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header.h
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header.h
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#include <stdio.h>
#include <stdlib.h>
#include <gmp.h>
typedef struct {
mpz_t x;
mpz_t y;
mpz_t z;
} POINT_t[1], *POINT;
typedef struct {
POINT_t P;
POINT_t Q;
mpz_t A;
mpz_t p;
mpz_t k;
} SMUL_t[1], *SMUL;
typedef struct {
POINT_t Xd;
POINT_t Xdd;
POINT_t P;
POINT_t Q;
mpz_t cd;
mpz_t dd;
mpz_t cdd;
mpz_t ddd;
mpz_t p;
mpz_t n;
mpz_t k;
} LOOP_t[1], *LOOP;
void sum(SMUL w) {
mpz_t x1, x2, y1, y2, z1, z2, temp1, temp2, temp3, temp4, tempx1, tempy1;
//initialize the temporary variables for operations
mpz_init(temp1);
mpz_init(temp2);
mpz_init(temp3);
mpz_init(temp4);
mpz_init(tempx1);
mpz_init(tempy1);
mpz_init(x1);
mpz_init(x2);
mpz_init(y1);
mpz_init(y2);
mpz_init(z1);
mpz_init(z2);
//setting the variables to multiplicands
mpz_set(x1, w->P->x);
mpz_set(x2, w->Q->x);
mpz_set(y1, w->P->y);
mpz_set(y2, w->Q->y);
mpz_set(z1, w->P->z);
mpz_set(z2, w->Q->z);
if (mpz_cmp_ui(x1, 0) == 0 && mpz_cmp_ui(y1, 1) == 0) {
mpz_set(w->P->x, x2);
mpz_set(w->P->y, y2);
mpz_set(w->P->z, z2);
} else if (mpz_cmp_ui(x2, 0) == 0 && mpz_cmp_ui(y2, 1) == 0) {
mpz_set(w->P->x, x1);
mpz_set(w->P->y, y1);
mpz_set(w->P->z, z1);
} else if (mpz_cmp(x1, x2) == 0) {
if (mpz_cmp(y1, y2) != 0) {
mpz_set_ui(w->P->x, 0);
mpz_set_ui(w->P->y, 1);
mpz_set_ui(w->P->z, 0);
} else if (mpz_cmp_ui(y2, 0) == 0) {
mpz_set_ui(w->P->x, 0);
mpz_set_ui(w->P->y, 1);
mpz_set_ui(w->P->z, 0);
} else
mpz_mul(temp1, x1, x1); //x^2
mpz_mod(temp1, temp1, w->p);
mpz_mul_ui(temp2, temp1, 3); //3*x^2
mpz_mod(temp2, temp2, w->p);
mpz_add(temp1, temp2, w->A); //3*x^2+A
mpz_mod(temp1, temp1, w->p);
mpz_mul_ui(temp2, y1, 2); //2*y1
mpz_mod(temp2, temp2, w->p);
mpz_invert(temp3, temp2, w->p);
mpz_mod(temp3, temp3, w->p);
mpz_mul(temp2, temp1, temp3); //(3*x^2+A)/(2*y1)
mpz_mod(temp2, temp2, w->p);
mpz_mul(temp1, temp2, temp2); //((3*x^2+A)/(2*y1))^2
mpz_mod(temp1, temp1, w->p);
mpz_mul_ui(temp2, x1, 2); //2*x1
mpz_mod(temp2, temp2, w->p);
mpz_sub(temp3, temp1, temp2); //((3*x^2+A)/(2*y1))^2-(2*x1)
mpz_mod(tempx1, temp3, w->p);
mpz_mul(temp1, x1, x1); //x^2
mpz_mod(temp1, temp1, w->p);
mpz_mul_ui(temp2, temp1, 3); //3*x^2
mpz_mod(temp2, temp2, w->p);
mpz_add(temp1, temp2, w->A); //3*x^2+A
mpz_mod(temp1, temp1, w->p);
mpz_mul_ui(temp2, y1, 2); //2*y1
mpz_mod(temp2, temp2, w->p);
mpz_invert(temp3, temp2, w->p);
mpz_mod(temp3, temp3, w->p);
mpz_mul(temp2, temp1, temp3); //(3*x^2+A)/(2*y1)
mpz_mod(temp2, temp2, w->p);
mpz_sub(temp1, x1, tempx1); //x1-x3
mpz_mod(temp1, temp1, w->p);
mpz_mul(temp3, temp2, temp1); //(3*x^2+A)/(2*y1)*(x1-x3)
mpz_mod(temp3, temp3, w->p);
mpz_sub(temp2, temp3, y1); //(3*x^2+A)/(2*y1)*(x1-x3)-y1
mpz_mod(tempy1, temp2, w->p);
mpz_set(w->P->x, tempx1);
mpz_set(w->P->y, tempy1);
mpz_set_ui(w->P->z, 1);
} else {
mpz_sub(temp1, y1, y2); //y1-y2
mpz_mod(temp1, temp1, w->p);
mpz_sub(temp2, x1, x2); //x1-x2
mpz_mod(temp2, temp2, w->p);
mpz_invert(temp3, temp2, w->p);
mpz_mod(temp3, temp3, w->p);
mpz_mul(temp2, temp1, temp3); //(y1- y2)/(x1-x2)
mpz_mod(temp2, temp2, w->p);
mpz_mul(temp1, temp2, temp2); //((y1- y2)/(x1-x2))^2
mpz_mod(temp1, temp1, w->p);
mpz_sub(temp2, temp1, x1); //((y1- y2)/(x1-x2))^2 - x1
mpz_mod(temp2, temp2, w->p);
mpz_sub(temp1, temp2, x2); //((y1- y2)/(x1-x2))^2 - x1- x2
mpz_mod(tempx1, temp1, w->p);
mpz_sub(temp1, y1, y2); //y1-y2
mpz_mod(temp1, temp1, w->p);
mpz_sub(temp2, x1, x2); //x1-x2
mpz_mod(temp2, temp2, w->p);
mpz_invert(temp3, temp2, w->p);
mpz_mod(temp3, temp3, w->p);
mpz_mul(temp2, temp1, temp3); //(y1- y2)/(x1-x2)
mpz_mod(temp2, temp2, w->p);
mpz_sub(temp1, x1, tempx1); //x1-x3
mpz_mod(temp1, temp1, w->p);
mpz_mul(temp3, temp2, temp1); //(y1- y2)/(x1-x2) * (x1-x3)
mpz_mod(temp3, temp3, w->p);
mpz_sub(temp2, temp3, y1); //(y1- y2)/(x1-x2) * (x1-x3) -y1
mpz_mod(tempy1, temp2, w->p);
mpz_set(w->P->x, tempx1);
mpz_set(w->P->y, tempy1);
mpz_set_ui(w->P->z, 1);
mpz_clear(temp1);
mpz_clear(temp2);
mpz_clear(temp3);
mpz_clear(temp4);
mpz_clear(tempx1);
mpz_clear(tempy1);
mpz_clear(x1);
mpz_clear(x2);
mpz_clear(y1);
mpz_clear(y2);
mpz_clear(z1);
mpz_clear(z2);
}
}
void dbl(SMUL wm) {
mpz_t x1, x2, y1, y2, z1, z2, temp1, temp2, temp3, temp4, tempx1, tempy1,
tempmod1, tempmod2, tempmod3;
//initialize the temporary variables for operations
mpz_init(temp1);
mpz_init(temp2);
mpz_init(temp3);
mpz_init(temp4);
mpz_init(tempx1);
mpz_init(tempy1);
mpz_init(tempmod1);
mpz_init(tempmod2);
mpz_init(tempmod3);
mpz_init(x1);
mpz_init(x2);
mpz_init(y1);
mpz_init(y2);
mpz_init(z1);
mpz_init(z2);
//setting the variables to multiplicands
mpz_set(x1, wm->P->x);
mpz_set(x2, wm->P->x);
mpz_set(y1, wm->P->y);
mpz_set(y2, wm->P->y);
mpz_set(z1, wm->P->z);
mpz_set(z2, wm->P->z);
if (mpz_cmp_ui(x1, 0) == 0 && mpz_cmp_ui(y1, 1) == 0) {
mpz_set(wm->P->x, x2);
mpz_set(wm->P->y, y2);
mpz_set(wm->P->z, z2);
} else if (mpz_cmp_ui(x2, 0) == 0 && mpz_cmp_ui(y2, 1) == 0) {
mpz_set(wm->P->x, x1);
mpz_set(wm->P->y, y1);
mpz_set(wm->P->z, z1);
} else if (mpz_cmp(x1, x2) == 0) {
if (mpz_cmp(y1, y2) != 0) {
mpz_set_ui(wm->P->x, 0);
mpz_set_ui(wm->P->y, 1);
mpz_set_ui(wm->P->z, 0);
} else if (mpz_cmp_ui(y2, 0) == 0) {
mpz_set_ui(wm->P->x, 0);
mpz_set_ui(wm->P->y, 1);
mpz_set_ui(wm->P->z, 0);
} else
mpz_mul(temp1, x1, x1);
mpz_mod(tempmod1, temp1, wm->p);
mpz_mul_ui(temp2, tempmod1, 3);
mpz_mod(tempmod2, temp2, wm->p);
mpz_add(temp3, tempmod2, wm->A);
mpz_mod(tempmod3, temp3, wm->p);
mpz_mul_ui(temp1, y1, 2);
mpz_mod(tempmod1, temp1, wm->p);
mpz_invert(temp2, tempmod1, wm->p);
mpz_mul(temp3, tempmod3, temp2);
mpz_mod(tempmod3, temp3, wm->p);
mpz_mul(temp1, tempmod3, tempmod3);
mpz_mod(tempmod1, temp1, wm->p);
mpz_mul_ui(temp2, x1, 2);
mpz_mod(tempmod2, temp2, wm->p);
mpz_sub(temp3, tempmod1, tempmod2);
mpz_mod(tempx1, temp3, wm->p);
mpz_sub(temp1, x1, tempx1);
mpz_mod(tempmod1, temp1, wm->p);
mpz_mul(temp2, tempmod3, tempmod1);
mpz_mod(tempmod2, temp2, wm->p);
mpz_sub(temp1, tempmod2, y1);
mpz_mod(tempy1, temp1, wm->p);
mpz_set(wm->P->x, tempx1);
mpz_set(wm->P->y, tempy1);
mpz_set_ui(wm->P->z, 1);
} else {
mpz_sub(temp1, y1, y2); //y1-y2
mpz_mod(temp1, temp1, wm->p);
mpz_sub(temp2, x1, x2); //x1-x2
mpz_mod(temp2, temp2, wm->p);
mpz_invert(temp3, temp2, wm->p);
mpz_mod(temp3, temp3, wm->p);
mpz_mul(temp2, temp1, temp3); //(y1- y2)/(x1-x2)
mpz_mod(temp2, temp2, wm->p);
mpz_mul(temp1, temp2, temp2); //((y1- y2)/(x1-x2))^2
mpz_mod(temp1, temp1, wm->p);
mpz_sub(temp2, temp1, x1); //((y1- y2)/(x1-x2))^2 - x1
mpz_mod(temp2, temp2, wm->p);
mpz_sub(temp1, temp2, x2); //((y1- y2)/(x1-x2))^2 - x1- x2
mpz_mod(tempx1, temp1, wm->p);
mpz_sub(temp1, y1, y2); //y1-y2
mpz_mod(temp1, temp1, wm->p);
mpz_sub(temp2, x1, x2); //x1-x2
mpz_mod(temp2, temp2, wm->p);
mpz_invert(temp3, temp2, wm->p);
mpz_mod(temp3, temp3, wm->p);
mpz_mul(temp2, temp1, temp3); //(y1- y2)/(x1-x2)
mpz_mod(temp2, temp2, wm->p);
mpz_sub(temp1, x1, tempx1); //x1-x3
mpz_mod(temp1, temp1, wm->p);
mpz_mul(temp3, temp2, temp1); //(y1- y2)/(x1-x2) * (x1-x3)
mpz_mod(temp3, temp3, wm->p);
mpz_sub(temp2, temp3, y1); //(y1- y2)/(x1-x2) * (x1-x3) -y1
mpz_mod(tempy1, temp2, wm->p);
mpz_set(wm->P->x, tempx1);
mpz_set(wm->P->y, tempy1);
mpz_set_ui(wm->P->z, 1);
mpz_clear(temp1);
mpz_clear(temp2);
mpz_clear(temp3);
mpz_clear(temp4);
mpz_clear(tempx1);
mpz_clear(tempy1);
mpz_clear(tempmod1);
mpz_clear(tempmod2);
mpz_clear(tempmod3);
mpz_clear(x1);
mpz_clear(x2);
mpz_clear(y1);
mpz_clear(y2);
mpz_clear(z1);
mpz_clear(z2);
}
}
void mult(SMUL w, mpz_t k) {
SMUL_t mul;
mp_bitcnt_t index;
mp_size_t size;
mpz_init(mul->P->x);
mpz_init(mul->P->y);
mpz_init(mul->P->z);
mpz_init(mul->Q->x);
mpz_init(mul->Q->y);
mpz_init(mul->Q->z);
mpz_init(mul->p);
mpz_init(mul->A);
mpz_set(mul->P->x, w->Q->x);
mpz_set(mul->P->y, w->Q->y);
mpz_set(mul->P->z, w->Q->z);
mpz_set(mul->Q->x, w->P->x);
mpz_set(mul->Q->y, w->P->y);
mpz_set(mul->Q->z, w->P->z);
mpz_set(mul->p, w->p);
mpz_set(mul->A, w->A);
size = mpz_sizeinbase(k, 2);
int i;
for (i = size - 1; i >= 0; i--) {
dbl(mul);
index = mpz_scan1(k, i);
if (index == i) {
sum(mul);
}
}
mpz_set(w->Q->x, mul->P->x);
mpz_set(w->Q->y, mul->P->y);
mpz_set(w->Q->z, mul->P->z);
mpz_clear(mul->P->x);
mpz_clear(mul->P->y);
mpz_clear(mul->P->z);
mpz_clear(mul->Q->x);
mpz_clear(mul->Q->y);
mpz_clear(mul->Q->z);
mpz_clear(mul->p);
mpz_clear(mul->A);
}
unsigned long Hfunc(LOOP v) {
//return w->P->x->_mp_d[0] % LT_LEN;
return v->Xd->x->_mp_d[0] & ((unsigned long) 31);
}
unsigned long HfuncD(LOOP v) {
//return w->P->x->_mp_d[0] % LT_LEN;
return v->Xdd->x->_mp_d[0] & ((unsigned long) 31);
}