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busybox/networking/tls_sp_c32.c
Denys Vlasenko 00f2cceb6a tls: P256: shrink sp_256_mul_add_8 a bit more 
function                                             old     new   delta
sp_256_mont_reduce_8                                 257     245     -12

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>
2021-10-06 10:15:29 +02:00

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/*
* Copyright (C) 2021 Denys Vlasenko
*
* Licensed under GPLv2, see file LICENSE in this source tree.
*/
#include "tls.h"
#define SP_DEBUG 0
#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)
{
char hexbuf[32 * 1024 + 4];
const uint8_t *p = vp;
bin2hex(hexbuf, (void*)p, len)[0] = '\0';
dbg(fmt, hexbuf);
}
#else
# define dbg(...) ((void)0)
# define dump_hex(...) ((void)0)
#endif
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
* and heavily modified.
* Header comment is kept intact:
*/
typedef struct sp_point {
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[8] = {
0xffffffff,0xffffffff,0xffffffff,0x00000000,
0x00000000,0x00000000,0x00000001,0xffffffff,
};
#define p256_mp_mod ((sp_digit)0x000001)
/* 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
*
* r A single precision integer.
* a Byte array.
*/
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;
}
}
/* Read big endian unsigned byte array into r.
*
* r A single precision integer.
* a Byte array.
* n Number of bytes in array to read.
*/
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* r)
{
uint8_t b32[32];
sp_256_to_bin_8(r, b32);
dump_hex(fmt, b32, 32);
}
static void dump_512(const char *fmt, const sp_digit* r)
{
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)
# define dump_512(...) ((void)0)
#endif
/* Convert a point of big-endian 32-byte x,y pair to type sp_point. */
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_8(p->x, bin2x32);
sp_256_from_bin_8(p->y, bin2x32 + 32);
p->z[0] = 1; /* p->z = 1 */
}
/* Compare a with b.
*
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static signed_sp_digit sp_256_cmp_8(const sp_digit* a, const sp_digit* b)
{
int i;
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 0;
}
/* Compare two numbers to determine if they are equal.
*
* return 1 when equal and 0 otherwise.
*/
static int sp_256_cmp_equal_8(const sp_digit* a, const sp_digit* b)
{
return sp_256_cmp_8(a, b) == 0;
}
/* 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;
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). 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;
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
}
/* Sub p256_mod from a into r. (r = a - p256_mod). */
static void sp_256_sub_8_p256_mod(sp_digit* r, const sp_digit* a)
{
#if ALLOW_ASM && defined(__GNUC__) && defined(__i386__)
sp_digit reg;
//p256_mod[7..0] = ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff
asm volatile (
"\n movl (%0), %2"
"\n subl $0xffffffff, %2"
"\n movl %2, (%1)"
"\n"
"\n movl 1*4(%0), %2"
"\n sbbl $0xffffffff, %2"
"\n movl %2, 1*4(%1)"
"\n"
"\n movl 2*4(%0), %2"
"\n sbbl $0xffffffff, %2"
"\n movl %2, 2*4(%1)"
"\n"
"\n movl 3*4(%0), %2"
"\n sbbl $0, %2"
"\n movl %2, 3*4(%1)"
"\n"
"\n movl 4*4(%0), %2"
"\n sbbl $0, %2"
"\n movl %2, 4*4(%1)"
"\n"
"\n movl 5*4(%0), %2"
"\n sbbl $0, %2"
"\n movl %2, 5*4(%1)"
"\n"
"\n movl 6*4(%0), %2"
"\n sbbl $1, %2"
"\n movl %2, 6*4(%1)"
"\n"
"\n movl 7*4(%0), %2"
"\n sbbl $0xffffffff, %2"
"\n movl %2, 7*4(%1)"
"\n"
: "=r" (a), "=r" (r), "=r" (reg)
: "0" (a), "1" (r)
: "memory"
);
#else
const sp_digit* b = p256_mod;
int 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;
}
#endif
}
/* Multiply a and b into r. (r = a * b) */
static void sp_256_mul_8(sp_digit* r, const sp_digit* a, const sp_digit* b)
{
#if ALLOW_ASM && defined(__GNUC__) && defined(__i386__)
sp_digit rr[15]; /* in case r coincides with a or b */
int k;
uint32_t accl;
uint32_t acch;
acch = accl = 0;
for (k = 0; k < 15; k++) {
int i, j;
uint32_t acc_hi;
i = k - 7;
if (i < 0)
i = 0;
j = k - i;
acc_hi = 0;
do {
////////////////////////
// uint64_t m = ((uint64_t)a[i]) * b[j];
// acc_hi:acch:accl += m;
asm volatile (
// a[i] is already loaded in %%eax
"\n mull %7"
"\n addl %%eax, %0"
"\n adcl %%edx, %1"
"\n adcl $0, %2"
: "=rm" (accl), "=rm" (acch), "=rm" (acc_hi)
: "0" (accl), "1" (acch), "2" (acc_hi), "a" (a[i]), "m" (b[j])
: "cc", "dx"
);
////////////////////////
j--;
i++;
} while (i != 8 && i <= k);
rr[k] = accl;
accl = acch;
acch = acc_hi;
}
r[15] = accl;
memcpy(r, rr, sizeof(rr));
#elif 0
//TODO: arm assembly (untested)
sp_digit tmp[16];
asm volatile (
"\n mov r5, #0"
"\n mov r6, #0"
"\n mov r7, #0"
"\n mov r8, #0"
"\n 1:"
"\n subs r3, r5, #28"
"\n movcc r3, #0"
"\n sub r4, r5, r3"
"\n 2:"
"\n ldr r14, [%[a], r3]"
"\n ldr r12, [%[b], r4]"
"\n umull r9, r10, r14, r12"
"\n adds r6, r6, r9"
"\n adcs r7, r7, r10"
"\n adc r8, r8, #0"
"\n add r3, r3, #4"
"\n sub r4, r4, #4"
"\n cmp r3, #32"
"\n beq 3f"
"\n cmp r3, r5"
"\n ble 2b"
"\n 3:"
"\n str r6, [%[r], r5]"
"\n mov r6, r7"
"\n mov r7, r8"
"\n mov r8, #0"
"\n add r5, r5, #4"
"\n cmp r5, #56"
"\n ble 1b"
"\n str r6, [%[r], r5]"
: [r] "r" (tmp), [a] "r" (a), [b] "r" (b)
: "memory", "r3", "r4", "r5", "r6", "r7", "r8", "r9", "r10", "r14", "r12"
);
memcpy(r, tmp, sizeof(tmp));
#else
sp_digit rr[15]; /* in case r coincides with a or b */
int i, j, k;
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;
do {
uint64_t m = ((uint64_t)a[i]) * b[j];
acc += m;
if (acc < m)
acc_hi++;
j--;
i++;
} while (i != 8 && i <= k);
rr[k] = acc;
acc = (acc >> 32) | ((uint64_t)acc_hi << 32);
}
r[15] = acc;
memcpy(r, rr, sizeof(rr));
#endif
}
/* Shift number right one bit. Bottom bit is lost. */
static void sp_256_rshift1_8(sp_digit* r, sp_digit* a, sp_digit carry)
{
int i;
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_8(sp_digit* r, const sp_digit* a, const sp_digit* m)
{
int carry = 0;
if (a[0] & 1)
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_8(sp_digit* r, const sp_digit* a, const sp_digit* b
/*, const sp_digit* m*/)
{
// const sp_digit* m = p256_mod;
int carry = sp_256_add_8(r, a, b);
sp_256_norm_8(r);
if (carry) {
sp_256_sub_8_p256_mod(r, r /*, m*/);
sp_256_norm_8(r);
}
}
/* Subtract two Montgomery form numbers (r = a - b % m) */
static void sp_256_mont_sub_8(sp_digit* r, const sp_digit* a, const sp_digit* b
/*, const sp_digit* m*/)
{
const sp_digit* m = p256_mod;
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_8(sp_digit* r, const sp_digit* a /*, const sp_digit* m*/)
{
// const sp_digit* m = p256_mod;
int carry = sp_256_add_8(r, a, a);
sp_256_norm_8(r);
if (carry)
sp_256_sub_8_p256_mod(r, r /*, m*/);
sp_256_norm_8(r);
}
/* Triple a Montgomery form number (r = a + a + a % m) */
static void sp_256_mont_tpl_8(sp_digit* r, const sp_digit* a /*, const sp_digit* m*/)
{
// const sp_digit* m = p256_mod;
int carry = sp_256_add_8(r, a, a);
sp_256_norm_8(r);
if (carry) {
sp_256_sub_8_p256_mod(r, r /*, m*/);
sp_256_norm_8(r);
}
carry = sp_256_add_8(r, r, a);
sp_256_norm_8(r);
if (carry) {
sp_256_sub_8_p256_mod(r, r /*, m*/);
sp_256_norm_8(r);
}
}
/* Shift the result in the high 256 bits down to the bottom. */
static void sp_256_mont_shift_8(sp_digit* r, const sp_digit* a)
{
int i;
for (i = 0; i < 8; i++) {
r[i] = a[i+8];
r[i+8] = 0;
}
}
/* Mul a by scalar b and add into r. (r += a * b) */
static int sp_256_mul_add_8(sp_digit* r /*, const sp_digit* a, sp_digit b*/)
{
// const sp_digit* a = p256_mod;
//a[7..0] = ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff
sp_digit b = r[0];
uint64_t t;
// t = 0;
// 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[8] += (sp_digit)t;
// Unroll, then optimize the above loop:
//uint32_t t_hi;
uint64_t m;
uint32_t t32;
//m = ((uint64_t)b * a[0]) + r[0];
// Since b is r[0] and a[0] is ffffffff, the above optimizes to:
// m = r[0] * ffffffff + r[0] = (r[0] * 100000000 - r[0]) + r[0] = r[0] << 32;
//t += m;
// t = r[0] << 32 = b << 32;
//t_hi = (t < m);
// t_hi = 0;
//r[0] = (sp_digit)t;
r[0] = 0;
//t = (t >> 32) | ((uint64_t)t_hi << 32);
// t = b;
//m = ((uint64_t)b * a[1]) + r[1];
// Since a[1] is ffffffff, the above optimizes to:
// m = b * ffffffff + r[1] = (b * 100000000 - b) + r[1] = (b << 32) - b + r[1];
//t += m;
// t = b + (b << 32) - b + r[1] = (b << 32) + r[1];
//t_hi = (t < m);
// t_hi = 0;
//r[1] = (sp_digit)t;
// r[1] = r[1];
//t = (t >> 32) | ((uint64_t)t_hi << 32);
// t = b;
//m = ((uint64_t)b * a[2]) + r[2];
// Since a[2] is ffffffff, the above optimizes to:
// m = b * ffffffff + r[2] = (b * 100000000 - b) + r[2] = (b << 32) - b + r[2];
//t += m;
// t = b + (b << 32) - b + r[2] = (b << 32) + r[2]
//t_hi = (t < m);
// t_hi = 0;
//r[2] = (sp_digit)t;
// r[2] = r[2];
//t = (t >> 32) | ((uint64_t)t_hi << 32);
// t = b;
//m = ((uint64_t)b * a[3]) + r[3];
// Since a[3] is 00000000, the above optimizes to:
// m = b * 0 + r[3] = r[3];
//t += m;
// t = b + r[3];
//t_hi = (t < m);
// t_hi = 0;
//r[3] = (sp_digit)t;
r[3] = r[3] + b;
//t = (t >> 32) | ((uint64_t)t_hi << 32);
t32 = (r[3] < b); // 0 or 1
//m = ((uint64_t)b * a[4]) + r[4];
// Since a[4] is 00000000, the above optimizes to:
// m = b * 0 + r[4] = r[4];
//t += m;
// t = t32 + r[4];
//t_hi = (t < m);
// t_hi = 0;
//r[4] = (sp_digit)t;
//t = (t >> 32) | ((uint64_t)t_hi << 32);
if (t32 != 0) {
r[4]++;
t32 = (r[4] == 0); // 0 or 1
//m = ((uint64_t)b * a[5]) + r[5];
// Since a[5] is 00000000, the above optimizes to:
// m = b * 0 + r[5] = r[5];
//t += m;
// t = t32 + r[5]; (t32 is 0 or 1)
//t_hi = (t < m);
// t_hi = 0;
//r[5] = (sp_digit)t;
//t = (t >> 32) | ((uint64_t)t_hi << 32);
if (t32 != 0) {
r[5]++;
t32 = (r[5] == 0); // 0 or 1
}
}
//m = ((uint64_t)b * a[6]) + r[6];
// Since a[6] is 00000001, the above optimizes to:
// m = (uint64_t)b + r[6]; // 33 bits at most
//t += m;
t = t32 + (uint64_t)b + r[6];
//t_hi = (t < m);
// t_hi = 0;
r[6] = (sp_digit)t;
//t = (t >> 32) | ((uint64_t)t_hi << 32);
t = (t >> 32);
//m = ((uint64_t)b * a[7]) + r[7];
// Since a[7] is ffffffff, the above optimizes to:
// m = b * ffffffff + r[7] = (b * 100000000 - b) + r[7]
m = ((uint64_t)b << 32) - b + r[7];
t += m;
//t_hi = (t < m);
// t_hi in fact is always 0 here (256bit * 32bit can't have more than 32 bits of overflow)
r[7] = (sp_digit)t;
//t = (t >> 32) | ((uint64_t)t_hi << 32);
t = (t >> 32);
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.
*
* a A single precision number to reduce in place.
* 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_8(sp_digit* a/*, const sp_digit* m, sp_digit mp*/)
{
// const sp_digit* m = p256_mod;
sp_digit mp = p256_mp_mod;
int i;
// sp_digit mu;
if (mp != 1) {
sp_digit word16th = 0;
for (i = 0; i < 8; i++) {
// mu = (sp_digit)(a[i] * mp);
if (sp_256_mul_add_8(a+i /*, m, mu*/)) {
int j = i + 8;
inc_next_word0:
if (++j > 15) { /* a[16] array has no more words? */
word16th++;
continue;
}
if (++a[j] == 0) /* did this overflow too? */
goto inc_next_word0;
}
}
sp_256_mont_shift_8(a, a);
if (word16th != 0)
sp_256_sub_8_p256_mod(a, a /*, m*/);
sp_256_norm_8(a);
}
else { /* Same code for explicit mp == 1 (which is always the case for P256) */
sp_digit word16th = 0;
for (i = 0; i < 8; i++) {
/*mu = a[i];*/
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;
}
}
sp_256_mont_shift_8(a, a);
if (word16th != 0)
sp_256_sub_8_p256_mod(a, a /*, m*/);
sp_256_norm_8(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)
*
* r Result of multiplication.
* a First number to multiply in Montogmery form.
* b Second number to multiply in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
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_8(r, a, b);
sp_256_mont_reduce_8(r /*, m, mp*/);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montogmery form.
* m Modulus (prime).
* mp Montogmery mulitplier.
*/
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_8(r, a, a /*, m, mp*/);
}
/* Invert the number, in Montgomery form, modulo the modulus (prime) of the
* P256 curve. (r = 1 / a mod m)
*
* r Inverse result.
* a Number to invert.
*/
#if 0
/* Mod-2 for the P256 curve. */
static const uint32_t p256_mod_2[8] = {
0xfffffffd,0xffffffff,0xffffffff,0x00000000,
0x00000000,0x00000000,0x00000001,0xffffffff,
};
//Bit pattern:
//2 2 2 2 2 2 2 1...1
//5 5 4 3 2 1 0 9...0 9...1
//543210987654321098765432109876543210987654321098765432109876543210...09876543210...09876543210
//111111111111111111111111111111110000000000000000000000000000000100...00000111111...11111111101
#endif
static void sp_256_mont_inv_8(sp_digit* r, sp_digit* a)
{
sp_digit t[2*8]; //can be just [8]?
int i;
memcpy(t, a, sizeof(sp_digit) * 8);
for (i = 254; i >= 0; i--) {
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_8(t, t, a /*, p256_mod, p256_mp_mod*/);
}
memcpy(r, t, sizeof(sp_digit) * 8);
}
/* Multiply a number by Montogmery normalizer mod modulus (prime).
*
* r The resulting Montgomery form number.
* a The number to convert.
*/
static void sp_256_mod_mul_norm_8(sp_digit* r, const sp_digit* a)
{
int64_t t[8];
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[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;
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;
o = t[7] >> 32; //t[7] &= 0xffffffff;
t[0] += o;
t[3] -= o;
t[6] -= o;
t[7] += o;
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.
*
* r Resulting affine co-ordinate point.
* p Montgomery form projective co-ordinate point.
*/
static void sp_256_map_8(sp_point* r, sp_point* p)
{
sp_digit t1[2*8];
sp_digit t2[2*8];
sp_256_mont_inv_8(t1, p->z);
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_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_8(r->x, p256_mod) >= 0)
sp_256_sub_8_p256_mod(r->x, r->x /*, p256_mod*/);
sp_256_norm_8(r->x);
/* y /= z^3 */
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_8(r->y, p256_mod) >= 0)
sp_256_sub_8_p256_mod(r->y, r->y /*, p256_mod*/);
sp_256_norm_8(r->y);
memset(r->z, 0, sizeof(r->z));
r->z[0] = 1;
}
/* Double the Montgomery form projective point p.
*
* r Result of doubling point.
* p Point to double.
*/
static void sp_256_proj_point_dbl_8(sp_point* r, sp_point* p)
{
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)
return;
if (SP_DEBUG) {
/* unused part of t2, may result in spurios
* differences in debug output. Clear it.
*/
memset(t2, 0, sizeof(t2));
}
/* T1 = Z * Z */
sp_256_mont_sqr_8(t1, r->z /*, p256_mod, p256_mp_mod*/);
/* Z = Y * Z */
sp_256_mont_mul_8(r->z, r->y, r->z /*, p256_mod, p256_mp_mod*/);
/* Z = 2Z */
sp_256_mont_dbl_8(r->z, r->z /*, p256_mod*/);
/* T2 = X - T1 */
sp_256_mont_sub_8(t2, r->x, t1 /*, p256_mod*/);
/* T1 = X + T1 */
sp_256_mont_add_8(t1, r->x, t1 /*, p256_mod*/);
/* T2 = T1 * T2 */
sp_256_mont_mul_8(t2, t1, t2 /*, p256_mod, p256_mp_mod*/);
/* T1 = 3T2 */
sp_256_mont_tpl_8(t1, t2 /*, p256_mod*/);
/* Y = 2Y */
sp_256_mont_dbl_8(r->y, r->y /*, p256_mod*/);
/* Y = Y * Y */
sp_256_mont_sqr_8(r->y, r->y /*, p256_mod, p256_mp_mod*/);
/* T2 = Y * Y */
sp_256_mont_sqr_8(t2, r->y /*, p256_mod, p256_mp_mod*/);
/* T2 = T2/2 */
sp_256_div2_8(t2, t2, p256_mod);
/* Y = Y * X */
sp_256_mont_mul_8(r->y, r->y, r->x /*, p256_mod, p256_mp_mod*/);
/* X = T1 * T1 */
sp_256_mont_mul_8(r->x, t1, t1 /*, p256_mod, p256_mp_mod*/);
/* X = X - Y */
sp_256_mont_sub_8(r->x, r->x, r->y /*, p256_mod*/);
/* X = X - Y */
sp_256_mont_sub_8(r->x, r->x, r->y /*, p256_mod*/);
/* Y = Y - X */
sp_256_mont_sub_8(r->y, r->y, r->x /*, p256_mod*/);
/* Y = Y * T1 */
sp_256_mont_mul_8(r->y, r->y, t1 /*, p256_mod, p256_mp_mod*/);
/* Y = Y - T2 */
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.
*
* r Result of addition.
* p Frist point to add.
* q Second point to add.
*/
static void sp_256_proj_point_add_8(sp_point* r, sp_point* p, sp_point* q)
{
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) {
sp_point* a = p;
p = q;
q = a;
}
/* Check double */
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_8(r, p);
}
else {
sp_point tp;
sp_point *v;
v = r;
if (p->infinity | q->infinity) {
memset(&tp, 0, sizeof(tp));
v = &tp;
}
*r = p->infinity ? *q : *p; /* struct copy */
/* U1 = X1*Z2^2 */
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_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_8(t3, t3, v->y /*, p256_mod, p256_mp_mod*/);
/* S2 = Y2*Z1^3 */
sp_256_mont_mul_8(t4, t4, q->y /*, p256_mod, p256_mp_mod*/);
/* H = U2 - U1 */
sp_256_mont_sub_8(t2, t2, t1 /*, p256_mod*/);
/* R = S2 - S1 */
sp_256_mont_sub_8(t4, t4, t3 /*, p256_mod*/);
/* Z3 = H*Z1*Z2 */
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_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_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*/);
}
}
/* Multiply the point by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* r Resulting point.
* g Point to multiply.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
*/
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 = n; /* for compiler */
int c, y;
memset(t, 0, sizeof(t));
/* t[0] = {0, 0, 1} * norm */
t[0].infinity = 1;
/* t[1] = {g->x, g->y, g->z} * norm */
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);
/* For every bit, starting from most significant... */
k += 7;
c = 256;
for (;;) {
if ((c & 0x1f) == 0) {
if (c == 0)
break;
n = *k--;
}
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));
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_8(r, &t[0]);
else
memcpy(r, &t[0], sizeof(sp_point));
memset(t, 0, sizeof(t)); //paranoia
}
/* Multiply the base point of P256 by the scalar and return the result.
* If map is true then convert result to affine co-ordinates.
*
* r Resulting point.
* k Scalar to multiply by.
* map Indicates whether to convert result to affine.
*/
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 = {...}",
* it would have more zeros than data.
*/
static const uint8_t p256_base_bin[] = {
/* x (big-endian) */
0x6b,0x17,0xd1,0xf2,0xe1,0x2c,0x42,0x47,0xf8,0xbc,0xe6,0xe5,0x63,0xa4,0x40,0xf2,0x77,0x03,0x7d,0x81,0x2d,0xeb,0x33,0xa0,0xf4,0xa1,0x39,0x45,0xd8,0x98,0xc2,0x96,
/* y */
0x4f,0xe3,0x42,0xe2,0xfe,0x1a,0x7f,0x9b,0x8e,0xe7,0xeb,0x4a,0x7c,0x0f,0x9e,0x16,0x2b,0xce,0x33,0x57,0x6b,0x31,0x5e,0xce,0xcb,0xb6,0x40,0x68,0x37,0xbf,0x51,0xf5,
/* z will be set to 1, infinity flag to "false" */
};
sp_point p256_base;
sp_256_point_from_bin2x32(&p256_base, p256_base_bin);
sp_256_ecc_mulmod_8(r, &p256_base, k /*, map*/);
}
/* Multiply the point by the scalar and serialize the X ordinate.
* The number is 0 padded to maximum size on output.
*
* priv Scalar to multiply the point by.
* pub2x32 Point to multiply.
* out32 Buffer to hold X ordinate.
*/
static void sp_ecc_secret_gen_256(const sp_digit priv[8], const uint8_t *pub2x32, uint8_t* out32)
{
sp_point point[1];
#if FIXED_PEER_PUBKEY
memset((void*)pub2x32, 0x55, 64);
#endif
dump_hex("peerkey %s\n", pub2x32, 32); /* in TLS, this is peer's public key */
dump_hex(" %s\n", pub2x32 + 32, 32);
sp_256_point_from_bin2x32(point, pub2x32);
dump_512("point->x %s\n", point->x);
dump_512("point->y %s\n", point->y);
sp_256_ecc_mulmod_8(point, point, priv);
sp_256_to_bin_8(point->x, out32);
dump_hex("out32: %s\n", out32, 32);
}
/* Generates a random scalar in [1..order-1] range. */
static void sp_256_ecc_gen_k_8(sp_digit k[8])
{
/* 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(k, 0x77, 8 * sizeof(k[0]));
#endif
// 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[8], uint8_t *pubkey)
{
sp_point point[1];
sp_256_ecc_gen_k_8(privkey);
dump_256("privkey %s\n", 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_8(point->x, pubkey);
sp_256_to_bin_8(point->y, pubkey + 32);
memset(point, 0, sizeof(point)); //paranoia
}
void FAST_FUNC curve_P256_compute_pubkey_and_premaster(
uint8_t *pubkey2x32, uint8_t *premaster32,
const uint8_t *peerkey2x32)
{
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);
/* Combine our privkey and peer's public key to generate premaster */
sp_ecc_secret_gen_256(privkey, /*x,y:*/peerkey2x32, premaster32);
dump_hex("premaster: %s\n", premaster32, 32);
}
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