/**
* 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);
}
}
void ep2_rhs(fp2_t rhs, ep2_t p) {
fp2_t t0;
fp2_t t1;
fp2_null(t0);
fp2_null(t1);
TRY {
fp2_new(t0);
fp2_new(t1);
/* t0 = x1^2. */
fp2_sqr(t0, p->x);
/* t1 = x1^3. */
fp2_mul(t1, t0, p->x);
ep2_curve_get_a(t0);
fp2_mul(t0, p->x, t0);
fp2_add(t1, t1, t0);
ep2_curve_get_b(t0);
fp2_add(t1, t1, t0);
fp2_copy(rhs, t1);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp2_free(t0);
fp2_free(t1);
}
}
/**
* Doubles a point represented in affine coordinates on an ordinary prime
* elliptic curve.
*
* @param[out] r - the result.
* @param[in] p - the point to double.
*/
static void ep2_dbl_projc_imp(ep2_t r, ep2_t p) {
fp2_t t0, t1, t2, t3;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
fp2_null(t3);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
fp2_new(t3);
fp2_sqr(t0, p->x);
fp2_add(t2, t0, t0);
fp2_add(t0, t2, t0);
fp2_sqr(t3, p->y);
fp2_mul(t1, t3, p->x);
fp2_add(t1, t1, t1);
fp2_add(t1, t1, t1);
fp2_sqr(r->x, t0);
fp2_add(t2, t1, t1);
fp2_sub(r->x, r->x, t2);
fp2_mul(r->z, p->z, p->y);
fp2_add(r->z, r->z, r->z);
fp2_add(t3, t3, t3);
fp2_sqr(t3, t3);
fp2_add(t3, t3, t3);
fp2_sub(t1, t1, r->x);
fp2_mul(r->y, t0, t1);
fp2_sub(r->y, r->y, t3);
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
fp2_free(t3);
}
}
/**
* Compute the Miller loop for pairings of type G_1 x G_2 over the bits of a
* given parameter.
*
* @param[out] r - the result.
* @param[out] t - the resulting point.
* @param[in] p - the first pairing argument in affine coordinates.
* @param[in] q - the second pairing argument in affine coordinates.
* @param[in] a - the loop parameter.
*/
static void pp_mil_lit_k2(fp2_t r, ep_t *t, ep_t *p, ep_t *q, int m, bn_t a) {
fp2_t l, _l;
ep_t _q[m];
int i, j;
fp2_null(_l);
ep_null(_q);
TRY {
fp2_new(_l);
for (j = 0; j < m; j++) {
ep_null(_q[j]);
ep_new(_q[j]);
ep_copy(t[j], p[j]);
ep_neg(_q[j], q[j]);
}
for (i = bn_bits(a) - 2; i >= 0; i--) {
fp2_sqr(r, r);
for (j = 0; j < m; j++) {
pp_dbl_k2(l, t[j], t[j], _q[j]);
fp_copy(_l[0], l[1]);
fp_copy(_l[1], l[0]);
fp2_mul(r, r, _l);
if (bn_get_bit(a, i)) {
pp_add_k2(l, t[j], p[j], q[j]);
fp_copy(_l[0], l[1]);
fp_copy(_l[1], l[0]);
fp2_mul(r, r, _l);
}
}
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(_l);
fp2_free(m);
ep_free(_q);
}
}
int ep2_is_valid(ep2_t p) {
ep2_t t;
int r = 0;
ep2_null(t);
TRY {
ep2_new(t);
ep2_norm(t, p);
ep2_rhs(t->x, t);
fp2_sqr(t->y, t->y);
r = (fp2_cmp(t->x, t->y) == CMP_EQ) || ep2_is_infty(p);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
ep2_free(t);
}
return r;
}
/**
* 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);
}
}
/**
* Doubles a point represented in affine coordinates on an ordinary prime
* elliptic curve.
*
* @param[out] r - the result.
* @param[in] p - the point to double.
*/
static void ep2_dbl_projc_imp(ep2_t r, ep2_t p) {
fp2_t t0, t1, t2, t3, t4, t5;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
fp2_null(t3);
fp2_null(t4);
fp2_null(t5);
TRY {
if (ep_curve_opt_a() == OPT_ZERO) {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
fp2_new(t3);
fp2_new(t4);
fp2_new(t5);
fp2_sqr(t0, p->x);
fp2_add(t2, t0, t0);
fp2_add(t0, t2, t0);
fp2_sqr(t3, p->y);
fp2_mul(t1, t3, p->x);
fp2_add(t1, t1, t1);
fp2_add(t1, t1, t1);
fp2_sqr(r->x, t0);
fp2_add(t2, t1, t1);
fp2_sub(r->x, r->x, t2);
fp2_mul(r->z, p->z, p->y);
fp2_add(r->z, r->z, r->z);
fp2_add(t3, t3, t3);
fp2_sqr(t3, t3);
fp2_add(t3, t3, t3);
fp2_sub(t1, t1, r->x);
fp2_mul(r->y, t0, t1);
fp2_sub(r->y, r->y, t3);
} else {
/* dbl-2007-bl formulas: 1M + 8S + 1*a + 10add + 1*8 + 2*2 + 1*3 */
/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-2007-bl */
/* t0 = x1^2, t1 = y1^2, t2 = y1^4. */
fp2_sqr(t0, p->x);
fp2_sqr(t1, p->y);
fp2_sqr(t2, t1);
if (!p->norm) {
/* t3 = z1^2. */
fp2_sqr(t3, p->z);
if (ep_curve_get_a() == OPT_ZERO) {
/* z3 = 2 * y1 * z1. */
fp2_mul(r->z, p->y, p->z);
fp2_dbl(r->z, r->z);
} else {
/* z3 = (y1 + z1)^2 - y1^2 - z1^2. */
fp2_add(r->z, p->y, p->z);
fp2_sqr(r->z, r->z);
fp2_sub(r->z, r->z, t1);
fp2_sub(r->z, r->z, t3);
}
} else {
/* z3 = 2 * y1. */
fp2_dbl(r->z, p->y);
}
/* t4 = S = 2*((x1 + y1^2)^2 - x1^2 - y1^4). */
fp2_add(t4, p->x, t1);
fp2_sqr(t4, t4);
fp2_sub(t4, t4, t0);
fp2_sub(t4, t4, t2);
fp2_dbl(t4, t4);
/* t5 = M = 3 * x1^2 + a * z1^4. */
fp2_dbl(t5, t0);
fp2_add(t5, t5, t0);
ep2_curve_get_a(t0);
if (!p->norm) {
fp2_sqr(t3, t3);
fp2_mul(t1, t0, t3);
fp2_add(t5, t5, t1);
} else {
fp2_add(t5, t5, t0);
}
/* x3 = T = M^2 - 2 * S. */
fp2_sqr(r->x, t5);
fp2_dbl(t1, t4);
fp2_sub(r->x, r->x, t1);
/* y3 = M * (S - T) - 8 * y1^4. */
fp2_dbl(t2, t2);
fp2_dbl(t2, t2);
fp2_dbl(t2, t2);
fp2_sub(t4, t4, r->x);
fp2_mul(t5, t5, t4);
fp2_sub(r->y, t5, t2);
}
r->norm = 0;
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
fp2_free(t3);
fp2_free(t4);
fp2_free(t5);
}
}
/**
* 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);
}
}
/**
* Adds two points represented in projective coordinates on an ordinary prime
* elliptic curve.
*
* @param r - the result.
* @param p - the first point to add.
* @param q - the second point to add.
*/
static void ep2_add_projc_imp(ep2_t r, ep2_t p, ep2_t q) {
#if defined(EP_MIXED) && defined(STRIP)
ep2_add_projc_mix(r, p, q);
#else /* General addition. */
fp2_t t0, t1, t2, t3, t4, t5, t6;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
fp2_null(t3);
fp2_null(t4);
fp2_null(t5);
fp2_null(t6);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
fp2_new(t3);
fp2_new(t4);
fp2_new(t5);
fp2_new(t6);
if (q->norm) {
ep2_add_projc_mix(r, p, q);
} else {
/* t0 = z1^2. */
fp2_sqr(t0, p->z);
/* t1 = z2^2. */
fp2_sqr(t1, q->z);
/* t2 = U1 = x1 * z2^2. */
fp2_mul(t2, p->x, t1);
/* t3 = U2 = x2 * z1^2. */
fp2_mul(t3, q->x, t0);
/* t6 = z1^2 + z2^2. */
fp2_add(t6, t0, t1);
/* t0 = S2 = y2 * z1^3. */
fp2_mul(t0, t0, p->z);
fp2_mul(t0, t0, q->y);
/* t1 = S1 = y1 * z2^3. */
fp2_mul(t1, t1, q->z);
fp2_mul(t1, t1, p->y);
/* t3 = H = U2 - U1. */
fp2_sub(t3, t3, t2);
/* t0 = R = 2 * (S2 - S1). */
fp2_sub(t0, t0, t1);
fp2_dbl(t0, t0);
/* If E is zero. */
if (fp2_is_zero(t3)) {
if (fp2_is_zero(t0)) {
/* If I is zero, p = q, should have doubled. */
ep2_dbl_projc(r, p);
} else {
/* If I is not zero, q = -p, r = infinity. */
ep2_set_infty(r);
}
} else {
/* t4 = I = (2*H)^2. */
fp2_dbl(t4, t3);
fp2_sqr(t4, t4);
/* t5 = J = H * I. */
fp2_mul(t5, t3, t4);
/* t4 = V = U1 * I. */
fp2_mul(t4, t2, t4);
/* x3 = R^2 - J - 2 * V. */
fp2_sqr(r->x, t0);
fp2_sub(r->x, r->x, t5);
fp2_dbl(t2, t4);
fp2_sub(r->x, r->x, t2);
/* y3 = R * (V - x3) - 2 * S1 * J. */
fp2_sub(t4, t4, r->x);
fp2_mul(t4, t4, t0);
fp2_mul(t1, t1, t5);
fp2_dbl(t1, t1);
fp2_sub(r->y, t4, t1);
/* z3 = ((z1 + z2)^2 - z1^2 - z2^2) * H. */
fp2_add(r->z, p->z, q->z);
fp2_sqr(r->z, r->z);
fp2_sub(r->z, r->z, t6);
fp2_mul(r->z, r->z, t3);
}
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
fp2_free(t3);
fp2_free(t4);
fp2_free(t5);
fp2_free(t6);
}
#endif
}
/**
* Adds a point represented in affine coordinates to a point represented in
* projective coordinates.
*
* @param r - the result.
* @param s - the slope.
* @param p - the affine point.
* @param q - the projective point.
*/
static void ep2_add_projc_mix(ep2_t r, ep2_t p, ep2_t q) {
fp2_t t0, t1, t2, t3, t4, t5, t6;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
fp2_null(t3);
fp2_null(t4);
fp2_null(t5);
fp2_null(t6);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
fp2_new(t3);
fp2_new(t4);
fp2_new(t5);
fp2_new(t6);
if (!p->norm) {
/* t0 = z1^2. */
fp2_sqr(t0, p->z);
/* t3 = U2 = x2 * z1^2. */
fp2_mul(t3, q->x, t0);
/* t1 = S2 = y2 * z1^3. */
fp2_mul(t1, t0, p->z);
fp2_mul(t1, t1, q->y);
/* t3 = H = U2 - x1. */
fp2_sub(t3, t3, p->x);
/* t1 = R = 2 * (S2 - y1). */
fp2_sub(t1, t1, p->y);
} else {
/* H = x2 - x1. */
fp2_sub(t3, q->x, p->x);
/* t1 = R = 2 * (y2 - y1). */
fp2_sub(t1, q->y, p->y);
}
/* t2 = HH = H^2. */
fp2_sqr(t2, t3);
/* If E is zero. */
if (fp2_is_zero(t3)) {
if (fp2_is_zero(t1)) {
/* If I is zero, p = q, should have doubled. */
ep2_dbl_projc(r, p);
} else {
/* If I is not zero, q = -p, r = infinity. */
ep2_set_infty(r);
}
} else {
/* t5 = J = H * HH. */
fp2_mul(t5, t3, t2);
/* t4 = V = x1 * HH. */
fp2_mul(t4, p->x, t2);
/* x3 = R^2 - J - 2 * V. */
fp2_sqr(r->x, t1);
fp2_sub(r->x, r->x, t5);
fp2_dbl(t6, t4);
fp2_sub(r->x, r->x, t6);
/* y3 = R * (V - x3) - Y1 * J. */
fp2_sub(t4, t4, r->x);
fp2_mul(t4, t4, t1);
fp2_mul(t1, p->y, t5);
fp2_sub(r->y, t4, t1);
if (!p->norm) {
/* z3 = z1 * H. */
fp2_mul(r->z, p->z, t3);
} else {
/* z3 = H. */
fp2_copy(r->z, t3);
}
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
fp2_free(t3);
fp2_free(t4);
fp2_free(t5);
fp2_free(t6);
}
}
/**
* Computes the constantes required for evaluating Frobenius maps.
*/
static void fp2_calc() {
bn_t e;
fp2_t t0;
fp2_t t1;
ctx_t *ctx = core_get();
bn_null(e);
fp2_null(t0);
fp2_null(t1);
TRY {
bn_new(e);
fp2_new(t0);
fp2_new(t1);
fp2_zero(t0);
fp_set_dig(t0[0], 1);
fp2_mul_nor(t0, t0);
e->used = FP_DIGS;
dv_copy(e->dp, fp_prime_get(), FP_DIGS);
bn_sub_dig(e, e, 1);
bn_div_dig(e, e, 6);
fp2_exp(t0, t0, e);
#if ALLOC == AUTO
fp2_copy(ctx->fp2_p[0], t0);
fp2_sqr(ctx->fp2_p[1], ctx->fp2_p[0]);
fp2_mul(ctx->fp2_p[2], ctx->fp2_p[1], ctx->fp2_p[0]);
fp2_sqr(ctx->fp2_p[3], ctx->fp2_p[1]);
fp2_mul(ctx->fp2_p[4], ctx->fp2_p[3], ctx->fp2_p[0]);
#else
fp_copy(ctx->fp2_p[0][0], t0[0]);
fp_copy(ctx->fp2_p[0][1], t0[1]);
fp2_sqr(t1, t0);
fp_copy(ctx->fp2_p[1][0], t1[0]);
fp_copy(ctx->fp2_p[1][1], t1[1]);
fp2_mul(t1, t1, t0);
fp_copy(ctx->fp2_p[2][0], t1[0]);
fp_copy(ctx->fp2_p[2][1], t1[1]);
fp2_sqr(t1, t0);
fp2_sqr(t1, t1);
fp_copy(ctx->fp2_p[3][0], t1[0]);
fp_copy(ctx->fp2_p[3][1], t1[1]);
fp2_mul(t1, t1, t0);
fp_copy(ctx->fp2_p[4][0], t1[0]);
fp_copy(ctx->fp2_p[4][1], t1[1]);
#endif
fp2_frb(t1, t0, 1);
fp2_mul(t0, t1, t0);
fp_copy(ctx->fp2_p2[0], t0[0]);
fp_sqr(ctx->fp2_p2[1], ctx->fp2_p2[0]);
fp_mul(ctx->fp2_p2[2], ctx->fp2_p2[1], ctx->fp2_p2[0]);
fp_sqr(ctx->fp2_p2[3], ctx->fp2_p2[1]);
for (int i = 0; i < 5; i++) {
fp_mul(ctx->fp2_p3[i][0], ctx->fp2_p2[i % 3], ctx->fp2_p[i][0]);
fp_mul(ctx->fp2_p3[i][1], ctx->fp2_p2[i % 3], ctx->fp2_p[i][1]);
}
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
bn_free(e);
fp2_free(t0);
fp2_free(t1);
}
}
void pp_dbl_k12_projc_lazyr(fp12_t l, ep2_t r, ep2_t q, ep_t p) {
fp2_t t0, t1, t2, t3, t4, t5, t6;
dv2_t u0, u1;
int one = 1, zero = 0;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
fp2_null(t3);
fp2_null(t4);
fp2_null(t5);
fp2_null(t6);
dv2_null(u0);
dv2_null(u1);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
fp2_new(t3);
fp2_new(t4);
fp2_new(t5);
fp2_new(t6);
dv2_new(u0);
dv2_new(u1);
if (ep2_curve_is_twist() == EP_MTYPE) {
one ^= 1;
zero ^= 1;
}
if (ep_curve_opt_b() == RLC_TWO) {
/* C = z1^2. */
fp2_sqr(t0, q->z);
/* B = y1^2. */
fp2_sqr(t1, q->y);
/* t5 = B + C. */
fp2_add(t5, t0, t1);
/* t3 = E = 3b'C = 3C * (1 - i). */
fp2_dbl(t3, t0);
fp2_add(t0, t0, t3);
fp_add(t2[0], t0[0], t0[1]);
fp_sub(t2[1], t0[1], t0[0]);
/* t0 = x1^2. */
fp2_sqr(t0, q->x);
/* t4 = A = (x1 * y1)/2. */
fp2_mul(t4, q->x, q->y);
fp_hlv(t4[0], t4[0]);
fp_hlv(t4[1], t4[1]);
/* t3 = F = 3E. */
fp2_dbl(t3, t2);
fp2_add(t3, t3, t2);
/* x3 = A * (B - F). */
fp2_sub(r->x, t1, t3);
fp2_mul(r->x, r->x, t4);
/* G = (B + F)/2. */
fp2_add(t3, t1, t3);
fp_hlv(t3[0], t3[0]);
fp_hlv(t3[1], t3[1]);
/* y3 = G^2 - 3E^2. */
fp2_sqrn_low(u0, t2);
fp2_addd_low(u1, u0, u0);
fp2_addd_low(u1, u1, u0);
fp2_sqrn_low(u0, t3);
fp2_subc_low(u0, u0, u1);
/* H = (Y + Z)^2 - B - C. */
fp2_add(t3, q->y, q->z);
fp2_sqr(t3, t3);
fp2_sub(t3, t3, t5);
fp2_rdcn_low(r->y, u0);
/* z3 = B * H. */
fp2_mul(r->z, t1, t3);
/* l11 = E - B. */
fp2_sub(l[1][1], t2, t1);
/* l10 = (3 * xp) * t0. */
fp_mul(l[one][zero][0], p->x, t0[0]);
fp_mul(l[one][zero][1], p->x, t0[1]);
/* l01 = F * (-yp). */
fp_mul(l[zero][zero][0], t3[0], p->y);
fp_mul(l[zero][zero][1], t3[1], p->y);
} else {
/* A = x1^2. */
fp2_sqr(t0, q->x);
/* B = y1^2. */
fp2_sqr(t1, q->y);
/* C = z1^2. */
fp2_sqr(t2, q->z);
/* D = 3bC, for general b. */
fp2_dbl(t3, t2);
fp2_add(t3, t3, t2);
ep2_curve_get_b(t4);
fp2_mul(t3, t3, t4);
/* E = (x1 + y1)^2 - A - B. */
fp2_add(t4, q->x, q->y);
fp2_sqr(t4, t4);
fp2_sub(t4, t4, t0);
fp2_sub(t4, t4, t1);
/* F = (y1 + z1)^2 - B - C. */
fp2_add(t5, q->y, q->z);
fp2_sqr(t5, t5);
fp2_sub(t5, t5, t1);
fp2_sub(t5, t5, t2);
/* G = 3D. */
fp2_dbl(t6, t3);
fp2_add(t6, t6, t3);
/* x3 = E * (B - G). */
fp2_sub(r->x, t1, t6);
fp2_mul(r->x, r->x, t4);
/* y3 = (B + G)^2 -12D^2. */
fp2_add(t6, t6, t1);
fp2_sqr(t6, t6);
fp2_sqr(t2, t3);
fp2_dbl(r->y, t2);
fp2_dbl(t2, r->y);
fp2_dbl(r->y, t2);
fp2_add(r->y, r->y, t2);
fp2_sub(r->y, t6, r->y);
/* z3 = 4B * F. */
fp2_dbl(r->z, t1);
fp2_dbl(r->z, r->z);
fp2_mul(r->z, r->z, t5);
/* l00 = D - B. */
fp2_sub(l[one][one], t3, t1);
/* l10 = (3 * xp) * A. */
fp_mul(l[one][zero][0], p->x, t0[0]);
fp_mul(l[one][zero][1], p->x, t0[1]);
/* l01 = F * (-yp). */
fp_mul(l[zero][zero][0], t5[0], p->y);
fp_mul(l[zero][zero][1], t5[1], p->y);
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
fp2_free(t3);
fp2_free(t4);
fp2_free(t5);
fp2_free(t6);
dv2_free(u0);
dv2_free(u1);
}
}
void fp12_sqr_pck_basic(fp12_t c, fp12_t a) {
fp2_t t0, t1, t2, t3, t4, t5, t6;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
fp2_null(t3);
fp2_null(t4);
fp2_null(t5);
fp2_null(t6);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
fp2_new(t3);
fp2_new(t4);
fp2_new(t5);
fp2_new(t6);
fp2_sqr(t0, a[0][1]);
fp2_sqr(t1, a[1][2]);
fp2_add(t5, a[0][1], a[1][2]);
fp2_sqr(t2, t5);
fp2_add(t3, t0, t1);
fp2_sub(t5, t2, t3);
fp2_add(t6, a[1][0], a[0][2]);
fp2_sqr(t3, t6);
fp2_sqr(t2, a[1][0]);
fp2_mul_nor(t6, t5);
fp2_add(t5, t6, a[1][0]);
fp2_dbl(t5, t5);
fp2_add(c[1][0], t5, t6);
fp2_mul_nor(t4, t1);
fp2_add(t5, t0, t4);
fp2_sub(t6, t5, a[0][2]);
fp2_sqr(t1, a[0][2]);
fp2_dbl(t6, t6);
fp2_add(c[0][2], t6, t5);
fp2_mul_nor(t4, t1);
fp2_add(t5, t2, t4);
fp2_sub(t6, t5, a[0][1]);
fp2_dbl(t6, t6);
fp2_add(c[0][1], t6, t5);
fp2_add(t0, t2, t1);
fp2_sub(t5, t3, t0);
fp2_add(t6, t5, a[1][2]);
fp2_dbl(t6, t6);
fp2_add(c[1][2], t5, t6);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
fp2_free(t3);
fp2_free(t4);
fp2_free(t5);
fp2_free(t6);
}
}
void fp12_sqr_cyc_basic(fp12_t c, fp12_t a) {
fp2_t t0, t1, t2, t3, t4, t5, t6;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
fp2_null(t3);
fp2_null(t4);
fp2_null(t5);
fp2_null(t6);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
fp2_new(t3);
fp2_new(t4);
fp2_new(t5);
fp2_new(t6);
/* Define z = sqrt(E) */
/* Now a is seen as (t0,t1) + (t2,t3) * w + (t4,t5) * w^2 */
/* (t0, t1) = (a00 + a11*z)^2. */
fp2_sqr(t2, a[0][0]);
fp2_sqr(t3, a[1][1]);
fp2_add(t1, a[0][0], a[1][1]);
fp2_mul_nor(t0, t3);
fp2_add(t0, t0, t2);
fp2_sqr(t1, t1);
fp2_sub(t1, t1, t2);
fp2_sub(t1, t1, t3);
fp2_sub(c[0][0], t0, a[0][0]);
fp2_add(c[0][0], c[0][0], c[0][0]);
fp2_add(c[0][0], t0, c[0][0]);
fp2_add(c[1][1], t1, a[1][1]);
fp2_add(c[1][1], c[1][1], c[1][1]);
fp2_add(c[1][1], t1, c[1][1]);
fp2_sqr(t0, a[0][1]);
fp2_sqr(t1, a[1][2]);
fp2_add(t5, a[0][1], a[1][2]);
fp2_sqr(t2, t5);
fp2_add(t3, t0, t1);
fp2_sub(t5, t2, t3);
fp2_add(t6, a[1][0], a[0][2]);
fp2_sqr(t3, t6);
fp2_sqr(t2, a[1][0]);
fp2_mul_nor(t6, t5);
fp2_add(t5, t6, a[1][0]);
fp2_dbl(t5, t5);
fp2_add(c[1][0], t5, t6);
fp2_mul_nor(t4, t1);
fp2_add(t5, t0, t4);
fp2_sub(t6, t5, a[0][2]);
fp2_sqr(t1, a[0][2]);
fp2_dbl(t6, t6);
fp2_add(c[0][2], t6, t5);
fp2_mul_nor(t4, t1);
fp2_add(t5, t2, t4);
fp2_sub(t6, t5, a[0][1]);
fp2_dbl(t6, t6);
fp2_add(c[0][1], t6, t5);
fp2_add(t0, t2, t1);
fp2_sub(t5, t3, t0);
fp2_add(t6, t5, a[1][2]);
fp2_dbl(t6, t6);
fp2_add(c[1][2], t5, t6);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
fp2_free(t3);
fp2_free(t4);
fp2_free(t5);
fp2_free(t6);
}
}