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3b411ebbf

Denys Vlasenko

2021-10-05

SUCCESS Duration: 155s

Subject

tls: replace "26-bit" P256 code with 32-bit one.

Binary

No binary (build failed)

Architecture & Compiler Flags

Architecture: x86_64-linux-gnu Compiler: gcc (Ubuntu 11.4.0-1ubuntu1~22.04.3) 11.4.0

—

Build Log

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Commit Diff GitHub →

networking/tls.c +7 -8 networking/tls_sp_c32.c +581 -490

networking/tls.c+7 -8

@@ -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(

networking/tls_sp_c32.c+581 -490

@@ -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] + 2a32[3] + 2a32[4] + a32[5] - a32[7] ;
-	//t[4] = 0 - a32[1] - a32[2] + 2a32[4] + 2a32[5] + a32[6] ;
-	//t[5] = 0 - a32[2] - a32[3] + 2a32[5] + 2a32[6] + a32[7] ;
-	//t[6] = 0 - a32[0] - a32[1] + a32[5] + 3a32[6] + 2a32[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 = X1Z2^2 /
-	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 = X2Z1^2 /
-	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 = Y1Z2^3 /
-	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 = Y2Z1^3 /
-	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 = HZ1Z2 */
-	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 - 2U1H^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(U1H^2 - X3) - S1H^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);