/*---------------------------------------------------------------------------*/
void
ecc_add(point_t * P0, point_t * P1, point_t * P2)
{
NN_DIGIT Z0[NUMWORDS];
NN_DIGIT Z1[NUMWORDS];
NN_DIGIT Z2[NUMWORDS];
p_clear(P0);
NN_AssignZero(Z0, NUMWORDS);
NN_AssignZero(Z1, NUMWORDS);
NN_AssignZero(Z2, NUMWORDS);
Z1[0] = 0x01;
Z2[0] = 0x01;
#ifdef ADD_MIX
c_add_mix(P0, Z0, P1, Z1, P2);
#else
ecc_add_proj(P0, Z0, P1, Z1, P2, Z2);
#endif
if(!Z_is_one(Z0)) {
NN_ModInv(Z1, Z0, param.p, NUMWORDS);
NN_ModMultOpt(Z0, Z1, Z1, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(P0->x, P0->x, Z0, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(Z0, Z0, Z1, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(P0->y, P0->y, Z0, param.p, param.omega, NUMWORDS);
}
}
/*
* scalar point multiplication
* P0 = n*basepoint
* pointArray is array of basepoint, pointArray[0] = basepoint, pointArray[1] = 2*basepoint ...
*/
void
ecc_win_mul(point_t * P0, NN_DIGIT * n, point_t * pointArray)
{
int16_t i, tmp;
int8_t j;
NN_DIGIT windex;
NN_DIGIT Z0[NUMWORDS];
NN_DIGIT Z1[NUMWORDS];
#ifndef REPEAT_DOUBLE
int8_t k;
#endif
p_clear(P0);
/* Convert to Jprojective coordinate */
NN_AssignZero(Z0, NUMWORDS);
NN_AssignZero(Z1, NUMWORDS);
Z1[0] = 0x01;
tmp = NN_Digits(n, NUMWORDS);
for(i = tmp - 1; i >= 0; i--) {
for(j = NN_DIGIT_BITS/W_BITS - 1; j >= 0; j--) {
#ifndef REPEAT_DOUBLE
for(k = 0; k < W_BITS; k++) {
ecc_dbl_proj(P0, Z0, P0, Z0);
}
#else
ecc_m_dbl_projective(P0, Z0, W_BITS);
#endif
windex = mask[j] & n[i];
if(windex) {
windex = windex >> (j*W_BITS);
#ifdef ADD_MIX
c_add_mix(P0, Z0, P0, Z0, &(pointArray[windex-1]));
#else
ecc_add_proj(P0, Z0, P0, Z0, &(pointArray[windex-1]), Z1);
#endif
}
}
}
/* Convert back to affine coordinate */
if(!Z_is_one(Z0)) {
NN_ModInv(Z1, Z0, param.p, NUMWORDS);
NN_ModMultOpt(Z0, Z1, Z1, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(P0->x, P0->x, Z0, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(Z0, Z0, Z1, param.p, param.omega, NUMWORDS);
NN_ModMultOpt(P0->y, P0->y, Z0, param.p, param.omega, NUMWORDS);
}
}
/*
* P0 = n * P1
*/
void
ecc_mul ( point_t* P0, point_t* P1, NN_DIGIT* n )
{
int16_t i, tmp;
NN_DIGIT Z0[NUMWORDS];
NN_DIGIT Z1[NUMWORDS];
/* clear point */
p_clear ( P0 );
/* convert to Jprojective coordinate */
NN_AssignZero ( Z0, NUMWORDS );
NN_AssignZero ( Z1, NUMWORDS );
Z1[0] = 0x01;
tmp = NN_Bits ( n, NUMWORDS );
for ( i = tmp-1; i >= 0; i-- )
{
ecc_dbl_proj ( P0, Z0, P0, Z0 );
if ( b_testbit ( n, i ) )
{
#ifdef ADD_MIX
c_add_mix ( P0, Z0, P0, Z0, P1 );
#else
ecc_add_proj ( P0, Z0, P0, Z0, P1, Z1 );
#endif
}
}
/* convert back to affine coordinate */
if ( !Z_is_one ( Z0 ) )
{
NN_ModInv ( Z1, Z0, param.p, NUMWORDS );
NN_ModMultOpt ( Z0, Z1, Z1, param.p, param.omega, NUMWORDS );
NN_ModMultOpt ( P0->x, P0->x, Z0, param.p, param.omega, NUMWORDS );
NN_ModMultOpt ( Z0, Z0, Z1, param.p, param.omega, NUMWORDS );
NN_ModMultOpt ( P0->y, P0->y, Z0, param.p, param.omega, 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);
}