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busybox/networking/tls_sp_c32.c
Denys Vlasenko 8514b4166d tls: P256: enable 64-bit version of montgomery reduction 
After more testing, (1) I'm more sure it is indeed correct, and
(2) it is a significant speedup - we do a lot of those multiplications.

function                                             old     new   delta
sp_512to256_mont_reduce_8                            191     223     +32

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>
2021-11-28 21:43:51 +01:00

1518 lines
38 KiB
C
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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;
/* 64-bit optimizations:
* if BB_UNALIGNED_MEMACCESS_OK && ULONG_MAX > 0xffffffff,
* then loads and stores can be done in 64-bit chunks.
*
* A narrower case is when arch is also little-endian (such as x86_64),
* then "LSW first", uint32[8] and uint64[4] representations are equivalent,
* and arithmetic can be done in 64 bits too.
*/
#if defined(__GNUC__) && defined(__x86_64__)
# define UNALIGNED_LE_64BIT 1
#else
# define UNALIGNED_LE_64BIT 0
#endif
/* The code below is taken from parts of
* wolfssl-3.15.3/wolfcrypt/src/sp_c32.c
* and heavily modified.
*/
typedef struct sp_point {
sp_digit x[8]
#if ULONG_MAX > 0xffffffff
/* Make sp_point[] arrays to not be 64-bit misaligned */
ALIGNED(8)
#endif
;
sp_digit y[8];
sp_digit z[8];
int infinity;
} sp_point;
/* The modulus (prime) of the curve P256. */
static const sp_digit p256_mod[8] ALIGNED(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.
*/
#if BB_UNALIGNED_MEMACCESS_OK && ULONG_MAX > 0xffffffff
static void sp_256_to_bin_8(const sp_digit* rr, uint8_t* a)
{
int i;
const uint64_t* r = (void*)rr;
sp_256_norm_8(rr);
r += 4;
for (i = 0; i < 4; i++) {
r--;
move_to_unaligned64(a, SWAP_BE64(*r));
a += 8;
}
}
#else
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;
}
}
#endif
/* Read big endian unsigned byte array into r.
*
* r A single precision integer.
* a Byte array.
* n Number of bytes in array to read.
*/
#if BB_UNALIGNED_MEMACCESS_OK && ULONG_MAX > 0xffffffff
static void sp_256_from_bin_8(sp_digit* rr, const uint8_t* a)
{
int i;
uint64_t* r = (void*)rr;
r += 4;
for (i = 0; i < 4; i++) {
uint64_t v;
move_from_unaligned64(v, a);
*--r = SWAP_BE64(v);
a += 8;
}
}
#else
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;
}
}
#endif
#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.
*/
#if UNALIGNED_LE_64BIT
static signed_sp_digit sp_256_cmp_8(const sp_digit* aa, const sp_digit* bb)
{
const uint64_t* a = (void*)aa;
const uint64_t* b = (void*)bb;
int i;
for (i = 3; i >= 0; i--) {
if (a[i] == b[i])
continue;
return (a[i] > b[i]) * 2 - 1;
}
return 0;
}
#else
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;
}
#endif
/* 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;
#elif ALLOW_ASM && defined(__GNUC__) && defined(__x86_64__)
uint64_t reg;
asm volatile (
"\n movq (%0), %3"
"\n addq (%1), %3"
"\n movq %3, (%2)"
"\n"
"\n movq 1*8(%0), %3"
"\n adcq 1*8(%1), %3"
"\n movq %3, 1*8(%2)"
"\n"
"\n movq 2*8(%0), %3"
"\n adcq 2*8(%1), %3"
"\n movq %3, 2*8(%2)"
"\n"
"\n movq 3*8(%0), %3"
"\n adcq 3*8(%1), %3"
"\n movq %3, 3*8(%2)"
"\n"
"\n sbbq %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;
#elif ALLOW_ASM && defined(__GNUC__) && defined(__x86_64__)
uint64_t reg;
asm volatile (
"\n movq (%0), %3"
"\n subq (%1), %3"
"\n movq %3, (%2)"
"\n"
"\n movq 1*8(%0), %3"
"\n sbbq 1*8(%1), %3"
"\n movq %3, 1*8(%2)"
"\n"
"\n movq 2*8(%0), %3"
"\n sbbq 2*8(%1), %3"
"\n movq %3, 2*8(%2)"
"\n"
"\n movq 3*8(%0), %3"
"\n sbbq 3*8(%1), %3"
"\n movq %3, 3*8(%2)"
"\n"
"\n sbbq %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 r. (r = r - p256_mod). */
#if ALLOW_ASM && defined(__GNUC__) && defined(__i386__)
static void sp_256_sub_8_p256_mod(sp_digit* r)
{
//p256_mod[7..0] = ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff
asm volatile (
"\n subl $0xffffffff, (%0)"
"\n sbbl $0xffffffff, 1*4(%0)"
"\n sbbl $0xffffffff, 2*4(%0)"
"\n sbbl $0, 3*4(%0)"
"\n sbbl $0, 4*4(%0)"
"\n sbbl $0, 5*4(%0)"
"\n sbbl $1, 6*4(%0)"
"\n sbbl $0xffffffff, 7*4(%0)"
"\n"
: "=r" (r)
: "0" (r)
: "memory"
);
}
#elif ALLOW_ASM && defined(__GNUC__) && defined(__x86_64__)
static void sp_256_sub_8_p256_mod(sp_digit* r)
{
uint64_t reg;
uint64_t ooff;
//p256_mod[3..0] = ffffffff00000001 0000000000000000 00000000ffffffff ffffffffffffffff
asm volatile (
"\n addq $1, (%0)" // adding 1 is the same as subtracting ffffffffffffffff
"\n cmc" // only carry bit needs inverting
"\n"
"\n sbbq %1, 1*8(%0)" // %1 holds 00000000ffffffff
"\n"
"\n sbbq $0, 2*8(%0)"
"\n"
"\n movq 3*8(%0), %2"
"\n sbbq $0, %2" // adding 00000000ffffffff (in %1)
"\n addq %1, %2" // is the same as subtracting ffffffff00000001
"\n movq %2, 3*8(%0)"
"\n"
: "=r" (r), "=r" (ooff), "=r" (reg)
: "0" (r), "1" (0x00000000ffffffff)
: "memory"
);
}
#else
static void sp_256_sub_8_p256_mod(sp_digit* r)
{
sp_256_sub_8(r, r, p256_mod);
}
#endif
/* Multiply a and b into r. (r = a * b)
* r should be [16] array (512 bits), and must not coincide with a or b.
*/
static void sp_256to512_mul_8(sp_digit* r, const sp_digit* a, const sp_digit* b)
{
#if ALLOW_ASM && defined(__GNUC__) && defined(__i386__)
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);
r[k] = accl;
accl = acch;
acch = acc_hi;
}
r[15] = accl;
#elif ALLOW_ASM && defined(__GNUC__) && defined(__x86_64__)
const uint64_t* aa = (const void*)a;
const uint64_t* bb = (const void*)b;
uint64_t* rr = (void*)r;
int k;
uint64_t accl;
uint64_t acch;
acch = accl = 0;
for (k = 0; k < 7; k++) {
int i, j;
uint64_t acc_hi;
i = k - 3;
if (i < 0)
i = 0;
j = k - i;
acc_hi = 0;
do {
////////////////////////
// uint128_t m = ((uint128_t)a[i]) * b[j];
// acc_hi:acch:accl += m;
asm volatile (
// aa[i] is already loaded in %%rax
"\n mulq %7"
"\n addq %%rax, %0"
"\n adcq %%rdx, %1"
"\n adcq $0, %2"
: "=rm" (accl), "=rm" (acch), "=rm" (acc_hi)
: "0" (accl), "1" (acch), "2" (acc_hi), "a" (aa[i]), "m" (bb[j])
: "cc", "dx"
);
////////////////////////
j--;
i++;
} while (i != 4 && i <= k);
rr[k] = accl;
accl = acch;
acch = acc_hi;
}
rr[7] = accl;
#elif 0
//TODO: arm assembly (untested)
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" (r), [a] "r" (a), [b] "r" (b)
: "memory", "r3", "r4", "r5", "r6", "r7", "r8", "r9", "r10", "r12", "r14"
);
#else
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);
r[k] = acc;
acc = (acc >> 32) | ((uint64_t)acc_hi << 32);
}
r[15] = acc;
#endif
}
/* Shift number right one bit. Bottom bit is lost. */
#if UNALIGNED_LE_64BIT
static void sp_256_rshift1_8(sp_digit* rr, uint64_t carry)
{
uint64_t *r = (void*)rr;
int i;
carry = (((uint64_t)!!carry) << 63);
for (i = 3; i >= 0; i--) {
uint64_t c = r[i] << 63;
r[i] = (r[i] >> 1) | carry;
carry = c;
}
}
#else
static void sp_256_rshift1_8(sp_digit* r, sp_digit carry)
{
int i;
carry = (((sp_digit)!!carry) << 31);
for (i = 7; i >= 0; i--) {
sp_digit c = r[i] << 31;
r[i] = (r[i] >> 1) | carry;
carry = c;
}
}
#endif
/* Divide the number by 2 mod the modulus (prime). (r = (r / 2) % m) */
static void sp_256_div2_8(sp_digit* r /*, const sp_digit* m*/)
{
const sp_digit* m = p256_mod;
int carry = 0;
if (r[0] & 1)
carry = sp_256_add_8(r, r, m);
sp_256_norm_8(r);
sp_256_rshift1_8(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);
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);
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);
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);
sp_256_norm_8(r);
}
}
/* Shift the result in the high 256 bits down to the bottom. */
static void sp_512to256_mont_shift_8(sp_digit* r, sp_digit* a)
{
memcpy(r, a + 8, sizeof(*r) * 8);
}
#if UNALIGNED_LE_64BIT
/* 64-bit little-endian optimized version.
* See generic 32-bit version below for explanation.
* The benefit of this version is: even though r[3] calculation is atrocious,
* we call sp_256_mul_add_4() four times, not 8.
* Measured run time improvement of curve_P256_compute_pubkey_and_premaster()
* call on x86-64: from ~1500us to ~900us. Code size +32 bytes.
*/
static int sp_256_mul_add_4(uint64_t *r /*, const uint64_t* a, uint64_t b*/)
{
uint64_t b = r[0];
# if 0
const uint64_t* a = (const void*)p256_mod;
//a[3..0] = ffffffff00000001 0000000000000000 00000000ffffffff ffffffffffffffff
uint128_t t;
int i;
t = 0;
for (i = 0; i < 4; i++) {
uint32_t t_hi;
uint128_t m = ((uint128_t)b * a[i]) + r[i];
t += m;
t_hi = (t < m);
r[i] = (uint64_t)t;
t = (t >> 64) | ((uint128_t)t_hi << 64);
}
r[4] += (uint64_t)t;
return (r[4] < (uint64_t)t); /* 1 if addition overflowed */
# else
// Unroll, then optimize the above loop:
//uint32_t t_hi;
//uint128_t m;
uint64_t t64, t64u;
//m = ((uint128_t)b * a[0]) + r[0];
// Since b is r[0] and a[0] is ffffffffffffffff, the above optimizes to:
// m = r[0] * ffffffffffffffff + r[0] = (r[0] << 64 - r[0]) + r[0] = r[0] << 64;
//t += m;
// t = r[0] << 64 = b << 64;
//t_hi = (t < m);
// t_hi = 0;
//r[0] = (uint64_t)t;
// r[0] = 0;
//the store can be eliminated since caller won't look at lower 256 bits of the result
//t = (t >> 64) | ((uint128_t)t_hi << 64);
// t = b;
//m = ((uint128_t)b * a[1]) + r[1];
// Since a[1] is 00000000ffffffff, 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] = (uint64_t)t;
r[1] += (b << 32);
//t = (t >> 64) | ((uint128_t)t_hi << 64);
t64 = (r[1] < (b << 32));
t64 += (b >> 32);
//m = ((uint128_t)b * a[2]) + r[2];
// Since a[2] is 0000000000000000, the above optimizes to:
// m = b * 0 + r[2] = r[2];
//t += m;
// t = t64 + r[2];
//t_hi = (t < m);
// t_hi = 0;
//r[2] = (uint64_t)t;
r[2] += t64;
//t = (t >> 64) | ((uint128_t)t_hi << 64);
t64 = (r[2] < t64);
//m = ((uint128_t)b * a[3]) + r[3];
// Since a[3] is ffffffff00000001, the above optimizes to:
// m = b * ffffffff00000001 + r[3];
// m = b + b*ffffffff00000000 + r[3]
// m = b + (b*ffffffff << 32) + r[3]
// m = b + (((b<<32) - b) << 32) + r[3]
//t += m;
// t = t64 + (uint128_t)b + ((((uint128_t)b << 32) - b) << 32) + r[3];
t64 += b;
t64u = (t64 < b);
t64 += r[3];
t64u += (t64 < r[3]);
{ // add ((((uint128_t)b << 32) - b) << 32):
uint64_t lo, hi;
//lo = (((b << 32) - b) << 32
//hi = (((uint128_t)b << 32) - b) >> 32
//but without uint128_t:
hi = (b << 32) - b; /* make lower 32 bits of "hi", part 1 */
b = (b >> 32) - (/*borrowed above?*/(b << 32) < b); /* upper 32 bits of "hi" are in b */
lo = hi << 32; /* (use "hi" value to calculate "lo",... */
t64 += lo; /* ...consume... */
t64u += (t64 < lo); /* ..."lo") */
hi >>= 32; /* make lower 32 bits of "hi", part 2 */
hi |= (b << 32); /* combine lower and upper 32 bits */
t64u += hi; /* consume "hi" */
}
//t_hi = (t < m);
// t_hi = 0;
//r[3] = (uint64_t)t;
r[3] = t64;
//t = (t >> 64) | ((uint128_t)t_hi << 64);
// t = t64u;
r[4] += t64u;
return (r[4] < t64u); /* 1 if addition overflowed */
# endif
}
static void sp_512to256_mont_reduce_8(sp_digit* r, sp_digit* aa/*, const sp_digit* m, sp_digit mp*/)
{
// const sp_digit* m = p256_mod;
int i;
uint64_t *a = (void*)aa;
sp_digit carry = 0;
for (i = 0; i < 4; i++) {
// mu = a[i];
if (sp_256_mul_add_4(a+i /*, m, mu*/)) {
int j = i + 4;
inc_next_word:
if (++j > 7) { /* a[8] array has no more words? */
carry++;
continue;
}
if (++a[j] == 0) /* did this overflow too? */
goto inc_next_word;
}
}
sp_512to256_mont_shift_8(r, aa);
if (carry != 0)
sp_256_sub_8_p256_mod(r);
sp_256_norm_8(r);
}
#else /* Generic 32-bit version */
/* Mul a by scalar b and add into r. (r += a * b)
* a = p256_mod
* b = r[0]
*/
static int sp_256_mul_add_8(sp_digit* r /*, const sp_digit* a, sp_digit b*/)
{
sp_digit b = r[0];
uint64_t t;
# if 0
const sp_digit* a = p256_mod;
//a[7..0] = ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff
int i;
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;
return (r[8] < (sp_digit)t); /* 1 if addition overflowed */
# else
// 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;
//the store can be eliminated since caller won't look at lower 256 bits of the result
//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 */
# endif
}
/* Reduce the number back to 256 bits using Montgomery reduction.
* Note: the result is NOT guaranteed to be less than p256_mod!
* (it is only guaranteed to fit into 256 bits).
*
* r Result.
* a Double-wide number to reduce. Clobbered.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*
* Montgomery reduction on multiprecision integers:
* Montgomery reduction requires products modulo R.
* When R is a power of B [in our case R=2^128, B=2^32], there is a variant
* of Montgomery reduction which requires products only of machine word sized
* integers. T is stored as an little-endian word array a[0..n]. The algorithm
* reduces it one word at a time. First an appropriate multiple of modulus
* is added to make T divisible by B. [In our case, it is p256_mp_mod * a[0].]
* Then a multiple of modulus is added to make T divisible by B^2.
* [In our case, it is (p256_mp_mod * a[1]) << 32.]
* And so on. Eventually T is divisible by R, and after division by R
* the algorithm is in the same place as the usual Montgomery reduction.
*
* TODO: Can conditionally use 64-bit (if bit-little-endian arch) logic?
*/
static void sp_512to256_mont_reduce_8(sp_digit* r, 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_512to256_mont_shift_8(r, a);
if (word16th != 0)
sp_256_sub_8_p256_mod(r);
sp_256_norm_8(r);
}
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_512to256_mont_shift_8(r, a);
if (word16th != 0)
sp_256_sub_8_p256_mod(r);
sp_256_norm_8(r);
}
}
#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 multiplier.
*/
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_digit t[2 * 8];
sp_256to512_mul_8(t, a, b);
sp_512to256_mont_reduce_8(r, t /*, 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 multiplier.
*/
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. Must not coincide with a.
* a Number to invert.
*/
static void sp_256_mont_inv_8(sp_digit* r, sp_digit* a)
{
int i;
memcpy(r, a, sizeof(sp_digit) * 8);
for (i = 254; i >= 0; i--) {
sp_256_mont_sqr_8(r, r /*, p256_mod, p256_mp_mod*/);
/* p256_mod - 2:
* ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff - 2
* 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
*/
/*if (p256_mod_minus_2[i / 32] & ((sp_digit)1 << (i % 32)))*/
if (i >= 224 || i == 192 || (i <= 95 && i != 1))
sp_256_mont_mul_8(r, r, a /*, p256_mod, p256_mp_mod*/);
}
}
/* 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[8];
sp_digit t2[8];
sp_digit rr[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(rr, p->x, t2 /*, p256_mod, p256_mp_mod*/);
memset(rr + 8, 0, sizeof(rr) / 2);
sp_512to256_mont_reduce_8(r->x, rr /*, 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);
sp_256_norm_8(r->x);
/* y /= z^3 */
sp_256_mont_mul_8(rr, p->y, t1 /*, p256_mod, p256_mp_mod*/);
memset(rr + 8, 0, sizeof(rr) / 2);
sp_512to256_mont_reduce_8(r->y, rr /*, 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);
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[8];
sp_digit t2[8];
/* Put point to double into result */
if (r != p)
*r = *p; /* struct copy */
if (r->infinity)
return;
/* 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 /*, 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 NOINLINE void sp_256_proj_point_add_8(sp_point* r, sp_point* p, sp_point* q)
{
sp_digit t1[8];
sp_digit t2[8];
sp_digit t3[8];
sp_digit t4[8];
sp_digit t5[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);
return;
}
if (p->infinity || q->infinity) {
*r = p->infinity ? *q : *p; /* struct copy */
return;
}
/* 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, r->x /*, p256_mod, p256_mp_mod*/);
/* U2 = X2*Z1^2 */
sp_256_mont_sqr_8(t2, r->z /*, p256_mod, p256_mp_mod*/);
sp_256_mont_mul_8(t4, t2, r->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, r->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(r->z, r->z, q->z /*, p256_mod, p256_mp_mod*/);
sp_256_mont_mul_8(r->z, r->z, t2 /*, p256_mod, p256_mp_mod*/);
/* X3 = R^2 - H^3 - 2*U1*H^2 */
sp_256_mont_sqr_8(r->x, t4 /*, p256_mod, p256_mp_mod*/);
sp_256_mont_sqr_8(t5, t2 /*, p256_mod, p256_mp_mod*/);
sp_256_mont_mul_8(r->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(r->x, r->x, t5 /*, p256_mod*/);
sp_256_mont_dbl_8(t1, r->y /*, p256_mod*/);
sp_256_mont_sub_8(r->x, r->x, t1 /*, p256_mod*/);
/* Y3 = R*(U1*H^2 - X3) - S1*H^3 */
sp_256_mont_sub_8(r->y, r->y, r->x /*, p256_mod*/);
sp_256_mont_mul_8(r->y, r->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(r->y, r->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);
t[2] = t[y]; /* struct copy */
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);
t[y] = t[2]; /* struct copy */
n <<= 1;
c--;
}
if (map)
sp_256_map_8(r, &t[0]);
else
*r = t[0]; /* struct copy */
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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