NN_UINT
omega_mul(NN_DIGIT *a, NN_DIGIT *b, NN_DIGIT *omega, NN_UINT digits)
{
#ifdef EIGHT_BIT_PROCESSOR
NN_Assign(a, b, digits);
NN_Add(a+8, a+8, b, digits+1);
return (digits+9);
/* EIGHT_BIT_PROCESSOR */
#elif defined(SIXTEEN_BIT_PROCESSOR)
NN_Assign(a, b, digits);
NN_Add(a+4, a+4, b, digits+1);
return (digits+5);
/* SIXTEEN_BIT_PROCESSOR */
#elif defined(THIRTYTWO_BIT_PROCESSOR)
NN_Assign(a, b, digits);
NN_Add(&a[2], &a[2], b, digits+1);
return (digits+3);
#endif /* THIRTYTWO_BIT_PROCESSOR */
}
NN_UINT
omega_mul(NN_DIGIT *a, NN_DIGIT *b, NN_DIGIT *omega, NN_UINT digits)
{
#ifdef EIGHT_BIT_PROCESSOR
NN_Assign(a, b, digits);
a[digits+12] += NN_AddDigitMult(&a[12], &a[12], omega[12], b, digits);
return (digits+13);
/* EIGHT_BIT_PROCESSOR */
#elif defined(SIXTEEN_BIT_PROCESSOR)
//memset(a, 0, digits*NN_DIGIT_LEN);
NN_Assign(a, b, digits);
a[digits+6] += NN_AddDigitMult(&a[6], &a[6], omega[6], b, digits);
return (digits+7);
/* SIXTEEN_BIT_PROCESSOR */
#elif defined(THIRTYTWO_BIT_PROCESSOR)
NN_Assign(a, b, digits);
a[digits+3] += NN_AddDigitMult(&a[3], &a[3], omega[3], b, digits);
return (digits+4);
#endif /* THIRTYTWO_BIT_PROCESSOR */
}
/*---------------------------------------------------------------------------*/
void
ecc_win_precompute(point_t * baseP, point_t * pointArray)
{
uint8_t i;
NN_Assign(pointArray[0].x, baseP->x, NUMWORDS);
NN_Assign(pointArray[0].y, baseP->y, NUMWORDS);
for(i = 1; i < NUM_POINTS; i++) {
ecc_add(&(pointArray[i]), &(pointArray[i-1]), baseP);
}
for(i = 0; i < NUM_MASKS; i++) {
mask[i] = BASIC_MASK << (W_BITS*i);
}
}
/* Generates a probable prime a between b and c such that a-1 is divisible by d.
Lengths: a[digits], b[digits], c[digits], d[digits].
Assumes b < c, digits < MAX_NN_DIGITS.
Returns RE_NEED_RANDOM if randomStruct not seeded, RE_DATA if
unsuccessful.
*/
int GeneratePrime(NN_DIGIT *a, NN_DIGIT *b, NN_DIGIT *c, NN_DIGIT *d, unsigned int digits, R_RANDOM_STRUCT *randomStruct)
{
int status;
unsigned char block[MAX_NN_DIGITS * NN_DIGIT_LEN];
NN_DIGIT t[MAX_NN_DIGITS], u[MAX_NN_DIGITS];
/* Generate random number between b and c.
*/
if ((status = R_GenerateBytes (block, digits * NN_DIGIT_LEN, randomStruct))!=0) return (status);
NN_Decode (a, digits, block, digits * NN_DIGIT_LEN);
NN_Sub (t, c, b, digits);
NN_ASSIGN_DIGIT (u, 1, digits);
NN_Add (t, t, u, digits);
NN_Mod (a, a, digits, t, digits);
NN_Add (a, a, b, digits);
/* Adjust so that a-1 is divisible by d.
*/
NN_Mod (t, a, digits, d, digits);
NN_Sub (a, a, t, digits);
NN_Add (a, a, u, digits);
if (NN_Cmp (a, b, digits) < 0) NN_Add (a, a, d, digits);
if (NN_Cmp (a, c, digits) > 0) NN_Sub (a, a, d, digits);
/* Search to c in steps of d.
*/
NN_Assign (t, c, digits);
NN_Sub (t, t, d, digits);
while (! ProbablePrime (a, digits)) {
if (NN_Cmp (a, t, digits) > 0) return (RE_DATA);
NN_Add(a, a, d, digits);
};
return (0);
}
/**
* \brief P0 = P1
*/
static void
p_copy(point_t * P0, point_t * P1)
{
NN_Assign(P0->x, P1->x, NUMWORDS);
NN_Assign(P0->y, P1->y, NUMWORDS);
}
/*---------------------------------------------------------------------------*/
void
ecc_add_proj(point_t * P0, NN_DIGIT *Z0, point_t * P1, NN_DIGIT * Z1, point_t * P2, NN_DIGIT * Z2)
{
NN_DIGIT n0[NUMWORDS];
NN_DIGIT n1[NUMWORDS];
NN_DIGIT n2[NUMWORDS];
NN_DIGIT n3[NUMWORDS];
NN_DIGIT n4[NUMWORDS];
NN_DIGIT n5[NUMWORDS];
NN_DIGIT n6[NUMWORDS];
if(NN_Zero(Z1, NUMWORDS)) {
p_copy(P0, P2);
NN_Assign(Z0, Z2, NUMWORDS);
return;
}
if(NN_Zero(Z2, NUMWORDS)) {
p_copy(P0, P1);
NN_Assign(Z0, Z1, NUMWORDS);
return;
}
/* double */
if(p_equal(P1, P2)) {
ecc_dbl_proj(P0, Z0, P1, Z1);
return;
}
/* add_proj
* n1, n2
*/
if(Z_is_one(Z2)) {
/* n1 = P1->x, n2 = P1->y */
NN_Assign(n1, P1->x, NUMWORDS);
NN_Assign(n2, P1->y, NUMWORDS);
} else {
/* n1 = P1->x * Z2^2 */
NN_ModSqrOpt(n0, Z2, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(n1, P1->x, n0, param.p, param.omega, NUMWORDS);
/* n2 = P1->y * Z2^3 */
NN_ModMultOpt(n0, n0, Z2, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(n2, P1->y, n0, param.p, param.omega, NUMWORDS);
}
/* n3, n4 */
if(Z_is_one(Z1)) {
/* n3 = P2->x, n4 = P2->y */
NN_Assign(n3, P2->x, NUMWORDS);
NN_Assign(n4, P2->y, NUMWORDS);
} else {
/* n3 = P2->x * Z1^2 */
NN_ModSqrOpt(n0, Z1, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(n3, P2->x, n0, param.p, param.omega, NUMWORDS);
/* n4 = P2->y * Z1^3 */
NN_ModMultOpt(n0, n0, Z1, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(n4, P2->y, n0, param.p, param.omega, NUMWORDS);
}
/* n5 = n1 - n3, n6 = n2 - n4 */
NN_ModSub(n5, n1, n3, param.p, NUMWORDS);
NN_ModSub(n6, n2, n4, param.p, NUMWORDS);
if(NN_Zero(n5, NUMWORDS)) {
if(NN_Zero(n6, NUMWORDS)) {
/* P1 and P2 are same point */
ecc_dbl_proj(P0, Z0, P1, Z1);
return;
}
} else {
/* P1 is the inverse of P2 */
NN_AssignZero(Z0, NUMWORDS);
return;
}
/* 'n7' = n1 + n3, 'n8' = n2 + n4 */
NN_ModAdd(n1, n1, n3, param.p, NUMWORDS);
NN_ModAdd(n2, n2, n4, param.p, NUMWORDS);
/* Z0 = Z1 * Z2 * n5 */
if(Z_is_one(Z1) && Z_is_one(Z2)) {
NN_Assign(Z0, n5, NUMWORDS);
} else {
if(Z_is_one(Z1)) {
NN_Assign(n0, Z2, NUMWORDS);
} else if(Z_is_one(Z2)) {
NN_Assign(n0, Z1, NUMWORDS);
} else {
NN_ModMultOpt(n0, Z1, Z2, param.p, param.omega, NUMWORDS);
}
NN_ModMultOpt(Z0, n0, n5, param.p, param.omega, NUMWORDS);
}
/* P0->x = n6^2 - n5^2 * 'n7' */
NN_ModSqrOpt(n0, n6, param.p, param.omega, NUMWORDS);
NN_ModSqrOpt(n4, n5, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(n3, n1, n4, param.p, param.omega, NUMWORDS);
NN_ModSub(P0->x, n0, n3, param.p, NUMWORDS);
/* 'n9' = n5^2 * 'n7' - 2 * P0->x */
NN_LShift(n0, P0->x, 1, NUMWORDS);
NN_ModSmall(n0, param.p, NUMWORDS);
NN_ModSub(n0, n3, n0, param.p, NUMWORDS);
/* P0->y = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */
NN_ModMultOpt(n0, n0, n6, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(n5, n4, n5, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(n1, n2, n5, param.p, param.omega, NUMWORDS);
NN_ModSub(n0, n0, n1, param.p, NUMWORDS);
if((n0[0] % 2) == 1) {
NN_Add(n0, n0, param.p, NUMWORDS);
}
NN_RShift(P0->y, n0, 1, NUMWORDS);
}
/*---------------------------------------------------------------------------*/
void
ecc_dbl_proj(point_t * P0, NN_DIGIT *Z0, point_t * P1, NN_DIGIT * Z1)
{
NN_DIGIT n0[NUMWORDS];
NN_DIGIT n1[NUMWORDS];
NN_DIGIT n2[NUMWORDS];
NN_DIGIT n3[NUMWORDS];
if(NN_Zero(Z1, NUMWORDS)) {
NN_AssignZero(Z0, NUMWORDS);
return;
}
// n1
if(Z_is_one(Z1)) {
/* n1 = 3 * P1->x^2 + param.E.a */
NN_ModSqrOpt(n0, P1->x, param.p, param.omega, NUMWORDS);
NN_LShift(n1, n0, 1, NUMWORDS);
NN_ModSmall(n1, param.p, NUMWORDS);
NN_ModAdd(n0, n0, n1, param.p, NUMWORDS);
NN_ModAdd(n1, n0, param.E.a, param.p, NUMWORDS);
} else {
if(param.E.a_minus3) {
/* for a = -3
* n1 = 3 * (X1 + Z1^2) * (X1 - Z1^2) = 3 * X1^2 - 3 * Z1^4
*/
NN_ModSqrOpt(n1, Z1, param.p, param.omega, NUMWORDS);
NN_ModAdd(n0, P1->x, n1, param.p, NUMWORDS);
NN_ModSub(n2, P1->x, n1, param.p, NUMWORDS);
NN_ModMultOpt(n1, n0, n2, param.p, param.omega, NUMWORDS);
NN_LShift(n0, n1, 1, NUMWORDS);
NN_ModSmall(n0, param.p, NUMWORDS);
NN_ModAdd(n1, n0, n1, param.p, NUMWORDS);
} else if (param.E.a_zero) {
/* n1 = 3 * P1->x^2 */
NN_ModSqrOpt(n0, P1->x, param.p, param.omega, NUMWORDS);
NN_LShift(n1, n0, 1, NUMWORDS);
NN_ModSmall(n1, param.p, NUMWORDS);
NN_ModAdd(n1, n0, n1, param.p, NUMWORDS);
} else {
/* n1 = 3 * P1->x^2 + param.E.a * Z1^4 */
NN_ModSqrOpt(n0, P1->x, param.p, param.omega, NUMWORDS);
NN_LShift(n1, n0, 1, NUMWORDS);
NN_ModSmall(n1, param.p, NUMWORDS);
NN_ModAdd(n0, n0, n1, param.p, NUMWORDS);
NN_ModSqrOpt(n1, Z1, param.p, param.omega, NUMWORDS);
NN_ModSqrOpt(n1, n1, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(n1, n1, param.E.a, param.p, param.omega, NUMWORDS);
NN_ModAdd(n1, n1, n0, param.p, NUMWORDS);
}
}
/* Z0 = 2 * P1->y * Z1 */
if(Z_is_one(Z1)) {
NN_Assign(n0, P1->y, NUMWORDS);
} else {
NN_ModMultOpt(n0, P1->y, Z1, param.p, param.omega, NUMWORDS);
}
NN_LShift(Z0, n0, 1, NUMWORDS);
NN_ModSmall(Z0, param.p, NUMWORDS);
/* n2 = 4 * P1->x * P1->y^2 */
NN_ModSqrOpt(n3, P1->y, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(n2, P1->x, n3, param.p, param.omega, NUMWORDS);
NN_LShift(n2, n2, 2, NUMWORDS);
NN_ModSmall(n2, param.p, NUMWORDS);
/* P0->x = n1^2 - 2 * n2 */
NN_LShift(n0, n2, 1, NUMWORDS);
NN_ModSmall(n0, param.p, NUMWORDS);
NN_ModSqrOpt(P0->x, n1, param.p, param.omega, NUMWORDS);
NN_ModSub(P0->x, P0->x, n0, param.p, NUMWORDS);
/* n3 = 8 * P1->y^4 */
NN_ModSqrOpt(n0, n3, param.p, param.omega, NUMWORDS);
NN_LShift(n3, n0, 3, NUMWORDS);
NN_ModSmall(n3, param.p, NUMWORDS);
/* P0->y = n1 * (n2 - P0->x) - n3 */
NN_ModSub(n0, n2, P0->x, param.p, NUMWORDS);
NN_ModMultOpt(n0, n1, n0, param.p, param.omega, NUMWORDS);
NN_ModSub(P0->y, n0, n3, param.p, NUMWORDS);
}
/*---------------------------------------------------------------------------*/
void
ecc_get_order(NN_DIGIT * order)
{
NN_Assign(order, param.r, NUMWORDS);
}
static void
c_add_mix(point_t * P0, NN_DIGIT *Z0, point_t * P1, NN_DIGIT * Z1, point_t * P2)
{
NN_DIGIT t1[NUMWORDS];
NN_DIGIT t2[NUMWORDS];
NN_DIGIT t3[NUMWORDS];
NN_DIGIT t4[NUMWORDS];
NN_DIGIT Z2[NUMWORDS];
/* P2 == infinity */
if(NN_Zero(P2->x, NUMWORDS)) {
if(NN_Zero(P2->y, NUMWORDS)) {
p_copy(P0, P1);
NN_Assign(Z0, Z1, NUMWORDS);
return;
}
}
/* P1 == infinity */
if(NN_Zero(Z1, NUMWORDS)) {
p_copy(P0, P2);
NN_AssignDigit(Z0, 1, NUMWORDS);
return;
}
/* T1 = Z1^2 */
NN_ModSqrOpt(t1, Z1, param.p, param.omega, NUMWORDS);
/* T2 = T1*Z1 */
NN_ModMultOpt(t2, t1, Z1, param.p, param.omega, NUMWORDS);
/* T1 = T1*P2->x */
NN_ModMultOpt(t1, t1, P2->x, param.p, param.omega, NUMWORDS);
/* T2 = T2*P2->y */
NN_ModMultOpt(t2, t2, P2->y, param.p, param.omega, NUMWORDS);
/* T1 = T1-P1->x */
NN_ModSub(t1, t1, P1->x, param.p, NUMWORDS);
/* T2 = T2-P1->y */
NN_ModSub(t2, t2, P1->y, param.p, NUMWORDS);
if(NN_Zero(t1, NUMWORDS)) {
if(NN_Zero(t2, NUMWORDS)) {
NN_AssignDigit(Z2, 1, NUMWORDS);
ecc_dbl_proj(P0, Z0, P2, Z2);
return;
} else {
NN_AssignDigit(Z0, 0, NUMWORDS);
return;
}
}
/* Z3 = Z1*T1 */
NN_ModMultOpt(Z0, Z1, t1, param.p, param.omega, NUMWORDS);
/* T3 = T1^2 */
NN_ModSqrOpt(t3, t1, param.p, param.omega, NUMWORDS);
/* T4 = T3*T1 */
NN_ModMultOpt(t4, t3, t1, param.p, param.omega, NUMWORDS);
/* T3 = T3*P1->x */
NN_ModMultOpt(t3, t3, P1->x, param.p, param.omega, NUMWORDS);
/* T1 = 2*T3 */
NN_LShift(t1, t3, 1, NUMWORDS);
NN_ModSmall(t1, param.p, NUMWORDS);
/* P0->x = T2^2 */
NN_ModSqrOpt(P0->x, t2, param.p, param.omega, NUMWORDS);
/* P0->x = P0->x-T1 */
NN_ModSub(P0->x, P0->x, t1, param.p, NUMWORDS);
/* P0->x = P0->x-T4 */
NN_ModSub(P0->x, P0->x, t4, param.p, NUMWORDS);
/* T3 = T3-P0->x */
NN_ModSub(t3, t3, P0->x, param.p, NUMWORDS);
/* T3 = T3*T2 */
NN_ModMultOpt(t3, t3, t2, param.p, param.omega, NUMWORDS);
/* T4 = T4*P1->y */
NN_ModMultOpt(t4, t4, P1->y, param.p, param.omega, NUMWORDS);
/* P0->y = T3-T4 */
NN_ModSub(P0->y, t3, t4, param.p, NUMWORDS);
return;
}