void pp_map_weilp_k2(fp2_t r, ep_t p, ep_t q) {
ep_t _p[1], _q[1], t0[1], t1[1];
fp2_t r0, r1;
bn_t n;
ep_null(_p[0]);
ep_null(_q[0]);
ep_null(t0[0]);
ep_null(t1[0]);
fp2_null(r0);
fp2_null(r1);
bn_null(n);
TRY {
ep_new(_p[0]);
ep_new(_q[0]);
ep_new(t0[0]);
ep_new(t1[0]);
fp2_new(r0);
fp2_new(r1);
bn_new(n);
ep_norm(_p[0], p);
ep_norm(_q[0], q);
ep_curve_get_ord(n);
/* Since p has order n, we do not have to perform last iteration. */
bn_sub_dig(n, n, 1);
fp2_set_dig(r0, 1);
fp2_set_dig(r1, 1);
if (!ep_is_infty(_p[0]) && !ep_is_infty(_q[0])) {
pp_mil_lit_k2(r0, t0, _p, _q, 1, n);
pp_mil_k2(r1, t1, _q, _p, 1, n);
fp2_inv(r1, r1);
fp2_mul(r0, r0, r1);
fp2_inv(r1, r0);
fp2_inv_uni(r0, r0);
}
fp2_mul(r, r0, r1);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
ep_free(_p[0]);
ep_free(_q[0]);
ep_free(t0[0]);
ep_free(t1[0]);
fp2_free(r0);
fp2_free(r1);
bn_free(n);
}
}
/**
* Doubles a point represented in affine coordinates on an ordinary prime
* elliptic curve.
*
* @param[out] r - the result.
* @param[out] s - the resulting slope.
* @param[in] p - the point to double.
*/
static void ep2_dbl_basic_imp(ep2_t r, fp2_t s, ep2_t p) {
fp2_t t0, t1, t2;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
/* t0 = 1/(2 * y1). */
fp2_dbl(t0, p->y);
fp2_inv(t0, t0);
/* t1 = 3 * x1^2 + a. */
fp2_sqr(t1, p->x);
fp2_copy(t2, t1);
fp2_dbl(t1, t1);
fp2_add(t1, t1, t2);
ep2_curve_get_a(t2);
fp2_add(t1, t1, t2);
/* t1 = (3 * x1^2 + a)/(2 * y1). */
fp2_mul(t1, t1, t0);
if (s != NULL) {
fp2_copy(s, t1);
}
/* t2 = t1^2. */
fp2_sqr(t2, t1);
/* x3 = t1^2 - 2 * x1. */
fp2_dbl(t0, p->x);
fp2_sub(t0, t2, t0);
/* y3 = t1 * (x1 - x3) - y1. */
fp2_sub(t2, p->x, t0);
fp2_mul(t1, t1, t2);
fp2_sub(r->y, t1, p->y);
fp2_copy(r->x, t0);
fp2_copy(r->z, p->z);
r->norm = 1;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
}
}
void fp6_inv(fp6_t c, fp6_t a) {
fp2_t v0;
fp2_t v1;
fp2_t v2;
fp2_t t0;
fp2_null(v0);
fp2_null(v1);
fp2_null(v2);
fp2_null(t0);
TRY {
fp2_new(v0);
fp2_new(v1);
fp2_new(v2);
fp2_new(t0);
/* v0 = a_0^2 - E * a_1 * a_2. */
fp2_sqr(t0, a[0]);
fp2_mul(v0, a[1], a[2]);
fp2_mul_nor(v2, v0);
fp2_sub(v0, t0, v2);
/* v1 = E * a_2^2 - a_0 * a_1. */
fp2_sqr(t0, a[2]);
fp2_mul_nor(v2, t0);
fp2_mul(v1, a[0], a[1]);
fp2_sub(v1, v2, v1);
/* v2 = a_1^2 - a_0 * a_2. */
fp2_sqr(t0, a[1]);
fp2_mul(v2, a[0], a[2]);
fp2_sub(v2, t0, v2);
fp2_mul(t0, a[1], v2);
fp2_mul_nor(c[1], t0);
fp2_mul(c[0], a[0], v0);
fp2_mul(t0, a[2], v1);
fp2_mul_nor(c[2], t0);
fp2_add(t0, c[0], c[1]);
fp2_add(t0, t0, c[2]);
fp2_inv(t0, t0);
fp2_mul(c[0], v0, t0);
fp2_mul(c[1], v1, t0);
fp2_mul(c[2], v2, t0);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp2_free(v0);
fp2_free(v1);
fp2_free(v2);
fp2_free(t0);
}
}
/**
* Normalizes a point represented in projective coordinates.
*
* @param r - the result.
* @param p - the point to normalize.
*/
void pp_norm_imp(ep2_t r, ep2_t p) {
fp2_inv(r->z, p->z);
fp2_mul(r->x, p->x, r->z);
fp2_mul(r->y, p->y, r->z);
fp_zero(r->z[0]);
fp_zero(r->z[1]);
fp_set_dig(r->z[0], 1);
r->norm = 1;
}
void fp2_inv_sim(fp2_t *c, fp2_t *a, int n) {
int i;
fp2_t u, t[n];
for (i = 0; i < n; i++) {
fp2_null(t[i]);
}
fp2_null(u);
TRY {
for (i = 0; i < n; i++) {
fp2_new(t[i]);
}
fp2_new(u);
fp2_copy(c[0], a[0]);
fp2_copy(t[0], a[0]);
for (i = 1; i < n; i++) {
fp2_copy(t[i], a[i]);
fp2_mul(c[i], c[i - 1], t[i]);
}
fp2_inv(u, c[n - 1]);
for (i = n - 1; i > 0; i--) {
fp2_mul(c[i], c[i - 1], u);
fp2_mul(u, u, t[i]);
}
fp2_copy(c[0], u);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
for (i = 0; i < n; i++) {
fp2_free(t[i]);
}
fp2_free(u);
}
}
/**
* Doubles a point represented in affine coordinates on an ordinary prime
* elliptic curve.
*
* @param[out] r - the result.
* @param[out] s - the resulting slope.
* @param[in] p - the point to double.
*/
static void ep2_dbl_basic_imp(ep2_t r, fp2_t s, ep2_t p) {
fp2_t t0, t1, t2;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
/* t0 = 1/(2 * y1). */
fp2_dbl(t0, p->y);
fp2_inv(t0, t0);
/* t1 = 3 * x1^2 + a. */
fp2_sqr(t1, p->x);
fp2_copy(t2, t1);
fp2_dbl(t1, t1);
fp2_add(t1, t1, t2);
if (ep2_curve_is_twist()) {
switch (ep_curve_opt_a()) {
case OPT_ZERO:
break;
case OPT_ONE:
fp_set_dig(t2[0], 1);
fp2_mul_art(t2, t2);
fp2_mul_art(t2, t2);
fp2_add(t1, t1, t2);
break;
case OPT_DIGIT:
fp_set_dig(t2[0], ep_curve_get_a()[0]);
fp2_mul_art(t2, t2);
fp2_mul_art(t2, t2);
fp2_add(t1, t1, t2);
break;
default:
fp_copy(t2[0], ep_curve_get_a());
fp_zero(t2[1]);
fp2_mul_art(t2, t2);
fp2_mul_art(t2, t2);
fp2_add(t1, t1, t2);
break;
}
}
/* t1 = (3 * x1^2 + a)/(2 * y1). */
fp2_mul(t1, t1, t0);
if (s != NULL) {
fp2_copy(s, t1);
}
/* t2 = t1^2. */
fp2_sqr(t2, t1);
/* x3 = t1^2 - 2 * x1. */
fp2_dbl(t0, p->x);
fp2_sub(t0, t2, t0);
/* y3 = t1 * (x1 - x3) - y1. */
fp2_sub(t2, p->x, t0);
fp2_mul(t1, t1, t2);
fp2_sub(r->y, t1, p->y);
fp2_copy(r->x, t0);
fp2_copy(r->z, p->z);
r->norm = 1;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
}
}
/**
* Adds two points represented in affine coordinates on an ordinary prime
* elliptic curve.
*
* @param r - the result.
* @param s - the resulting slope.
* @param p - the first point to add.
* @param q - the second point to add.
*/
static void ep2_add_basic_imp(ep2_t r, fp2_t s, ep2_t p, ep2_t q) {
fp2_t t0, t1, t2;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
/* t0 = x2 - x1. */
fp2_sub(t0, q->x, p->x);
/* t1 = y2 - y1. */
fp2_sub(t1, q->y, p->y);
/* If t0 is zero. */
if (fp2_is_zero(t0)) {
if (fp2_is_zero(t1)) {
/* If t1 is zero, q = p, should have doubled. */
ep2_dbl_basic(r, p);
} else {
/* If t1 is not zero and t0 is zero, q = -p and r = infty. */
ep2_set_infty(r);
}
} else {
/* t2 = 1/(x2 - x1). */
fp2_inv(t2, t0);
/* t2 = lambda = (y2 - y1)/(x2 - x1). */
fp2_mul(t2, t1, t2);
/* x3 = lambda^2 - x2 - x1. */
fp2_sqr(t1, t2);
fp2_sub(t0, t1, p->x);
fp2_sub(t0, t0, q->x);
/* y3 = lambda * (x1 - x3) - y1. */
fp2_sub(t1, p->x, t0);
fp2_mul(t1, t2, t1);
fp2_sub(r->y, t1, p->y);
fp2_copy(r->x, t0);
fp2_copy(r->z, p->z);
if (s != NULL) {
fp2_copy(s, t2);
}
r->norm = 1;
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
}
}
void pp_map_sim_weilp_k2(fp2_t r, ep_t *p, ep_t *q, int m) {
ep_t _p[m], _q[m], t0[m], t1[m];
fp2_t r0, r1;
bn_t n;
int i, j;
fp2_null(r0);
fp2_null(r1);
bn_null(r);
TRY {
fp2_new(r0);
fp2_new(r1);
bn_new(n);
for (i = 0; i < m; i++) {
ep_null(_p[i]);
ep_null(_q[i]);
ep_null(t0[i]);
ep_null(t1[i]);
ep_new(_p[i]);
ep_new(_q[i]);
ep_new(t0[i]);
ep_new(t1[i]);
}
j = 0;
for (i = 0; i < m; i++) {
if (!ep_is_infty(p[i]) && !ep_is_infty(q[i])) {
ep_norm(_p[j], p[i]);
ep_norm(_q[j++], q[i]);
}
}
ep_curve_get_ord(n);
bn_sub_dig(n, n, 1);
fp2_set_dig(r0, 1);
fp2_set_dig(r1, 1);
if (j > 0) {
pp_mil_lit_k2(r0, t0, _p, _q, j, n);
pp_mil_k2(r1, t1, _q, _p, j, n);
fp2_inv(r1, r1);
fp2_mul(r0, r0, r1);
fp2_inv(r1, r0);
fp2_inv_uni(r0, r0);
}
fp2_mul(r, r0, r1);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(r0);
fp2_free(r1);
bn_free(n);
for (i = 0; i < m; i++) {
ep_free(_p[i]);
ep_free(_q[i]);
ep_free(t0[i]);
ep_free(t1[i]);
}
}
}
