y, p256_mod);
+ sp_256_mont_sub_8(r->x, r->x, r->y, p256_mod);
/* Y = Y - X */
- sp_256_mont_sub_10(r->y, r->y, r->x, p256_mod);
+ sp_256_mont_sub_8(r->y, r->y, r->x, p256_mod);
/* Y = Y * T1 */
- sp_256_mont_mul_10(r->y, r->y, t1 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(r->y, r->y, t1 /*, p256_mod, p256_mp_mod*/);
/* Y = Y - T2 */
- sp_256_mont_sub_10(r->y, r->y, t2, p256_mod);
+ sp_256_mont_sub_8(r->y, r->y, t2, p256_mod);
+ dump_512("y2 %s\n", r->y);
}
/* Add two Montgomery form projective points.
@@ -709,13 +810,13 @@ static void sp_256_proj_point_dbl_10(sp_point* r, sp_point* p)
* p Frist point to add.
* q Second point to add.
*/
-static void sp_256_proj_point_add_10(sp_point* r, sp_point* p, sp_point* q)
+static void sp_256_proj_point_add_8(sp_point* r, sp_point* p, sp_point* q)
{
- sp_digit t1[2*10];
- sp_digit t2[2*10];
- sp_digit t3[2*10];
- sp_digit t4[2*10];
- sp_digit t5[2*10];
+ sp_digit t1[2*8];
+ sp_digit t2[2*8];
+ sp_digit t3[2*8];
+ sp_digit t4[2*8];
+ sp_digit t5[2*8];
/* Ensure only the first point is the same as the result. */
if (q == r) {
@@ -725,13 +826,13 @@ static void sp_256_proj_point_add_10(sp_point* r, sp_point* p, sp_point* q)
}
/* Check double */
- sp_256_sub_10(t1, p256_mod, q->y);
- sp_256_norm_10(t1);
- if (sp_256_cmp_equal_10(p->x, q->x)
- && sp_256_cmp_equal_10(p->z, q->z)
- && (sp_256_cmp_equal_10(p->y, q->y) || sp_256_cmp_equal_10(p->y, t1))
+ sp_256_sub_8(t1, p256_mod, q->y);
+ sp_256_norm_8(t1);
+ if (sp_256_cmp_equal_8(p->x, q->x)
+ && sp_256_cmp_equal_8(p->z, q->z)
+ && (sp_256_cmp_equal_8(p->y, q->y) || sp_256_cmp_equal_8(p->y, t1))
) {
- sp_256_proj_point_dbl_10(r, p);
+ sp_256_proj_point_dbl_8(r, p);
}
else {
sp_point tp;
@@ -746,37 +847,37 @@ static void sp_256_proj_point_add_10(sp_point* r, sp_point* p, sp_point* q)
*r = p->infinity ? *q : *p; /* struct copy */
/* U1 = X1*Z2^2 */
- sp_256_mont_sqr_10(t1, q->z /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_mul_10(t3, t1, q->z /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_mul_10(t1, t1, v->x /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_sqr_8(t1, q->z /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(t3, t1, q->z /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(t1, t1, v->x /*, p256_mod, p256_mp_mod*/);
/* U2 = X2*Z1^2 */
- sp_256_mont_sqr_10(t2, v->z /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_mul_10(t4, t2, v->z /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_mul_10(t2, t2, q->x /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_sqr_8(t2, v->z /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(t4, t2, v->z /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(t2, t2, q->x /*, p256_mod, p256_mp_mod*/);
/* S1 = Y1*Z2^3 */
- sp_256_mont_mul_10(t3, t3, v->y /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(t3, t3, v->y /*, p256_mod, p256_mp_mod*/);
/* S2 = Y2*Z1^3 */
- sp_256_mont_mul_10(t4, t4, q->y /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(t4, t4, q->y /*, p256_mod, p256_mp_mod*/);
/* H = U2 - U1 */
- sp_256_mont_sub_10(t2, t2, t1, p256_mod);
+ sp_256_mont_sub_8(t2, t2, t1, p256_mod);
/* R = S2 - S1 */
- sp_256_mont_sub_10(t4, t4, t3, p256_mod);
+ sp_256_mont_sub_8(t4, t4, t3, p256_mod);
/* Z3 = H*Z1*Z2 */
- sp_256_mont_mul_10(v->z, v->z, q->z /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_mul_10(v->z, v->z, t2 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(v->z, v->z, q->z /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(v->z, v->z, t2 /*, p256_mod, p256_mp_mod*/);
/* X3 = R^2 - H^3 - 2*U1*H^2 */
- sp_256_mont_sqr_10(v->x, t4 /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_sqr_10(t5, t2 /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_mul_10(v->y, t1, t5 /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_mul_10(t5, t5, t2 /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_sub_10(v->x, v->x, t5, p256_mod);
- sp_256_mont_dbl_10(t1, v->y, p256_mod);
- sp_256_mont_sub_10(v->x, v->x, t1, p256_mod);
+ sp_256_mont_sqr_8(v->x, t4 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_sqr_8(t5, t2 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(v->y, t1, t5 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(t5, t5, t2 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_sub_8(v->x, v->x, t5, p256_mod);
+ sp_256_mont_dbl_8(t1, v->y, p256_mod);
+ sp_256_mont_sub_8(v->x, v->x, t1, p256_mod);
/* Y3 = R*(U1*H^2 - X3) - S1*H^3 */
- sp_256_mont_sub_10(v->y, v->y, v->x, p256_mod);
- sp_256_mont_mul_10(v->y, v->y, t4 /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_mul_10(t5, t5, t3 /*, p256_mod, p256_mp_mod*/);
- sp_256_mont_sub_10(v->y, v->y, t5, p256_mod);
+ sp_256_mont_sub_8(v->y, v->y, v->x, p256_mod);
+ sp_256_mont_mul_8(v->y, v->y, t4 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_mul_8(t5, t5, t3 /*, p256_mod, p256_mp_mod*/);
+ sp_256_mont_sub_8(v->y, v->y, t5, p256_mod);
}
}
@@ -788,12 +889,11 @@ static void sp_256_proj_point_add_10(sp_point* r, sp_point* p, sp_point* q)
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
*/
-static void sp_256_ecc_mulmod_10(sp_point* r, const sp_point* g, const sp_digit* k /*, int map*/)
+static void sp_256_ecc_mulmod_8(sp_point* r, const sp_point* g, const sp_digit* k /*, int map*/)
{
enum { map = 1 }; /* we always convert result to affine coordinates */
sp_point t[3];
- sp_digit n;
- int i;
+ sp_digit n = n; /* for compiler */
int c, y;
memset(t, 0, sizeof(t));
@@ -801,36 +901,44 @@ static void sp_256_ecc_mulmod_10(sp_point* r, const sp_point* g, const sp_digit*
/* t[0] = {0, 0, 1} * norm */
t[0].infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
- sp_256_mod_mul_norm_10(t[1].x, g->x);
- sp_256_mod_mul_norm_10(t[1].y, g->y);
- sp_256_mod_mul_norm_10(t[1].z, g->z);
- dump_512("t[1].x %s\n", t[1].x);
- dump_512("t[1].y %s\n", t[1].y);
- dump_512("t[1].z %s\n", t[1].z);
-
- i = 9;
- c = 22;
- n = k[i--] << (26 - c);
- for (; ; c--) {
- if (c == 0) {
- if (i == -1)
- break;
+ sp_256_mod_mul_norm_8(t[1].x, g->x);
+ sp_256_mod_mul_norm_8(t[1].y, g->y);
+ sp_256_mod_mul_norm_8(t[1].z, g->z);
- n = k[i--];
- c = 26;
+ /* For every bit, starting from most significant... */
+ k += 7;
+ c = 256;
+ for (;;) {
+ if ((c & 0x1f) == 0) {
+ if (c == 0)
+ break;
+ n = *k--;
}
- y = (n >> 25) & 1;
- n <<= 1;
-
- sp_256_proj_point_add_10(&t[y^1], &t[0], &t[1]);
+ y = (n >> 31);
+ dbg("y:%d t[%d] = t[0]+t[1]\n", y, y^1);
+ sp_256_proj_point_add_8(&t[y^1], &t[0], &t[1]);
+ dump_512("t[0].x %s\n", t[0].x);
+ dump_512("t[0].y %s\n", t[0].y);
+ dump_512("t[0].z %s\n", t[0].z);
+ dump_512("t[1].x %s\n", t[1].x);
+ dump_512("t[1].y %s\n", t[1].y);
+ dump_512("t[1].z %s\n", t[1].z);
+ dbg("t[2] = t[%d]\n", y);
memcpy(&t[2], &t[y], sizeof(sp_point));
- sp_256_proj_point_dbl_10(&t[2], &t[2]);
+ dbg("t[2] *= 2\n");
+ sp_256_proj_point_dbl_8(&t[2], &t[2]);
+ dump_512("t[2].x %s\n", t[2].x);
+ dump_512("t[2].y %s\n", t[2].y);
+ dump_512("t[2].z %s\n", t[2].z);
memcpy(&t[y], &t[2], sizeof(sp_point));
+
+ n <<= 1;
+ c--;
}
if (map)
- sp_256_map_10(r, &t[0]);
+ sp_256_map_8(r, &t[0]);
else
memcpy(r, &t[0], sizeof(sp_point));
@@ -844,7 +952,7 @@ static void sp_256_ecc_mulmod_10(sp_point* r, const sp_point* g, const sp_digit*
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
*/
-static void sp_256_ecc_mulmod_base_10(sp_point* r, sp_digit* k /*, int map*/)
+static void sp_256_ecc_mulmod_base_8(sp_point* r, sp_digit* k /*, int map*/)
{
/* Since this function is called only once, save space:
* don't have "static const sp_point p256_base = {...}",
@@ -861,7 +969,7 @@ static void sp_256_ecc_mulmod_base_10(sp_point* r, sp_digit* k /*, int map*/)
sp_256_point_from_bin2x32(&p256_base, p256_base_bin);
- sp_256_ecc_mulmod_10(r, &p256_base, k /*, map*/);
+ sp_256_ecc_mulmod_8(r, &p256_base, k /*, map*/);
}
/* Multiply the point by the scalar and serialize the X ordinate.
@@ -871,7 +979,7 @@ static void sp_256_ecc_mulmod_base_10(sp_point* r, sp_digit* k /*, int map*/)
* pub2x32 Point to multiply.
* out32 Buffer to hold X ordinate.
*/
-static void sp_ecc_secret_gen_256(const sp_digit priv[10], const uint8_t *pub2x32, uint8_t* out32)
+static void sp_ecc_secret_gen_256(const sp_digit priv[8], const uint8_t *pub2x32, uint8_t* out32)
{
sp_point point[1];
@@ -885,66 +993,48 @@ static void sp_ecc_secret_gen_256(const sp_digit priv[10], const uint8_t *pub2x3
dump_512("point->x %s\n", point->x);
dump_512("point->y %s\n", point->y);
- sp_256_ecc_mulmod_10(point, point, priv);
+ sp_256_ecc_mulmod_8(point, point, priv);
- sp_256_to_bin_10(point->x, out32);
+ sp_256_to_bin_8(point->x, out32);
dump_hex("out32: %s\n", out32, 32);
}
-/* Generates a scalar that is in the range 1..order-1. */
-#define SIMPLIFY 1
-/* Add 1 to a. (a = a + 1) */
-static void sp_256_add_one_10(sp_digit* a)
-{
- a[0]++;
- sp_256_norm_10(a);
-}
-static void sp_256_ecc_gen_k_10(sp_digit k[10])
+/* Generates a random scalar in [1..order-1] range. */
+static void sp_256_ecc_gen_k_8(sp_digit k[8])
{
-#if !SIMPLIFY
- /* The order of the curve P256 minus 2. */
- static const sp_digit p256_order2[10] = {
- 0x063254f,0x272b0bf,0x1e84f3b,0x2b69c5e,0x3bce6fa,
- 0x3ffffff,0x3ffffff,0x00003ff,0x3ff0000,0x03fffff,
- };
-#endif
- uint8_t buf[32];
-
- for (;;) {
- tls_get_random(buf, sizeof(buf));
+ /* Since 32-bit words are "dense", no need to use
+ * sp_256_from_bin_8(k, buf) to convert random stream
+ * to sp_digit array - just store random bits there directly.
+ */
+ tls_get_random(k, 8 * sizeof(k[0]));
#if FIXED_SECRET
- memset(buf, 0x77, sizeof(buf));
+ memset(k, 0x77, 8 * sizeof(k[0]));
#endif
- sp_256_from_bin_10(k, buf);
-#if !SIMPLIFY
- if (sp_256_cmp_10(k, p256_order2) < 0)
- break;
-#else
- /* non-loopy version (and not needing p256_order2[]):
- * if most-significant word seems that k can be larger
- * than p256_order2, fix it up:
- */
- if (k[9] >= 0x03fffff)
- k[9] = 0x03ffffe;
- break;
-#endif
- }
- sp_256_add_one_10(k);
-#undef SIMPLIFY
+
+// If scalar is too large, try again (pseudo-code)
+// if (k >= 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 - 1) // order of P256
+// goto pick_another_random;
+// k++; // ensure non-zero
+ /* Simpler alternative, at the cost of not choosing some valid
+ * random values, and slightly non-uniform distribution */
+ if (k[0] == 0)
+ k[0] = 1;
+ if (k[7] >= 0xffffffff)
+ k[7] = 0xfffffffe;
}
/* Makes a random EC key pair. */
-static void sp_ecc_make_key_256(sp_digit privkey[10], uint8_t *pubkey)
+static void sp_ecc_make_key_256(sp_digit privkey[8], uint8_t *pubkey)
{
sp_point point[1];
- sp_256_ecc_gen_k_10(privkey);
+ sp_256_ecc_gen_k_8(privkey);
dump_256("privkey %s\n", privkey);
- sp_256_ecc_mulmod_base_10(point, privkey);
+ sp_256_ecc_mulmod_base_8(point, privkey);
dump_512("point->x %s\n", point->x);
dump_512("point->y %s\n", point->y);
- sp_256_to_bin_10(point->x, pubkey);
- sp_256_to_bin_10(point->y, pubkey + 32);
+ sp_256_to_bin_8(point->x, pubkey);
+ sp_256_to_bin_8(point->y, pubkey + 32);
memset(point, 0, sizeof(point)); //paranoia
}
@@ -953,8 +1043,9 @@ void FAST_FUNC curve_P256_compute_pubkey_and_premaster(
uint8_t *pubkey2x32, uint8_t *premaster32,
const uint8_t *peerkey2x32)
{
- sp_digit privkey[10];
+ sp_digit privkey[8];
+ dump_hex("peerkey2x32: %s\n", peerkey2x32, 64);
sp_ecc_make_key_256(privkey, pubkey2x32);
dump_hex("pubkey: %s\n", pubkey2x32, 32);
dump_hex(" %s\n", pubkey2x32 + 32, 32);
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