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ecc.c
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ecc.c
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#include "ecc.h"
#include <string.h>
#include <stdlib.h>
typedef unsigned int uint;
#define CONCAT1(a, b) a##b
#define CONCAT(a, b) CONCAT1(a, b)
#define Curve_P_16 { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFD, 0xFF, 0xFF, 0xFF }
#define Curve_P_24 { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF }
#define Curve_P_32 { 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \
0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF }
#define Curve_P_48 { 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0x00, \
0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF }
#define Curve_B_16 { 0xD3, 0x5E, 0xEE, 0x2C, 0x3C, 0x99, 0x24, 0xD8, 0x3D, \
0xF4, 0x79, 0x10, 0xC1, 0x79, 0x75, 0xE8 }
#define Curve_B_24 { 0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE, 0x49, \
0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F, 0xE7, 0x80, 0x9C, 0xE5, 0x19, \
0x05, 0x21, 0x64 }
#define Curve_B_32 { 0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B, 0xF6, \
0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65, 0xBC, 0x86, 0x98, 0x76, 0x55, \
0xBD, 0xEB, 0xB3, 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A }
#define Curve_B_48 { 0xEF, 0x2A, 0xEC, 0xD3, 0xED, 0xC8, 0x85, 0x2A, 0x9D, \
0xD1, 0x2E, 0x8A, 0x8D, 0x39, 0x56, 0xC6, 0x5A, 0x87, 0x13, 0x50, 0x8F, \
0x08, 0x14, 0x03, 0x12, 0x41, 0x81, 0xFE, 0x6E, 0x9C, 0x1D, 0x18, 0x19, \
0x2D, 0xF8, 0xE3, 0x6B, 0x05, 0x8E, 0x98, 0xE4, 0xE7, 0x3E, 0xE2, 0xA7, \
0x2F, 0x31, 0xB3 }
#define Curve_G_16 { \
{0x86, 0x5B, 0x2C, 0xA5, 0x7C, 0x60, 0x28, 0x0C, 0x2D, 0x9B, 0x89, 0x8B, \
0x52, 0xF7, 0x1F, 0x16}, \
{0x83, 0x7A, 0xED, 0xDD, 0x92, 0xA2, 0x2D, 0xC0, 0x13, 0xEB, 0xAF, 0x5B, \
0x39, 0xC8, 0x5A, 0xCF}}
#define Curve_G_24 { \
{0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4, 0x00, 0x88, 0xA1, 0x43, \
0xEB, 0x20, 0xBF, 0x7C, 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, \
0x18}, \
{0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73, 0xD5, 0xCD, 0x24, 0x6B, \
0xED, 0x11, 0x10, 0x63, 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, \
0x07}}
#define Curve_G_32 { \
{0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4, 0xA0, 0x33, 0xEB, 0x2D, \
0x81, 0x7D, 0x03, 0x77, 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, \
0xF8, 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B}, \
{0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB, 0xCE, 0x5E, 0x31, 0x6B, \
0x57, 0x33, 0xCE, 0x2B, 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, \
0x8E, 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F}}
#define Curve_G_48 { \
{0xB7, 0x0A, 0x76, 0x72, 0x38, 0x5E, 0x54, 0x3A, 0x6C, 0x29, 0x55, 0xBF, \
0x5D, 0xF2, 0x02, 0x55, 0x38, 0x2A, 0x54, 0x82, 0xE0, 0x41, 0xF7, \
0x59, 0x98, 0x9B, 0xA7, 0x8B, 0x62, 0x3B, 0x1D, 0x6E, 0x74, 0xAD, \
0x20, 0xF3, 0x1E, 0xC7, 0xB1, 0x8E, 0x37, 0x05, 0x8B, 0xBE, 0x22, \
0xCA, 0x87, 0xAA}, \
{0x5F, 0x0E, 0xEA, 0x90, 0x7C, 0x1D, 0x43, 0x7A, 0x9D, 0x81, 0x7E, 0x1D, \
0xCE, 0xB1, 0x60, 0x0A, 0xC0, 0xB8, 0xF0, 0xB5, 0x13, 0x31, 0xDA, \
0xE9, 0x7C, 0x14, 0x9A, 0x28, 0xBD, 0x1D, 0xF4, 0xF8, 0x29, 0xDC, \
0x92, 0x92, 0xBF, 0x98, 0x9E, 0x5D, 0x6F, 0x2C, 0x26, 0x96, 0x4A, \
0xDE, 0x17, 0x36}}
#define Curve_N_16 { 0x15, 0xA1, 0x38, 0x90, 0x1B, 0x0D, 0xA3, 0x75, 0x00, \
0x00, 0x00, 0x00, 0xFE, 0xFF, 0xFF, 0xFF }
#define Curve_N_24 { 0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14, 0x36, \
0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF}
#define Curve_N_32 { 0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3, 0x84, \
0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF }
#define Curve_N_48 { 0x73, 0x29, 0xC5, 0xCC, 0x6A, 0x19, 0xEC, 0xEC, 0x7A, \
0xA7, 0xB0, 0x48, 0xB2, 0x0D, 0x1A, 0x58, 0xDF, 0x2D, 0x37, 0xF4, 0x81, \
0x4D, 0x63, 0xC7, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
0xFF, 0xFF, 0xFF}
static uint8_t curve_p[NUM_ECC_DIGITS] = CONCAT(Curve_P_, ECC_CURVE);
static uint8_t curve_b[NUM_ECC_DIGITS] = CONCAT(Curve_B_, ECC_CURVE);
static EccPoint curve_G = CONCAT(Curve_G_, ECC_CURVE);
static uint8_t curve_n[NUM_ECC_DIGITS] = CONCAT(Curve_N_, ECC_CURVE);
static void vli_clear(uint8_t *p_vli)
{
uint i;
for(i=0; i<NUM_ECC_DIGITS; ++i)
{
p_vli[i] = 0;
}
}
/* Returns 1 if p_vli == 0, 0 otherwise. */
static int vli_isZero(uint8_t *p_vli)
{
uint i;
for(i = 0; i < NUM_ECC_DIGITS; ++i)
{
if(p_vli[i])
{
return 0;
}
}
return 1;
}
/* Returns nonzero if bit p_bit of p_vli is set. */
static uint8_t vli_testBit(uint8_t *p_vli, uint p_bit)
{
return (p_vli[p_bit/8] & (1 << (p_bit % 8)));
}
/* Counts the number of 8-bit "digits" in p_vli. */
static uint vli_numDigits(uint8_t *p_vli)
{
int i;
/* Search from the end until we find a non-zero digit.
We do it in reverse because we expect that most digits will be nonzero. */
for(i = NUM_ECC_DIGITS - 1; i >= 0 && p_vli[i] == 0; --i)
{
}
return (i + 1);
}
/* Counts the number of bits required for p_vli. */
static uint vli_numBits(uint8_t *p_vli)
{
uint i;
uint8_t l_digit;
uint l_numDigits = vli_numDigits(p_vli);
if(l_numDigits == 0)
{
return 0;
}
l_digit = p_vli[l_numDigits - 1];
for(i=0; l_digit; ++i)
{
l_digit >>= 1;
}
return ((l_numDigits - 1) * 8 + i);
}
/* Sets p_dest = p_src. */
static void vli_set(uint8_t *p_dest, uint8_t *p_src)
{
uint i;
for(i=0; i<NUM_ECC_DIGITS; ++i)
{
p_dest[i] = p_src[i];
}
}
/* Returns sign of p_left - p_right. */
static int vli_cmp(uint8_t *p_left, uint8_t *p_right)
{
int i;
for(i = NUM_ECC_DIGITS-1; i >= 0; --i)
{
if(p_left[i] > p_right[i])
{
return 1;
}
else if(p_left[i] < p_right[i])
{
return -1;
}
}
return 0;
}
/* Computes p_result = p_in << c, returning carry. Can modify in place (if p_result == p_in). 0 < p_shift < 8. */
static uint8_t vli_lshift(uint8_t *p_result, uint8_t *p_in, uint p_shift)
{
uint8_t l_carry = 0;
uint i;
for(i = 0; i < NUM_ECC_DIGITS; ++i)
{
uint8_t l_temp = p_in[i];
p_result[i] = (l_temp << p_shift) | l_carry;
l_carry = l_temp >> (8 - p_shift);
}
return l_carry;
}
/* Computes p_vli = p_vli >> 1. */
static void vli_rshift1(uint8_t *p_vli)
{
uint8_t *l_end = p_vli;
uint8_t l_carry = 0;
p_vli += NUM_ECC_DIGITS;
while(p_vli-- > l_end)
{
uint8_t l_temp = *p_vli;
*p_vli = (l_temp >> 1) | l_carry;
l_carry = l_temp << 7;
}
}
/* Computes p_result = p_left + p_right, returning carry. Can modify in place. */
static uint8_t vli_add(uint8_t *p_result, uint8_t *p_left, uint8_t *p_right)
{
uint8_t l_carry = 0;
uint i;
for(i=0; i<NUM_ECC_DIGITS; ++i)
{
uint8_t l_sum = p_left[i] + p_right[i] + l_carry;
if(l_sum != p_left[i])
{
l_carry = (l_sum < p_left[i]);
}
p_result[i] = l_sum;
}
return l_carry;
}
/* Computes p_result = p_left - p_right, returning borrow. Can modify in place. */
static uint8_t vli_sub(uint8_t *p_result, uint8_t *p_left, uint8_t *p_right)
{
uint8_t l_borrow = 0;
uint i;
for(i=0; i<NUM_ECC_DIGITS; ++i)
{
uint8_t l_diff = p_left[i] - p_right[i] - l_borrow;
if(l_diff != p_left[i])
{
l_borrow = (l_diff > p_left[i]);
}
p_result[i] = l_diff;
}
return l_borrow;
}
/* Computes p_result = p_left * p_right. */
static void vli_mult(uint8_t *p_result, uint8_t *p_left, uint8_t *p_right)
{
uint16_t r01 = 0;
uint8_t r2 = 0;
uint i, k;
/* Compute each digit of p_result in sequence, maintaining the carries. */
for(k=0; k < NUM_ECC_DIGITS*2 - 1; ++k)
{
uint l_min = (k < NUM_ECC_DIGITS ? 0 : (k + 1) - NUM_ECC_DIGITS);
for(i=l_min; i<=k && i<NUM_ECC_DIGITS; ++i)
{
uint16_t l_product = (uint16_t)p_left[i] * p_right[k-i];
r01 += l_product;
r2 += (r01 < l_product);
}
p_result[k] = (uint8_t)r01;
r01 = (r01 >> 8) | (((uint16_t)r2) << 8);
r2 = 0;
}
p_result[NUM_ECC_DIGITS*2 - 1] = (uint8_t)r01;
}
/* Computes p_result = (p_left + p_right) % p_mod.
Assumes that p_left < p_mod and p_right < p_mod, p_result != p_mod. */
static void vli_modAdd(uint8_t *p_result, uint8_t *p_left, uint8_t *p_right, uint8_t *p_mod)
{
uint8_t l_carry = vli_add(p_result, p_left, p_right);
if(l_carry || vli_cmp(p_result, p_mod) >= 0)
{ /* p_result > p_mod (p_result = p_mod + remainder), so subtract p_mod to get remainder. */
vli_sub(p_result, p_result, p_mod);
}
}
/* Computes p_result = (p_left - p_right) % p_mod.
Assumes that p_left < p_mod and p_right < p_mod, p_result != p_mod. */
static void vli_modSub(uint8_t *p_result, uint8_t *p_left, uint8_t *p_right, uint8_t *p_mod)
{
uint8_t l_borrow = vli_sub(p_result, p_left, p_right);
if(l_borrow)
{ /* In this case, p_result == -diff == (max int) - diff.
Since -x % d == d - x, we can get the correct result from p_result + p_mod (with overflow). */
vli_add(p_result, p_result, p_mod);
}
}
#if ECC_CURVE == secp128r1
/* Computes p_result = p_product % curve_p.
See algorithm 5 and 6 from http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf */
static void vli_mmod_fast(uint8_t *p_result, uint8_t *p_product)
{
uint8_t l_tmp[NUM_ECC_DIGITS];
int l_carry;
vli_set(p_result, p_product);
l_tmp[0] = p_product[16];
l_tmp[1] = p_product[17];
l_tmp[2] = p_product[18];
l_tmp[3] = p_product[19];
l_tmp[4] = p_product[20];
l_tmp[5] = p_product[21];
l_tmp[6] = p_product[22];
l_tmp[7] = p_product[23];
l_tmp[8] = p_product[24];
l_tmp[9] = p_product[25];
l_tmp[10] = p_product[26];
l_tmp[11] = p_product[27];
l_tmp[12] = (p_product[28] & 1) | (p_product[16] << 1);
l_tmp[13] = (p_product[16] >> 7) | (p_product[17] << 1);
l_tmp[14] = (p_product[17] >> 7) | (p_product[18] << 1);
l_tmp[15] = (p_product[18] >> 7) | (p_product[19] << 1);
l_carry = vli_add(p_result, p_result, l_tmp);
l_tmp[0] = (p_product[19] >> 7) | (p_product[20] << 1);
l_tmp[1] = (p_product[20] >> 7) | (p_product[21] << 1);
l_tmp[2] = (p_product[21] >> 7) | (p_product[22] << 1);
l_tmp[3] = (p_product[22] >> 7) | (p_product[23] << 1);
l_tmp[4] = (p_product[23] >> 7) | (p_product[24] << 1);
l_tmp[5] = (p_product[24] >> 7) | (p_product[25] << 1);
l_tmp[6] = (p_product[25] >> 7) | (p_product[26] << 1);
l_tmp[7] = (p_product[26] >> 7) | (p_product[27] << 1);
l_tmp[8] = (p_product[27] >> 7) | (p_product[28] << 1);
l_tmp[9] = (p_product[28] >> 7) | (p_product[29] << 1);
l_tmp[10] = (p_product[29] >> 7) | (p_product[30] << 1);
l_tmp[11] = (p_product[30] >> 7) | (p_product[31] << 1);
l_tmp[12] = (p_product[31] >> 7) | ((p_product[19] & 0x80) >> 6) | (p_product[20] << 2);
l_tmp[13] = (p_product[20] >> 6) | (p_product[21] << 2);
l_tmp[14] = (p_product[21] >> 6) | (p_product[22] << 2);
l_tmp[15] = (p_product[22] >> 6) | (p_product[23] << 2);
l_carry += vli_add(p_result, p_result, l_tmp);
l_tmp[0] = (p_product[23] >> 6) | (p_product[24] << 2);
l_tmp[1] = (p_product[24] >> 6) | (p_product[25] << 2);
l_tmp[2] = (p_product[25] >> 6) | (p_product[26] << 2);
l_tmp[3] = (p_product[26] >> 6) | (p_product[27] << 2);
l_tmp[4] = (p_product[27] >> 6) | (p_product[28] << 2);
l_tmp[5] = (p_product[28] >> 6) | (p_product[29] << 2);
l_tmp[6] = (p_product[29] >> 6) | (p_product[30] << 2);
l_tmp[7] = (p_product[30] >> 6) | (p_product[31] << 2);
l_tmp[8] = (p_product[31] >> 6);
l_tmp[9] = 0;
l_tmp[10] = 0;
l_tmp[11] = 0;
l_tmp[12] = ((p_product[23] & 0xC0) >> 5) | (p_product[24] << 3);
l_tmp[13] = (p_product[24] >> 5) | (p_product[25] << 3);
l_tmp[14] = (p_product[25] >> 5) | (p_product[26] << 3);
l_tmp[15] = (p_product[26] >> 5) | (p_product[27] << 3);
l_carry += vli_add(p_result, p_result, l_tmp);
l_tmp[0] = (p_product[27] >> 5) | (p_product[28] << 3);
l_tmp[1] = (p_product[28] >> 5) | (p_product[29] << 3);
l_tmp[2] = (p_product[29] >> 5) | (p_product[30] << 3);
l_tmp[3] = (p_product[30] >> 5) | (p_product[31] << 3);
l_tmp[4] = (p_product[31] >> 5);
l_tmp[5] = 0;
l_tmp[6] = 0;
l_tmp[7] = 0;
l_tmp[8] = 0;
l_tmp[9] = 0;
l_tmp[10] = 0;
l_tmp[11] = 0;
l_tmp[12] = ((p_product[27] & 0xE0) >> 4) | (p_product[28] << 4);
l_tmp[13] = (p_product[28] >> 4) | (p_product[29] << 4);
l_tmp[14] = (p_product[29] >> 4) | (p_product[30] << 4);
l_tmp[15] = (p_product[30] >> 4) | (p_product[31] << 4);
l_carry += vli_add(p_result, p_result, l_tmp);
l_tmp[0] = (p_product[31] >> 4);
l_tmp[1] = 0;
l_tmp[2] = 0;
l_tmp[3] = 0;
l_tmp[4] = 0;
l_tmp[5] = 0;
l_tmp[6] = 0;
l_tmp[7] = 0;
l_tmp[8] = 0;
l_tmp[9] = 0;
l_tmp[10] = 0;
l_tmp[11] = 0;
l_tmp[12] = (p_product[28] & 0xFE);
l_tmp[13] = p_product[29];
l_tmp[14] = p_product[30];
l_tmp[15] = p_product[31];
l_carry += vli_add(p_result, p_result, l_tmp);
l_tmp[0] = 0;
l_tmp[1] = 0;
l_tmp[2] = 0;
l_tmp[3] = 0;
l_tmp[4] = 0;
l_tmp[5] = 0;
l_tmp[6] = 0;
l_tmp[7] = 0;
l_tmp[8] = 0;
l_tmp[9] = 0;
l_tmp[10] = 0;
l_tmp[11] = 0;
l_tmp[12] = ((p_product[31] & 0xF0) >> 3);
l_tmp[13] = 0;
l_tmp[14] = 0;
l_tmp[15] = 0;
l_carry += vli_add(p_result, p_result, l_tmp);
while(l_carry || vli_cmp(curve_p, p_result) != 1)
{
l_carry -= vli_sub(p_result, p_result, curve_p);
}
}
#elif ECC_CURVE == secp192r1
/* Computes p_result = p_product % curve_p.
See algorithm 5 and 6 from http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf */
static void vli_mmod_fast(uint8_t *p_result, uint8_t *p_product)
{
uint8_t l_tmp[NUM_ECC_DIGITS];
int l_carry;
vli_set(p_result, p_product);
vli_set(l_tmp, &p_product[NUM_ECC_DIGITS]); // the top 192 bits of result
l_carry = vli_add(p_result, p_result, l_tmp);
l_tmp[0] = l_tmp[1] = l_tmp[2] = l_tmp[3] = 0;
l_tmp[4] = l_tmp[5] = l_tmp[6] = l_tmp[7] = 0;
l_tmp[8] = p_product[24];
l_tmp[9] = p_product[25];
l_tmp[10] = p_product[26];
l_tmp[11] = p_product[27];
l_tmp[12] = p_product[28];
l_tmp[13] = p_product[29];
l_tmp[14] = p_product[30];
l_tmp[15] = p_product[31];
l_tmp[16] = p_product[32];
l_tmp[17] = p_product[33];
l_tmp[18] = p_product[34];
l_tmp[19] = p_product[35];
l_tmp[20] = p_product[36];
l_tmp[21] = p_product[37];
l_tmp[22] = p_product[38];
l_tmp[23] = p_product[39];
l_carry += vli_add(p_result, p_result, l_tmp);
l_tmp[0] = l_tmp[8] = p_product[40];
l_tmp[1] = l_tmp[9] = p_product[41];
l_tmp[2] = l_tmp[10] = p_product[42];
l_tmp[3] = l_tmp[11] = p_product[43];
l_tmp[4] = l_tmp[12] = p_product[44];
l_tmp[5] = l_tmp[13] = p_product[45];
l_tmp[6] = l_tmp[14] = p_product[46];
l_tmp[7] = l_tmp[15] = p_product[47];
l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = 0;
l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0;
l_carry += vli_add(p_result, p_result, l_tmp);
while(l_carry || vli_cmp(curve_p, p_result) != 1)
{
l_carry -= vli_sub(p_result, p_result, curve_p);
}
}
#elif ECC_CURVE == secp256r1
/* Computes p_result = p_product % curve_p
from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void vli_mmod_fast(uint8_t *p_result, uint8_t *p_product)
{
uint8_t l_tmp[NUM_ECC_DIGITS];
int l_carry;
/* t */
vli_set(p_result, p_product);
/* s1 */
l_tmp[0] = l_tmp[1] = l_tmp[2] = l_tmp[3] = 0;
l_tmp[4] = l_tmp[5] = l_tmp[6] = l_tmp[7] = 0;
l_tmp[8] = l_tmp[9] = l_tmp[10] = l_tmp[11] = 0;
l_tmp[12] = p_product[44];
l_tmp[13] = p_product[45];
l_tmp[14] = p_product[46];
l_tmp[15] = p_product[47];
l_tmp[16] = p_product[48];
l_tmp[17] = p_product[49];
l_tmp[18] = p_product[50];
l_tmp[19] = p_product[51];
l_tmp[20] = p_product[52];
l_tmp[21] = p_product[53];
l_tmp[22] = p_product[54];
l_tmp[23] = p_product[55];
l_tmp[24] = p_product[56];
l_tmp[25] = p_product[57];
l_tmp[26] = p_product[58];
l_tmp[27] = p_product[59];
l_tmp[28] = p_product[60];
l_tmp[29] = p_product[61];
l_tmp[30] = p_product[62];
l_tmp[31] = p_product[63];
l_carry = vli_lshift(l_tmp, l_tmp, 1);
l_carry += vli_add(p_result, p_result, l_tmp);
/* s2 */
l_tmp[12] = p_product[48];
l_tmp[13] = p_product[49];
l_tmp[14] = p_product[50];
l_tmp[15] = p_product[51];
l_tmp[16] = p_product[52];
l_tmp[17] = p_product[53];
l_tmp[18] = p_product[54];
l_tmp[19] = p_product[55];
l_tmp[20] = p_product[56];
l_tmp[21] = p_product[57];
l_tmp[22] = p_product[58];
l_tmp[23] = p_product[59];
l_tmp[24] = p_product[60];
l_tmp[25] = p_product[61];
l_tmp[26] = p_product[62];
l_tmp[27] = p_product[63];
l_tmp[28] = 0;
l_tmp[29] = 0;
l_tmp[30] = 0;
l_tmp[31] = 0;
l_carry += vli_lshift(l_tmp, l_tmp, 1);
l_carry += vli_add(p_result, p_result, l_tmp);
/* s3 */
l_tmp[0] = p_product[32];
l_tmp[1] = p_product[33];
l_tmp[2] = p_product[34];
l_tmp[3] = p_product[35];
l_tmp[4] = p_product[36];
l_tmp[5] = p_product[37];
l_tmp[6] = p_product[38];
l_tmp[7] = p_product[39];
l_tmp[8] = p_product[40];
l_tmp[9] = p_product[41];
l_tmp[10] = p_product[42];
l_tmp[11] = p_product[43];
l_tmp[12] = l_tmp[13] = l_tmp[14] = l_tmp[15] = 0;
l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = 0;
l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0;
l_tmp[24] = p_product[56];
l_tmp[25] = p_product[57];
l_tmp[26] = p_product[58];
l_tmp[27] = p_product[59];
l_tmp[28] = p_product[60];
l_tmp[29] = p_product[61];
l_tmp[30] = p_product[62];
l_tmp[31] = p_product[63];
l_carry += vli_add(p_result, p_result, l_tmp);
/* s4 */
l_tmp[0] = p_product[36];
l_tmp[1] = p_product[37];
l_tmp[2] = p_product[38];
l_tmp[3] = p_product[39];
l_tmp[4] = p_product[40];
l_tmp[5] = p_product[41];
l_tmp[6] = p_product[42];
l_tmp[7] = p_product[43];
l_tmp[8] = p_product[44];
l_tmp[9] = p_product[45];
l_tmp[10] = p_product[46];
l_tmp[11] = p_product[47];
l_tmp[12] = p_product[52];
l_tmp[13] = p_product[53];
l_tmp[14] = p_product[54];
l_tmp[15] = p_product[55];
l_tmp[16] = p_product[56];
l_tmp[17] = p_product[57];
l_tmp[18] = p_product[58];
l_tmp[19] = p_product[59];
l_tmp[20] = p_product[60];
l_tmp[21] = p_product[61];
l_tmp[22] = p_product[62];
l_tmp[23] = p_product[63];
l_tmp[24] = p_product[52];
l_tmp[25] = p_product[53];
l_tmp[26] = p_product[54];
l_tmp[27] = p_product[55];
l_tmp[28] = p_product[32];
l_tmp[29] = p_product[33];
l_tmp[30] = p_product[34];
l_tmp[31] = p_product[35];
l_carry += vli_add(p_result, p_result, l_tmp);
/* d1 */
l_tmp[0] = p_product[44];
l_tmp[1] = p_product[45];
l_tmp[2] = p_product[46];
l_tmp[3] = p_product[47];
l_tmp[4] = p_product[48];
l_tmp[5] = p_product[49];
l_tmp[6] = p_product[50];
l_tmp[7] = p_product[51];
l_tmp[8] = p_product[52];
l_tmp[9] = p_product[53];
l_tmp[10] = p_product[54];
l_tmp[11] = p_product[55];
l_tmp[12] = l_tmp[13] = l_tmp[14] = l_tmp[15] = 0;
l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = 0;
l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0;
l_tmp[24] = p_product[32];
l_tmp[25] = p_product[33];
l_tmp[26] = p_product[34];
l_tmp[27] = p_product[35];
l_tmp[28] = p_product[40];
l_tmp[29] = p_product[41];
l_tmp[30] = p_product[42];
l_tmp[31] = p_product[43];
l_carry -= vli_sub(p_result, p_result, l_tmp);
/* d2 */
l_tmp[0] = p_product[48];
l_tmp[1] = p_product[49];
l_tmp[2] = p_product[50];
l_tmp[3] = p_product[51];
l_tmp[4] = p_product[52];
l_tmp[5] = p_product[53];
l_tmp[6] = p_product[54];
l_tmp[7] = p_product[55];
l_tmp[8] = p_product[56];
l_tmp[9] = p_product[57];
l_tmp[10] = p_product[58];
l_tmp[11] = p_product[59];
l_tmp[12] = p_product[60];
l_tmp[13] = p_product[61];
l_tmp[14] = p_product[62];
l_tmp[15] = p_product[63];
l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = 0;
l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0;
l_tmp[24] = p_product[36];
l_tmp[25] = p_product[37];
l_tmp[26] = p_product[38];
l_tmp[27] = p_product[39];
l_tmp[28] = p_product[44];
l_tmp[29] = p_product[45];
l_tmp[30] = p_product[46];
l_tmp[31] = p_product[47];
l_carry -= vli_sub(p_result, p_result, l_tmp);
/* d3 */
l_tmp[0] = p_product[52];
l_tmp[1] = p_product[53];
l_tmp[2] = p_product[54];
l_tmp[3] = p_product[55];
l_tmp[4] = p_product[56];
l_tmp[5] = p_product[57];
l_tmp[6] = p_product[58];
l_tmp[7] = p_product[59];
l_tmp[8] = p_product[60];
l_tmp[9] = p_product[61];
l_tmp[10] = p_product[62];
l_tmp[11] = p_product[63];
l_tmp[12] = p_product[32];
l_tmp[13] = p_product[33];
l_tmp[14] = p_product[34];
l_tmp[15] = p_product[35];
l_tmp[16] = p_product[36];
l_tmp[17] = p_product[37];
l_tmp[18] = p_product[38];
l_tmp[19] = p_product[39];
l_tmp[20] = p_product[40];
l_tmp[21] = p_product[41];
l_tmp[22] = p_product[42];
l_tmp[23] = p_product[43];
l_tmp[24] = l_tmp[25] = l_tmp[26] = l_tmp[27] = 0;
l_tmp[28] = p_product[48];
l_tmp[29] = p_product[49];
l_tmp[30] = p_product[50];
l_tmp[31] = p_product[51];
l_carry -= vli_sub(p_result, p_result, l_tmp);
/* d4 */
l_tmp[0] = p_product[56];
l_tmp[1] = p_product[57];
l_tmp[2] = p_product[58];
l_tmp[3] = p_product[59];
l_tmp[4] = p_product[60];
l_tmp[5] = p_product[61];
l_tmp[6] = p_product[62];
l_tmp[7] = p_product[63];
l_tmp[8] = l_tmp[9] = l_tmp[10] = l_tmp[11] = 0;
l_tmp[12] = p_product[36];
l_tmp[13] = p_product[37];
l_tmp[14] = p_product[38];
l_tmp[15] = p_product[39];
l_tmp[16] = p_product[40];
l_tmp[17] = p_product[41];
l_tmp[18] = p_product[42];
l_tmp[19] = p_product[43];
l_tmp[20] = p_product[44];
l_tmp[21] = p_product[45];
l_tmp[22] = p_product[46];
l_tmp[23] = p_product[47];
l_tmp[24] = l_tmp[25] = l_tmp[26] = l_tmp[27] = 0;
l_tmp[28] = p_product[52];
l_tmp[29] = p_product[53];
l_tmp[30] = p_product[54];
l_tmp[31] = p_product[55];
l_carry -= vli_sub(p_result, p_result, l_tmp);
if(l_carry < 0)
{
do
{
l_carry += vli_add(p_result, p_result, curve_p);
} while(l_carry < 0);
}
else
{
while(l_carry || vli_cmp(curve_p, p_result) != 1)
{
l_carry -= vli_sub(p_result, p_result, curve_p);
}
}
}
#elif ECC_CURVE == secp384r1
static void omega_mult(uint8_t *p_result, uint8_t *p_right)
{
/* Multiply by (2^128 + 2^96 - 2^32 + 1). */
vli_set(p_result, p_right); /* 1 */
p_result[16 + NUM_ECC_DIGITS] = vli_add(p_result + 12, p_result + 12, p_right); /* 2^96 + 1 */
p_result[17 + NUM_ECC_DIGITS] = 0;
p_result[18 + NUM_ECC_DIGITS] = 0;
p_result[19 + NUM_ECC_DIGITS] = 0;
p_result[20 + NUM_ECC_DIGITS] = vli_add(p_result + 16, p_result + 16, p_right); /* 2^128 + 2^96 + 1 */
p_result[21 + NUM_ECC_DIGITS] = 0;
p_result[22 + NUM_ECC_DIGITS] = 0;
p_result[23 + NUM_ECC_DIGITS] = 0;
if(vli_sub(p_result + 4, p_result + 4, p_right)) /* 2^128 + 2^96 - 2^32 + 1 */
{ /* Propagate borrow if necessary. */
uint i;
for(i = 4 + NUM_ECC_DIGITS; ; ++i)
{
--p_result[i];
if(p_result[i] != 0xff)
{
break;
}
}
}
}
/* Computes p_result = p_product % curve_p
see PDF "Comparing Elliptic Curve Cryptography and RSA on 8-bit CPUs"
section "Curve-Specific Optimizations" */
static void vli_mmod_fast(uint8_t *p_result, uint8_t *p_product)
{
uint8_t l_tmp[2*NUM_ECC_DIGITS];
while(!vli_isZero(p_product + NUM_ECC_DIGITS)) /* While c1 != 0 */
{
uint8_t l_carry = 0;
uint i;
vli_clear(l_tmp);
vli_clear(l_tmp + NUM_ECC_DIGITS);
omega_mult(l_tmp, p_product + NUM_ECC_DIGITS); /* tmp = w * c1 */
vli_clear(p_product + NUM_ECC_DIGITS); /* p = c0 */
/* (c1, c0) = c0 + w * c1 */
for(i=0; i<NUM_ECC_DIGITS+20; ++i)
{
uint8_t l_sum = p_product[i] + l_tmp[i] + l_carry;
if(l_sum != p_product[i])
{
l_carry = (l_sum < p_product[i]);
}
p_product[i] = l_sum;
}
}
while(vli_cmp(p_product, curve_p) > 0)
{
vli_sub(p_product, p_product, curve_p);
}
vli_set(p_result, p_product);
}
#endif
/* Computes p_result = (p_left * p_right) % curve_p. */
static void vli_modMult_fast(uint8_t *p_result, uint8_t *p_left, uint8_t *p_right)
{
uint8_t l_product[2 * NUM_ECC_DIGITS];
vli_mult(l_product, p_left, p_right);
vli_mmod_fast(p_result, l_product);
}
#if ECC_SQUARE_FUNC
/* Computes p_result = p_left^2. */
static void vli_square(uint8_t *p_result, uint8_t *p_left)
{
uint16_t r01 = 0;
uint8_t r2 = 0;
uint i, k;
for(k=0; k < NUM_ECC_DIGITS*2 - 1; ++k)
{
uint l_min = (k < NUM_ECC_DIGITS ? 0 : (k + 1) - NUM_ECC_DIGITS);
for(i=l_min; i<=k && i<=k-i; ++i)
{
uint16_t l_product = (uint16_t)p_left[i] * p_left[k-i];
if(i < k-i)
{
r2 += l_product >> 15;
l_product *= 2;
}
r01 += l_product;
r2 += (r01 < l_product);
}
p_result[k] = (uint8_t)r01;
r01 = (r01 >> 8) | (((uint16_t)r2) << 8);
r2 = 0;
}
p_result[NUM_ECC_DIGITS*2 - 1] = (uint8_t)r01;
}
/* Computes p_result = p_left^2 % curve_p. */
static void vli_modSquare_fast(uint8_t *p_result, uint8_t *p_left)
{
uint8_t l_product[2 * NUM_ECC_DIGITS];
vli_square(l_product, p_left);
vli_mmod_fast(p_result, l_product);
}
#else /* ECC_SQUARE_FUNC */
#define vli_square(result, left, size) vli_mult((result), (left), (left), (size))
#define vli_modSquare_fast(result, left) vli_modMult_fast((result), (left), (left))
#endif /* ECC_SQUARE_FUNC */
#define EVEN(vli) (!(vli[0] & 1))
/* Computes p_result = (1 / p_input) % p_mod. All VLIs are the same size.
See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf */
static void vli_modInv(uint8_t *p_result, uint8_t *p_input, uint8_t *p_mod)
{
uint8_t a[NUM_ECC_DIGITS], b[NUM_ECC_DIGITS], u[NUM_ECC_DIGITS], v[NUM_ECC_DIGITS];
uint8_t l_carry;
vli_set(a, p_input);
vli_set(b, p_mod);
vli_clear(u);
u[0] = 1;
vli_clear(v);
int l_cmpResult;
while((l_cmpResult = vli_cmp(a, b)) != 0)
{
l_carry = 0;
if(EVEN(a))
{
vli_rshift1(a);
if(!EVEN(u))
{
l_carry = vli_add(u, u, p_mod);
}
vli_rshift1(u);
if(l_carry)
{
u[NUM_ECC_DIGITS-1] |= 0x80;
}
}
else if(EVEN(b))
{
vli_rshift1(b);
if(!EVEN(v))
{
l_carry = vli_add(v, v, p_mod);
}
vli_rshift1(v);
if(l_carry)
{
v[NUM_ECC_DIGITS-1] |= 0x80;
}
}
else if(l_cmpResult > 0)
{
vli_sub(a, a, b);
vli_rshift1(a);
if(vli_cmp(u, v) < 0)
{
vli_add(u, u, p_mod);
}
vli_sub(u, u, v);
if(!EVEN(u))
{
l_carry = vli_add(u, u, p_mod);
}
vli_rshift1(u);
if(l_carry)
{
u[NUM_ECC_DIGITS-1] |= 0x80;
}
}
else
{
vli_sub(b, b, a);
vli_rshift1(b);
if(vli_cmp(v, u) < 0)
{
vli_add(v, v, p_mod);
}
vli_sub(v, v, u);
if(!EVEN(v))
{
l_carry = vli_add(v, v, p_mod);
}
vli_rshift1(v);
if(l_carry)
{
v[NUM_ECC_DIGITS-1] |= 0x80;
}
}
}
vli_set(p_result, u);
}
/* ------ Point operations ------ */
/* Returns 1 if p_point is the point at infinity, 0 otherwise. */
static int EccPoint_isZero(EccPoint *p_point)
{
return (vli_isZero(p_point->x) && vli_isZero(p_point->y));
}
/* Point multiplication algorithm using Montgomery's ladder with co-Z coordinates.
From http://eprint.iacr.org/2011/338.pdf
*/
/* Double in place */
static void EccPoint_double_jacobian(uint8_t *X1, uint8_t *Y1, uint8_t *Z1)
{
/* t1 = X, t2 = Y, t3 = Z */
uint8_t t4[NUM_ECC_DIGITS];
uint8_t t5[NUM_ECC_DIGITS];
if(vli_isZero(Z1))
{
return;
}
vli_modSquare_fast(t4, Y1); /* t4 = y1^2 */
vli_modMult_fast(t5, X1, t4); /* t5 = x1*y1^2 = A */
vli_modSquare_fast(t4, t4); /* t4 = y1^4 */
vli_modMult_fast(Y1, Y1, Z1); /* t2 = y1*z1 = z3 */
vli_modSquare_fast(Z1, Z1); /* t3 = z1^2 */
vli_modAdd(X1, X1, Z1, curve_p); /* t1 = x1 + z1^2 */
vli_modAdd(Z1, Z1, Z1, curve_p); /* t3 = 2*z1^2 */
vli_modSub(Z1, X1, Z1, curve_p); /* t3 = x1 - z1^2 */
vli_modMult_fast(X1, X1, Z1); /* t1 = x1^2 - z1^4 */
vli_modAdd(Z1, X1, X1, curve_p); /* t3 = 2*(x1^2 - z1^4) */
vli_modAdd(X1, X1, Z1, curve_p); /* t1 = 3*(x1^2 - z1^4) */
if(vli_testBit(X1, 0))
{
uint8_t l_carry = vli_add(X1, X1, curve_p);
vli_rshift1(X1);
X1[NUM_ECC_DIGITS-1] |= l_carry << 7;
}
else
{
vli_rshift1(X1);
}
/* t1 = 3/2*(x1^2 - z1^4) = B */
vli_modSquare_fast(Z1, X1); /* t3 = B^2 */
vli_modSub(Z1, Z1, t5, curve_p); /* t3 = B^2 - A */
vli_modSub(Z1, Z1, t5, curve_p); /* t3 = B^2 - 2A = x3 */
vli_modSub(t5, t5, Z1, curve_p); /* t5 = A - x3 */
vli_modMult_fast(X1, X1, t5); /* t1 = B * (A - x3) */
vli_modSub(t4, X1, t4, curve_p); /* t4 = B * (A - x3) - y1^4 = y3 */
vli_set(X1, Z1);
vli_set(Z1, Y1);
vli_set(Y1, t4);
}
/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
static void apply_z(uint8_t *X1, uint8_t *Y1, uint8_t *Z)