void ep_rhs(fp_t rhs, const ep_t p) {
fp_t t0;
fp_t t1;
fp_null(t0);
fp_null(t1);
TRY {
fp_new(t0);
fp_new(t1);
/* t0 = x1^2. */
fp_sqr(t0, p->x);
/* t1 = x1^3. */
fp_mul(t1, t0, p->x);
/* t1 = x1^3 + a * x1 + b. */
switch (ep_curve_opt_a()) {
case OPT_ZERO:
break;
case OPT_ONE:
fp_add(t1, t1, p->x);
break;
#if FP_RDC != MONTY
case OPT_DIGIT:
fp_mul_dig(t0, p->x, ep_curve_get_a()[0]);
fp_add(t1, t1, t0);
break;
#endif
default:
fp_mul(t0, p->x, ep_curve_get_a());
fp_add(t1, t1, t0);
break;
}
switch (ep_curve_opt_b()) {
case OPT_ZERO:
break;
case OPT_ONE:
fp_add_dig(t1, t1, 1);
break;
#if FP_RDC != MONTY
case OPT_DIGIT:
fp_add_dig(t1, t1, ep_curve_get_b()[0]);
break;
#endif
default:
fp_add(t1, t1, ep_curve_get_b());
break;
}
fp_copy(rhs, t1);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp_free(t0);
fp_free(t1);
}
}
int fp2_srt(fp2_t c, fp2_t a) {
int r = 0;
fp_t t1;
fp_t t2;
fp_t t3;
fp_null(t1);
fp_null(t2);
fp_null(t3);
TRY {
fp_new(t1);
fp_new(t2);
fp_new(t3);
/* t1 = a[0]^2 - u^2 * a[1]^2 */
fp_sqr(t1, a[0]);
fp_sqr(t2, a[1]);
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_add(t1, t1, t2);
}
for (int i = 0; i <= fp_prime_get_qnr(); i++) {
fp_sub(t1, t1, t2);
}
fp_add(t1, t1, t2);
if (fp_srt(t2, t1)) {
/* t1 = (a_0 + sqrt(t1)) / 2 */
fp_add(t1, a[0], t2);
fp_set_dig(t3, 2);
fp_inv(t3, t3);
fp_mul(t1, t1, t3);
if (!fp_srt(t3, t1)) {
/* t1 = (a_0 - sqrt(t1)) / 2 */
fp_sub(t1, a[0], t2);
fp_set_dig(t3, 2);
fp_inv(t3, t3);
fp_mul(t1, t1, t3);
fp_srt(t3, t1);
}
/* c_0 = sqrt(t1) */
fp_copy(c[0], t3);
/* c_1 = a_1 / (2 * sqrt(t1)) */
fp_dbl(t3, t3);
fp_inv(t3, t3);
fp_mul(c[1], a[1], t3);
r = 1;
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t1);
fp_free(t2);
fp_free(t3);
}
return r;
}
/**
* Normalizes a point represented in projective coordinates.
*
* @param r - the result.
* @param p - the point to normalize.
*/
static void ep_norm_imp(ep_t r, const ep_t p, int inverted) {
if (!p->norm) {
fp_t t0, t1;
fp_null(t0);
fp_null(t1);
TRY {
fp_new(t0);
fp_new(t1);
if (inverted) {
fp_copy(t1, p->z);
} else {
fp_inv(t1, p->z);
}
fp_sqr(t0, t1);
fp_mul(r->x, p->x, t0);
fp_mul(t0, t0, t1);
fp_mul(r->y, p->y, t0);
fp_set_dig(r->z, 1);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
}
}
void fp2_sqr_basic(fp2_t c, fp2_t a) {
fp_t t0, t1, t2;
fp_null(t0);
fp_null(t1);
fp_null(t2);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
/* t0 = (a_0 + a_1). */
fp_add(t0, a[0], a[1]);
/* t1 = (a_0 - a_1). */
fp_sub(t1, a[0], a[1]);
/* t1 = a_0 + u^2 * a_1. */
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_sub(t1, t1, a[1]);
}
for (int i = 0; i <= fp_prime_get_qnr(); i++) {
fp_add(t1, t1, a[1]);
}
if (fp_prime_get_qnr() == -1) {
/* t2 = 2 * a_0. */
fp_dbl(t2, a[0]);
/* c_1 = 2 * a_0 * a_1. */
fp_mul(c[1], t2, a[1]);
/* c_0 = a_0^2 + a_1^2 * u^2. */
fp_mul(c[0], t0, t1);
} else {
/* c_1 = a_0 * a_1. */
fp_mul(c[1], a[0], a[1]);
/* c_0 = a_0^2 + a_1^2 * u^2. */
fp_mul(c[0], t0, t1);
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_add(c[0], c[0], c[1]);
}
for (int i = 0; i <= fp_prime_get_qnr(); i++) {
fp_sub(c[0], c[0], c[1]);
}
/* c_1 = 2 * a_0 * a_1. */
fp_dbl(c[1], c[1]);
}
/* c = c_0 + c_1 * u. */
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
}
}
void fp2_inv(fp2_t c, fp2_t a) {
fp_t t0, t1;
fp_null(t0);
fp_null(t1);
TRY {
fp_new(t0);
fp_new(t1);
/* t0 = a_0^2, t1 = a_1^2. */
fp_sqr(t0, a[0]);
fp_sqr(t1, a[1]);
/* t1 = 1/(a_0^2 + a_1^2). */
#ifndef FP_QNRES
if (fp_prime_get_qnr() != -1) {
if (fp_prime_get_qnr() == -2) {
fp_dbl(t1, t1);
fp_add(t0, t0, t1);
} else {
if (fp_prime_get_qnr() < 0) {
fp_mul_dig(t1, t1, -fp_prime_get_qnr());
fp_add(t0, t0, t1);
} else {
fp_mul_dig(t1, t1, fp_prime_get_qnr());
fp_sub(t0, t0, t1);
}
}
} else {
fp_add(t0, t0, t1);
}
#else
fp_add(t0, t0, t1);
#endif
fp_inv(t1, t0);
/* c_0 = a_0/(a_0^2 + a_1^2). */
fp_mul(c[0], a[0], t1);
/* c_1 = - a_1/(a_0^2 + a_1^2). */
fp_mul(c[1], a[1], t1);
fp_neg(c[1], c[1]);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
}
}
void ed_norm_sim(ed_t *r, const ed_t *t, int n) {
int i;
fp_t a[n];
for (i = 0; i < n; i++) {
fp_null(a[i]);
}
TRY {
for (i = 0; i < n; i++) {
fp_new(a[i]);
fp_copy(a[i], t[i]->z);
}
fp_inv_sim(a, (const fp_t *)a, n);
for (i = 0; i < n; i++) {
fp_mul(r[i]->x, t[i]->x, a[i]);
fp_mul(r[i]->y, t[i]->y, a[i]);
#if ED_ADD == EXTND
fp_mul(r[i]->t, t[i]->t, a[i]);
#endif
fp_set_dig(r[i]->z, 1);
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
for (i = 0; i < n; i++) {
fp_free(a[i]);
}
}
}
int fp_cmp_dig(const fp_t a, dig_t b) {
#if FP_RDC == MONTY
fp_t t;
int r = CMP_EQ;
fp_null(t);
TRY {
fp_new(t);
fp_prime_conv_dig(t, b);
r = fp_cmp(a, t);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp_free(t);
}
return r;
#else
for (int i = 1; i < FP_DIGS; i++) {
if (a[i] > 0) {
return CMP_GT;
}
}
return fp_cmp1_low(a[0], b);
#endif
}
int ep_upk(ep_t r, const ep_t p) {
fp_t t;
int result = 0;
fp_null(t);
TRY {
fp_new(t);
ep_rhs(t, p);
/* t0 = sqrt(x1^3 + a * x1 + b). */
result = fp_srt(t, t);
if (result) {
/* Verify if least significant bit of the result matches the
* compressed y-coordinate. */
if (fp_get_bit(t, 0) != fp_get_bit(p->y, 0)) {
fp_neg(t, t);
}
fp_copy(r->x, p->x);
fp_copy(r->y, t);
fp_set_dig(r->z, 1);
r->norm = 1;
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t);
}
return result;
}
void fp2_mul_art(fp2_t c, fp2_t a) {
fp_t t;
fp_null(t);
TRY {
fp_new(t);
#ifdef FP_QNRES
/* (a_0 + a_1 * i) * i = -a_1 + a_0 * i. */
fp_copy(t, a[0]);
fp_neg(c[0], a[1]);
fp_copy(c[1], t);
#else
/* (a_0 + a_1 * u) * u = (a_1 * u^2) + a_0 * u. */
fp_copy(t, a[0]);
fp_neg(c[0], a[1]);
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_sub(c[0], c[0], a[1]);
}
fp_copy(c[1], t);
#endif
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t);
}
}
/**
* Normalizes a point represented in projective coordinates.
*
* @param r - the result.
* @param p - the point to normalize.
*/
void ed_norm(ed_t r, const ed_t p) {
if (ed_is_infty(p)) {
ed_set_infty(r);
return;
}
if (fp_cmp_dig(p->z, 1) == CMP_EQ) {
/* If the point is represented in affine coordinates, we just copy it. */
ed_copy(r, p);
} else {
fp_t z_inv;
fp_null(z_inv);
fp_new(z_inv);
fp_inv(z_inv, p->z);
fp_mul(r->x, p->x, z_inv);
fp_mul(r->y, p->y, z_inv);
#if ED_ADD == EXTND
fp_mul(r->t, p->t, z_inv);
#endif
fp_set_dig(r->z, 1);
fp_free(z_inv);
}
}
int fp2_upk(fp2_t c, fp2_t a) {
int result, b = fp_get_bit(a[1], 0);
fp_t t;
fp_null(t);
TRY {
fp_new(t);
/* a_0^2 + a_1^2 = 1, thus a_1^2 = 1 - a_0^2. */
fp_sqr(t, a[0]);
fp_sub_dig(t, t, 1);
fp_neg(t, t);
/* a1 = sqrt(a_0^2). */
result = fp_srt(t, t);
if (result) {
/* Verify if least significant bit of the result matches the
* compressed second coordinate. */
if (fp_get_bit(t, 0) != b) {
fp_neg(t, t);
}
fp_copy(c[0], a[0]);
fp_copy(c[1], t);
}
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp_free(t);
}
return result;
}
void fp_exp_monty(fp_t c, const fp_t a, const bn_t b) {
fp_t t[2];
fp_null(t[0]);
fp_null(t[1]);
if (bn_is_zero(b)) {
fp_set_dig(c, 1);
return;
}
TRY {
fp_new(t[0]);
fp_new(t[1]);
fp_set_dig(t[0], 1);
fp_copy(t[1], a);
for (int i = bn_bits(b) - 1; i >= 0; i--) {
int j = bn_get_bit(b, i);
dv_swap_cond(t[0], t[1], FP_DIGS, j ^ 1);
fp_mul(t[0], t[0], t[1]);
fp_sqr(t[1], t[1]);
dv_swap_cond(t[0], t[1], FP_DIGS, j ^ 1);
}
if (bn_sign(b) == BN_NEG) {
fp_inv(c, t[0]);
} else {
fp_copy(c, t[0]);
}
} CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t[1]);
fp_free(t[0]);
}
}
int ed_affine_is_valid(const fp_t x, const fp_t y) {
fp_t tmpFP0;
fp_t tmpFP1;
fp_t tmpFP2;
fp_null(tmpFP0);
fp_null(tmpFP1);
fp_null(tmpFP2);
int r = 0;
TRY {
fp_new(tmpFP0);
fp_new(tmpFP1);
fp_new(tmpFP2);
// a * X^2 + Y^2 - 1 - d * X^2 * Y^2 =?= 0
fp_sqr(tmpFP0, x);
fp_mul(tmpFP0, core_get()->ed_a, tmpFP0);
fp_sqr(tmpFP1, y);
fp_add(tmpFP1, tmpFP0, tmpFP1);
fp_sub_dig(tmpFP1, tmpFP1, 1);
fp_sqr(tmpFP0, x);
fp_mul(tmpFP0, core_get()->ed_d, tmpFP0);
fp_sqr(tmpFP2, y);
fp_mul(tmpFP2, tmpFP0, tmpFP2);
fp_sub(tmpFP0, tmpFP1, tmpFP2);
r = fp_is_zero(tmpFP0);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp_free(tmpFP0);
fp_free(tmpFP1);
fp_free(tmpFP2);
}
return r;
}
int ed_is_valid(const ed_t p) {
ed_t t;
#if ED_ADD == EXTND
fp_t x_times_y;
#endif
int r = 0;
ed_null(t);
#if ED_ADD == EXTND
fp_null(x_times_y);
#endif
if (fp_is_zero(p->z)) {
r = 0;
} else {
TRY {
#if ED_ADD == EXTND
fp_new(x_times_y);
#endif
ed_new(t);
ed_norm(t, p);
// check t coordinate
#if ED_ADD == PROJC
r = ed_affine_is_valid(t->x, t->y);
#elif ED_ADD == EXTND
fp_mul(x_times_y, t->x, t->y);
if (fp_cmp(x_times_y, t->t) != CMP_EQ) {
r = 0;
} else {
r = ed_affine_is_valid(t->x, t->y);
}
#endif
// if (r == 0) {
// util_printf("\n\n(X, Y, T, Z) = \n");
// ed_print(p);
// }
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
#if ED_ADD == EXTND
fp_free(x_times_y);
#endif
ed_free(t);
}
}
return r;
}
int fp_cmp_dig(const fp_t a, dig_t b) {
fp_t t;
int r = RLC_EQ;
fp_null(t);
TRY {
fp_new(t);
fp_prime_conv_dig(t, b);
r = fp_cmp(a, t);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp_free(t);
}
return r;
}
int ed_is_infty(const ed_t p) {
assert(!fp_is_zero(p->z));
int ret = 0;
fp_t norm_y;
fp_null(norm_y);
fp_new(norm_y);
fp_inv(norm_y, p->z);
fp_mul(norm_y, p->y, norm_y);
if (fp_cmp_dig(norm_y, 1) == CMP_EQ && fp_is_zero(p->x)) {
ret = 1;
}
fp_free(norm_y);
return ret;
}
/**
* Detects an optimization based on the curve coefficients.
*
* @param[out] opt - the resulting optimization.
* @param[in] a - the curve coefficient.
*/
static void detect_opt(int *opt, fp_t a) {
fp_t t;
fp_null(t);
TRY {
fp_new(t);
fp_prime_conv_dig(t, 3);
fp_neg(t, t);
if (fp_cmp(a, t) == CMP_EQ) {
*opt = OPT_MINUS3;
} else {
if (fp_is_zero(a)) {
*opt = OPT_ZERO;
} else {
fp_set_dig(t, 1);
if (fp_cmp_dig(a, 1) == CMP_EQ) {
*opt = OPT_ONE;
} else {
if (fp_cmp_dig(a, 2) == CMP_EQ) {
*opt = OPT_TWO;
} else {
if (fp_bits(a) <= FP_DIGIT) {
*opt = OPT_DIGIT;
} else {
*opt = RELIC_OPT_NONE;
}
}
}
}
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t);
}
}
void fp3_mul_art(fp3_t c, fp3_t a) {
fp_t t;
fp_null(t);
TRY {
fp_new(t);
/* (a_0 + a_1 * u + a_1 * u^2) * u = a_0 * u + a_1 * u^2 + a_1 * u^3. */
fp_copy(t, a[0]);
fp_dbl(c[0], a[2]);
fp_neg(c[0], c[0]);
fp_copy(c[2], a[1]);
fp_copy(c[1], t);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t);
}
}
void fp_exp_basic(fp_t c, const fp_t a, const bn_t b) {
int i, l;
fp_t r;
fp_null(r);
if (bn_is_zero(b)) {
fp_set_dig(c, 1);
return;
}
TRY {
fp_new(r);
l = bn_bits(b);
fp_copy(r, a);
for (i = l - 2; i >= 0; i--) {
fp_sqr(r, r);
if (bn_get_bit(b, i)) {
fp_mul(r, r, a);
}
}
if (bn_sign(b) == BN_NEG) {
fp_inv(c, r);
} else {
fp_copy(c, r);
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(r);
}
}
void pp_dbl_k2_basic(fp2_t l, ep_t r, ep_t p, ep_t q) {
fp_t s;
ep_t t;
fp_null(s);
ep_null(t);
TRY {
fp_new(s);
ep_new(t);
ep_copy(t, p);
ep_dbl_slp_basic(r, s, p);
fp_add(l[0], t->x, q->x);
fp_mul(l[0], l[0], s);
fp_sub(l[0], t->y, l[0]);
fp_copy(l[1], q->y);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp_free(s);
ep_free(t);
}
}
void fp_exp_slide(fp_t c, const fp_t a, const bn_t b) {
fp_t t[1 << (FP_WIDTH - 1)], r;
int i, j, l;
uint8_t win[FP_BITS + 1];
fp_null(r);
if (bn_is_zero(b)) {
fp_set_dig(c, 1);
return;
}
/* Initialize table. */
for (i = 0; i < (1 << (FP_WIDTH - 1)); i++) {
fp_null(t[i]);
}
TRY {
for (i = 0; i < (1 << (FP_WIDTH - 1)); i ++) {
fp_new(t[i]);
}
fp_new(r);
fp_copy(t[0], a);
fp_sqr(r, a);
/* Create table. */
for (i = 1; i < 1 << (FP_WIDTH - 1); i++) {
fp_mul(t[i], t[i - 1], r);
}
fp_set_dig(r, 1);
l = FP_BITS + 1;
bn_rec_slw(win, &l, b, FP_WIDTH);
for (i = 0; i < l; i++) {
if (win[i] == 0) {
fp_sqr(r, r);
} else {
for (j = 0; j < util_bits_dig(win[i]); j++) {
fp_sqr(r, r);
}
fp_mul(r, r, t[win[i] >> 1]);
}
}
if (bn_sign(b) == BN_NEG) {
fp_inv(c, r);
} else {
fp_copy(c, r);
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
for (i = 0; i < (1 << (FP_WIDTH - 1)); i++) {
fp_free(t[i]);
}
fp_free(r);
}
}
/**
* Adds two points represented in affine coordinates on an ordinary prime
* elliptic curve.
*
* @param[out] r - the result.
* @param[out] s - the slope.
* @param[in] p - the first point to add.
* @param[in] q - the second point to add.
*/
static void ep_add_basic_imp(ep_t r, fp_t s, const ep_t p, const ep_t q) {
fp_t t0, t1, t2;
fp_null(t0);
fp_null(t1);
fp_null(t2);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
/* t0 = x2 - x1. */
fp_sub(t0, q->x, p->x);
/* t1 = y2 - y1. */
fp_sub(t1, q->y, p->y);
/* If t0 is zero. */
if (fp_is_zero(t0)) {
if (fp_is_zero(t1)) {
/* If t1 is zero, q = p, should have doubled. */
ep_dbl_basic(r, p);
} else {
/* If t1 is not zero and t0 is zero, q = -p and r = infinity. */
ep_set_infty(r);
}
} else {
/* t2 = 1/(x2 - x1). */
fp_inv(t2, t0);
/* t2 = lambda = (y2 - y1)/(x2 - x1). */
fp_mul(t2, t1, t2);
/* x3 = lambda^2 - x2 - x1. */
fp_sqr(t1, t2);
fp_sub(t0, t1, p->x);
fp_sub(t0, t0, q->x);
/* y3 = lambda * (x1 - x3) - y1. */
fp_sub(t1, p->x, t0);
fp_mul(t1, t2, t1);
fp_sub(r->y, t1, p->y);
fp_copy(r->x, t0);
fp_copy(r->z, p->z);
if (s != NULL) {
fp_copy(s, t2);
}
r->norm = 1;
}
fp_free(t0);
fp_free(t1);
fp_free(t2);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
}
}
void pp_dbl_k2_projc_lazyr(fp2_t l, ep_t r, ep_t p, ep_t q) {
fp_t t0, t1, t2, t3, t4, t5;
dv_t u0, u1;
fp_null(t0);
fp_null(t1);
fp_null(t2);
fp_null(t3);
fp_null(t4);
fp_null(t5);
dv_null(u0);
dv_null(u1);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
fp_new(t3);
fp_new(t4);
fp_new(t5);
dv_new(u0);
dv_new(u1);
/* For these curves, we always can choose a = -3. */
/* dbl-2001-b formulas: 3M + 5S + 8add + 1*4 + 2*8 + 1*3 */
/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b */
/* t0 = delta = z1^2. */
fp_sqr(t0, p->z);
/* t1 = gamma = y1^2. */
fp_sqr(t1, p->y);
/* t2 = beta = x1 * y1^2. */
fp_mul(t2, p->x, t1);
/* t3 = alpha = 3 * (x1 - z1^2) * (x1 + z1^2). */
fp_sub(t3, p->x, t0);
fp_add(t4, p->x, t0);
fp_mul(t4, t3, t4);
fp_dbl(t3, t4);
fp_add(t3, t3, t4);
/* t2 = 4 * beta. */
fp_dbl(t2, t2);
fp_dbl(t2, t2);
/* z3 = (y1 + z1)^2 - gamma - delta. */
fp_add(r->z, p->y, p->z);
fp_sqr(r->z, r->z);
fp_sub(r->z, r->z, t1);
fp_sub(r->z, r->z, t0);
/* l0 = 2 * gamma - alpha * (delta * xq + x1). */
fp_dbl(t1, t1);
fp_mul(t5, t0, q->x);
fp_add(t5, t5, p->x);
fp_mul(t5, t5, t3);
fp_sub(l[0], t1, t5);
/* x3 = alpha^2 - 8 * beta. */
fp_dbl(t5, t2);
fp_sqr(r->x, t3);
fp_sub(r->x, r->x, t5);
/* y3 = alpha * (4 * beta - x3) - 8 * gamma^2. */
fp_sqrn_low(u0, t1);
fp_addc_low(u0, u0, u0);
fp_subm_low(r->y, t2, r->x);
fp_muln_low(u1, r->y, t3);
fp_subc_low(u1, u1, u0);
fp_rdcn_low(r->y, u1);
/* l1 = - z3 * delta * yq. */
fp_mul(l[1], r->z, t0);
fp_mul(l[1], l[1], q->y);
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
fp_free(t3);
fp_free(t4);
fp_free(t5);
dv_free(u0);
dv_free(u1);
}
}
int fp_srt(fp_t c, const fp_t a) {
bn_t e;
fp_t t0;
fp_t t1;
int r = 0;
bn_null(e);
fp_null(t0);
fp_null(t1);
TRY {
bn_new(e);
fp_new(t0);
fp_new(t1);
/* Make e = p. */
e->used = FP_DIGS;
dv_copy(e->dp, fp_prime_get(), FP_DIGS);
if (fp_prime_get_mod8() == 3 || fp_prime_get_mod8() == 7) {
/* Easy case, compute a^((p + 1)/4). */
bn_add_dig(e, e, 1);
bn_rsh(e, e, 2);
fp_exp(t0, a, e);
fp_sqr(t1, t0);
r = (fp_cmp(t1, a) == CMP_EQ);
fp_copy(c, t0);
} else {
int f = 0, m = 0;
/* First, check if there is a root. Compute t1 = a^((p - 1)/2). */
bn_rsh(e, e, 1);
fp_exp(t0, a, e);
if (fp_cmp_dig(t0, 1) != CMP_EQ) {
/* Nope, there is no square root. */
r = 0;
} else {
r = 1;
/* Find a quadratic non-residue modulo p, that is a number t2
* such that (t2 | p) = t2^((p - 1)/2)!= 1. */
do {
fp_rand(t1);
fp_exp(t0, t1, e);
} while (fp_cmp_dig(t0, 1) == CMP_EQ);
/* Write p - 1 as (e * 2^f), odd e. */
bn_lsh(e, e, 1);
while (bn_is_even(e)) {
bn_rsh(e, e, 1);
f++;
}
/* Compute t2 = t2^e. */
fp_exp(t1, t1, e);
/* Compute t1 = a^e, c = a^((e + 1)/2) = a^(e/2 + 1), odd e. */
bn_rsh(e, e, 1);
fp_exp(t0, a, e);
fp_mul(e->dp, t0, a);
fp_sqr(t0, t0);
fp_mul(t0, t0, a);
fp_copy(c, e->dp);
while (1) {
if (fp_cmp_dig(t0, 1) == CMP_EQ) {
break;
}
fp_copy(e->dp, t0);
for (m = 0; (m < f) && (fp_cmp_dig(t0, 1) != CMP_EQ); m++) {
fp_sqr(t0, t0);
}
fp_copy(t0, e->dp);
for (int i = 0; i < f - m - 1; i++) {
fp_sqr(t1, t1);
}
fp_mul(c, c, t1);
fp_sqr(t1, t1);
fp_mul(t0, t0, t1);
f = m;
}
}
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(e);
fp_free(t0);
fp_free(t1);
}
return r;
}
/**
* Adds two points represented in projective coordinates on an ordinary prime
* elliptic curve.
*
* @param[out] r - the result.
* @param[in] p - the first point to add.
* @param[in] q - the second point to add.
*/
static void ep_add_projc_imp(ep_t r, const ep_t p, const ep_t q) {
#if defined(EP_MIXED) && defined(STRIP)
/* If code size is a problem, leave only the mixed version. */
ep_add_projc_mix(r, p, q);
#else /* General addition. */
#if defined(EP_MIXED) || !defined(STRIP)
/* Test if z2 = 1 only if mixed coordinates are turned on. */
if (q->norm) {
ep_add_projc_mix(r, p, q);
return;
}
#endif
fp_t t0, t1, t2, t3, t4, t5, t6;
fp_null(t0);
fp_null(t1);
fp_null(t2);
fp_null(t3);
fp_null(t4);
fp_null(t5);
fp_null(t6);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
fp_new(t3);
fp_new(t4);
fp_new(t5);
fp_new(t6);
/* add-2007-bl formulas: 11M + 5S + 9add + 4*2 */
/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl */
/* t0 = z1^2. */
fp_sqr(t0, p->z);
/* t1 = z2^2. */
fp_sqr(t1, q->z);
/* t2 = U1 = x1 * z2^2. */
fp_mul(t2, p->x, t1);
/* t3 = U2 = x2 * z1^2. */
fp_mul(t3, q->x, t0);
/* t6 = z1^2 + z2^2. */
fp_add(t6, t0, t1);
/* t0 = S2 = y2 * z1^3. */
fp_mul(t0, t0, p->z);
fp_mul(t0, t0, q->y);
/* t1 = S1 = y1 * z2^3. */
fp_mul(t1, t1, q->z);
fp_mul(t1, t1, p->y);
/* t3 = H = U2 - U1. */
fp_sub(t3, t3, t2);
/* t0 = R = 2 * (S2 - S1). */
fp_sub(t0, t0, t1);
fp_dbl(t0, t0);
/* If E is zero. */
if (fp_is_zero(t3)) {
if (fp_is_zero(t0)) {
/* If I is zero, p = q, should have doubled. */
ep_dbl_projc(r, p);
} else {
/* If I is not zero, q = -p, r = infinity. */
ep_set_infty(r);
}
} else {
/* t4 = I = (2*H)^2. */
fp_dbl(t4, t3);
fp_sqr(t4, t4);
/* t5 = J = H * I. */
fp_mul(t5, t3, t4);
/* t4 = V = U1 * I. */
fp_mul(t4, t2, t4);
/* x3 = R^2 - J - 2 * V. */
fp_sqr(r->x, t0);
fp_sub(r->x, r->x, t5);
fp_dbl(t2, t4);
fp_sub(r->x, r->x, t2);
/* y3 = R * (V - x3) - 2 * S1 * J. */
fp_sub(t4, t4, r->x);
fp_mul(t4, t4, t0);
fp_mul(t1, t1, t5);
fp_dbl(t1, t1);
fp_sub(r->y, t4, t1);
/* z3 = ((z1 + z2)^2 - z1^2 - z2^2) * H. */
fp_add(r->z, p->z, q->z);
fp_sqr(r->z, r->z);
fp_sub(r->z, r->z, t6);
fp_mul(r->z, r->z, t3);
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
fp_free(t3);
fp_free(t4);
fp_free(t5);
fp_free(t6);
}
#endif
}
void pp_dbl_lit_k12(fp12_t l, ep_t r, ep_t p, ep2_t q) {
fp_t t0, t1, t2, t3, t4, t5, t6;
int one = 1, zero = 0;
fp_null(t0);
fp_null(t1);
fp_null(t2);
fp_null(t3);
fp_null(t4);
fp_null(t5);
fp_null(t6);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
fp_new(t3);
fp_new(t4);
fp_new(t5);
fp_new(t6);
fp_sqr(t0, p->x);
fp_sqr(t1, p->y);
fp_sqr(t2, p->z);
fp_mul(t4, ep_curve_get_b(), t2);
fp_dbl(t3, t4);
fp_add(t3, t3, t4);
fp_add(t4, p->x, p->y);
fp_sqr(t4, t4);
fp_sub(t4, t4, t0);
fp_sub(t4, t4, t1);
fp_add(t5, p->y, p->z);
fp_sqr(t5, t5);
fp_sub(t5, t5, t1);
fp_sub(t5, t5, t2);
fp_dbl(t6, t3);
fp_add(t6, t6, t3);
fp_sub(r->x, t1, t6);
fp_mul(r->x, r->x, t4);
fp_add(r->y, t1, t6);
fp_sqr(r->y, r->y);
fp_sqr(t4, t3);
fp_dbl(t6, t4);
fp_add(t6, t6, t4);
fp_dbl(t6, t6);
fp_dbl(t6, t6);
fp_sub(r->y, r->y, t6);
fp_mul(r->z, t1, t5);
fp_dbl(r->z, r->z);
fp_dbl(r->z, r->z);
r->norm = 0;
if (ep2_curve_is_twist() == EP_MTYPE) {
one ^= 1;
zero ^= 1;
}
fp2_dbl(l[zero][one], q->x);
fp2_add(l[zero][one], l[zero][one], q->x);
fp_mul(l[zero][one][0], l[zero][one][0], t0);
fp_mul(l[zero][one][1], l[zero][one][1], t0);
fp_sub(l[zero][zero][0], t3, t1);
fp_zero(l[zero][zero][1]);
fp_mul(l[one][one][0], q->y[0], t5);
fp_mul(l[one][one][1], q->y[1], t5);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
fp_free(t3);
fp_free(t4);
fp_free(t5);
fp_free(t6);
}
}
/**
* Doubles a point represented in projective coordinates on an ordinary prime
* elliptic curve.
*
* @param r - the result.
* @param p - the point to double.
*/
static void ep_dbl_projc_imp(ep_t r, const ep_t p) {
fp_t t0, t1, t2, t3, t4, t5;
fp_null(t1);
fp_null(t2);
fp_null(t3);
fp_null(t4);
fp_null(t5);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
fp_new(t3);
fp_new(t4);
fp_new(t5);
if (!p->norm && ep_curve_opt_a() == OPT_MINUS3) {
/* dbl-2001-b formulas: 3M + 5S + 8add + 1*4 + 2*8 + 1*3 */
/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b */
/* t0 = delta = z1^2. */
fp_sqr(t0, p->z);
/* t1 = gamma = y1^2. */
fp_sqr(t1, p->y);
/* t2 = beta = x1 * y1^2. */
fp_mul(t2, p->x, t1);
/* t3 = alpha = 3 * (x1 - z1^2) * (x1 + z1^2). */
fp_sub(t3, p->x, t0);
fp_add(t4, p->x, t0);
fp_mul(t4, t3, t4);
fp_dbl(t3, t4);
fp_add(t3, t3, t4);
/* x3 = alpha^2 - 8 * beta. */
fp_dbl(t2, t2);
fp_dbl(t2, t2);
fp_dbl(t5, t2);
fp_sqr(r->x, t3);
fp_sub(r->x, r->x, t5);
/* z3 = (y1 + z1)^2 - gamma - delta. */
fp_add(r->z, p->y, p->z);
fp_sqr(r->z, r->z);
fp_sub(r->z, r->z, t1);
fp_sub(r->z, r->z, t0);
/* y3 = alpha * (4 * beta - x3) - 8 * gamma^2. */
fp_dbl(t1, t1);
fp_sqr(t1, t1);
fp_dbl(t1, t1);
fp_sub(r->y, t2, r->x);
fp_mul(r->y, r->y, t3);
fp_sub(r->y, r->y, t1);
} else if (ep_curve_opt_a() == OPT_ZERO) {
/* dbl-2009-l formulas: 2M + 5S + 6add + 1*8 + 3*2 + 1*3. */
/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l */
/* A = X1^2 */
fp_sqr(t0, p->x);
/* B = Y1^2 */
fp_sqr(t1, p->y);
/* C = B^2 */
fp_sqr(t2, t1);
/* D = 2*((X1+B)^2-A-C) */
fp_add(t1, t1, p->x);
fp_sqr(t1, t1);
fp_sub(t1, t1, t0);
fp_sub(t1, t1, t2);
fp_dbl(t1, t1);
/* E = 3*A */
fp_dbl(t3, t0);
fp_add(t0, t3, t0);
/* F = E^2 */
fp_sqr(t3, t0);
/* Z3 = 2*Y1*Z1 */
fp_mul(r->z, p->y, p->z);
fp_dbl(r->z, r->z);
/* X3 = F-2*D */
fp_sub(r->x, t3, t1);
fp_sub(r->x, r->x, t1);
/* Y3 = E*(D-X3)-8*C */
fp_sub(r->y, t1, r->x);
fp_mul(r->y, r->y, t0);
fp_dbl(t2, t2);
fp_dbl(t2, t2);
fp_dbl(t2, t2);
fp_sub(r->y, r->y, t2);
} 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. */
fp_sqr(t0, p->x);
fp_sqr(t1, p->y);
fp_sqr(t2, t1);
if (!p->norm) {
/* t3 = z1^2. */
fp_sqr(t3, p->z);
if (ep_curve_get_a() == OPT_ZERO) {
/* z3 = 2 * y1 * z1. */
fp_mul(r->z, p->y, p->z);
fp_dbl(r->z, r->z);
} else {
/* z3 = (y1 + z1)^2 - y1^2 - z1^2. */
fp_add(r->z, p->y, p->z);
fp_sqr(r->z, r->z);
fp_sub(r->z, r->z, t1);
fp_sub(r->z, r->z, t3);
}
} else {
/* z3 = 2 * y1. */
fp_dbl(r->z, p->y);
}
/* t4 = S = 2*((x1 + y1^2)^2 - x1^2 - y1^4). */
fp_add(t4, p->x, t1);
fp_sqr(t4, t4);
fp_sub(t4, t4, t0);
fp_sub(t4, t4, t2);
fp_dbl(t4, t4);
/* t5 = M = 3 * x1^2 + a * z1^4. */
fp_dbl(t5, t0);
fp_add(t5, t5, t0);
if (!p->norm) {
fp_sqr(t3, t3);
switch (ep_curve_opt_a()) {
case OPT_ZERO:
break;
case OPT_ONE:
fp_add(t5, t5, ep_curve_get_a());
break;
case OPT_DIGIT:
fp_mul_dig(t1, t3, ep_curve_get_a()[0]);
fp_add(t5, t5, t1);
break;
default:
fp_mul(t1, ep_curve_get_a(), t3);
fp_add(t5, t5, t1);
break;
}
} else {
switch (ep_curve_opt_a()) {
case OPT_ZERO:
break;
case OPT_ONE:
fp_add_dig(t5, t5, (dig_t)1);
break;
case OPT_DIGIT:
fp_add_dig(t5, t5, ep_curve_get_a()[0]);
break;
default:
fp_add(t5, t5, ep_curve_get_a());
break;
}
}
/* x3 = T = M^2 - 2 * S. */
fp_sqr(r->x, t5);
fp_dbl(t1, t4);
fp_sub(r->x, r->x, t1);
/* y3 = M * (S - T) - 8 * y1^4. */
fp_dbl(t2, t2);
fp_dbl(t2, t2);
fp_dbl(t2, t2);
fp_sub(t4, t4, r->x);
fp_mul(t5, t5, t4);
fp_sub(r->y, t5, t2);
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
fp_free(t3);
fp_free(t4);
fp_free(t5);
}
}
/**
* Adds a point represented in affine coordinates to a point represented in
* projective coordinates.
*
* @param[out] r - the result.
* @param[in] p - the projective point.
* @param[in] q - the affine point.
*/
static void ep_add_projc_mix(ep_t r, const ep_t p, const ep_t q) {
fp_t t0, t1, t2, t3, t4, t5, t6;
fp_null(t0);
fp_null(t1);
fp_null(t2);
fp_null(t3);
fp_null(t4);
fp_null(t5);
fp_null(t6);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
fp_new(t3);
fp_new(t4);
fp_new(t5);
fp_new(t6);
/* madd-2007-bl formulas: 7M + 4S + 9add + 1*4 + 3*2. */
/* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-madd-2007-bl */
if (!p->norm) {
/* t0 = z1^2. */
fp_sqr(t0, p->z);
/* t3 = U2 = x2 * z1^2. */
fp_mul(t3, q->x, t0);
/* t1 = S2 = y2 * z1^3. */
fp_mul(t1, t0, p->z);
fp_mul(t1, t1, q->y);
/* t3 = H = U2 - x1. */
fp_sub(t3, t3, p->x);
/* t1 = R = 2 * (S2 - y1). */
fp_sub(t1, t1, p->y);
fp_dbl(t1, t1);
} else {
/* H = x2 - x1. */
fp_sub(t3, q->x, p->x);
/* t1 = R = 2 * (y2 - y1). */
fp_sub(t1, q->y, p->y);
fp_dbl(t1, t1);
}
/* t2 = HH = H^2. */
fp_sqr(t2, t3);
/* If E is zero. */
if (fp_is_zero(t3)) {
if (fp_is_zero(t1)) {
/* If I is zero, p = q, should have doubled. */
ep_dbl_projc(r, p);
} else {
/* If I is not zero, q = -p, r = infinity. */
ep_set_infty(r);
}
} else {
/* t4 = I = 4*HH. */
fp_dbl(t4, t2);
fp_dbl(t4, t4);
/* t5 = J = H * I. */
fp_mul(t5, t3, t4);
/* t4 = V = x1 * I. */
fp_mul(t4, p->x, t4);
/* x3 = R^2 - J - 2 * V. */
fp_sqr(r->x, t1);
fp_sub(r->x, r->x, t5);
fp_dbl(t6, t4);
fp_sub(r->x, r->x, t6);
/* y3 = R * (V - x3) - 2 * Y1 * J. */
fp_sub(t4, t4, r->x);
fp_mul(t4, t4, t1);
fp_mul(t1, p->y, t5);
fp_dbl(t1, t1);
fp_sub(r->y, t4, t1);
if (!p->norm) {
/* z3 = (z1 + H)^2 - z1^2 - HH. */
fp_add(r->z, p->z, t3);
fp_sqr(r->z, r->z);
fp_sub(r->z, r->z, t0);
fp_sub(r->z, r->z, t2);
} else {
/* z3 = 2 * H. */
fp_dbl(r->z, t3);
}
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
fp_free(t3);
fp_free(t4);
fp_free(t5);
fp_free(t6);
}
}
void ep_param_set(int param) {
int plain = 0, endom = 0, super = 0;
char str[2 * FP_BYTES + 2];
fp_t a, b, beta;
ep_t g;
bn_t r, h, lamb;
fp_null(a);
fp_null(b);
fp_null(beta);
bn_null(lamb);
ep_null(g);
bn_null(r);
bn_null(h);
TRY {
fp_new(a);
fp_new(b);
fp_new(beta);
bn_new(lamb);
ep_new(g);
bn_new(r);
bn_new(h);
core_get()->ep_id = 0;
switch (param) {
#if defined(EP_ENDOM) && FP_PRIME == 158
case BN_P158:
ASSIGNK(BN_P158, BN_158);
endom = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 160
case SECG_P160:
ASSIGN(SECG_P160, SECG_160);
plain = 1;
break;
#endif
#if defined(EP_ENDOM) && FP_PRIME == 160
case SECG_K160:
ASSIGNK(SECG_K160, SECG_160D);
endom = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 192
case NIST_P192:
ASSIGN(NIST_P192, NIST_192);
plain = 1;
break;
#endif
#if defined(EP_ENDOM) && FP_PRIME == 192
case SECG_K192:
ASSIGNK(SECG_K192, SECG_192);
endom = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 221
case CURVE_22103:
ASSIGN(CURVE_22103, PRIME_22103);
plain = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 224
case NIST_P224:
ASSIGN(NIST_P224, NIST_224);
plain = 1;
break;
#endif
#if defined(EP_ENDOM) && FP_PRIME == 224
case SECG_K224:
ASSIGNK(SECG_K224, SECG_224);
endom = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 226
case CURVE_4417:
ASSIGN(CURVE_4417, PRIME_22605);
plain = 1;
break;
#endif
#if defined(EP_ENDOM) && FP_PRIME == 254
case BN_P254:
ASSIGNK(BN_P254, BN_254);
endom = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 251
case CURVE_1174:
ASSIGN(CURVE_1174, PRIME_25109);
plain = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 255
case CURVE_25519:
ASSIGN(CURVE_25519, PRIME_25519);
plain = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 256
case NIST_P256:
ASSIGN(NIST_P256, NIST_256);
plain = 1;
break;
#endif
#if defined(EP_ENDOM) && FP_PRIME == 256
case SECG_K256:
ASSIGNK(SECG_K256, SECG_256);
endom = 1;
break;
case BN_P256:
ASSIGNK(BN_P256, BN_256);
endom = 1;
break;
#endif
#if defined(EP_PLAIN) & FP_PRIME == 382
case CURVE_67254:
ASSIGN(CURVE_67254, PRIME_382105);
plain = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 383
case CURVE_383187:
ASSIGN(CURVE_383187, PRIME_383187);
plain = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 384
case NIST_P384:
ASSIGN(NIST_P384, NIST_384);
plain = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 477
case B24_P477:
ASSIGN(B24_P477, B24_477);
plain = 1;
break;
#endif
#if defined(EP_ENDOM) && FP_PRIME == 508
case KSS_P508:
ASSIGNK(KSS_P508, KSS_508);
endom = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 511
case CURVE_511187:
ASSIGN(CURVE_511187, PRIME_511187);
plain = 1;
break;
#endif
#if defined(EP_PLAIN) && FP_PRIME == 521
case NIST_P521:
ASSIGN(NIST_P521, NIST_521);
plain = 1;
break;
#endif
#if defined(EP_ENDOM) && FP_PRIME == 638
case BN_P638:
ASSIGNK(BN_P638, BN_638);
endom = 1;
break;
case B12_P638:
ASSIGNK(B12_P638, B12_638);
endom = 1;
break;
#endif
#if defined(EP_SUPER) && FP_PRIME == 1536
case SS_P1536:
ASSIGN(SS_P1536, SS_1536);
super = 1;
break;
#endif
default:
(void)str;
THROW(ERR_NO_VALID);
break;
}
/* Do not generate warnings. */
(void)endom;
(void)plain;
(void)beta;
fp_zero(g->z);
fp_set_dig(g->z, 1);
g->norm = 1;
#if defined(EP_PLAIN)
if (plain) {
ep_curve_set_plain(a, b, g, r, h);
core_get()->ep_id = param;
}
#endif
#if defined(EP_ENDOM)
if (endom) {
ep_curve_set_endom(b, g, r, h, beta, lamb);
core_get()->ep_id = param;
}
#endif
#if defined(EP_SUPER)
if (super) {
ep_curve_set_super(a, b, g, r, h);
core_get()->ep_id = param;
}
#endif
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(a);
fp_free(b);
fp_free(beta);
bn_free(lamb);
ep_free(g);
bn_free(r);
bn_free(h);
}
}
/**
* Doubles a point represented in affine coordinates on an ordinary prime
* elliptic curve.
*
* @param[out] r - the result.
* @param[out] s - the slope.
* @param[in] p - the point to double.
*/
static void ep_dbl_basic_imp(ep_t r, fp_t s, const ep_t p) {
fp_t t0, t1, t2;
fp_null(t0);
fp_null(t1);
fp_null(t2);
TRY {
fp_new(t0);
fp_new(t1);
fp_new(t2);
/* t0 = 1/2 * y1. */
fp_dbl(t0, p->y);
fp_inv(t0, t0);
/* t1 = 3 * x1^2 + a. */
fp_sqr(t1, p->x);
fp_copy(t2, t1);
fp_dbl(t1, t1);
fp_add(t1, t1, t2);
switch (ep_curve_opt_a()) {
case OPT_ZERO:
break;
case OPT_ONE:
fp_add_dig(t1, t1, (dig_t)1);
break;
#if FP_RDC != MONTY
case OPT_DIGIT:
fp_add_dig(t1, t1, ep_curve_get_a()[0]);
break;
#endif
default:
fp_add(t1, t1, ep_curve_get_a());
break;
}
/* t1 = (3 * x1^2 + a)/(2 * y1). */
fp_mul(t1, t1, t0);
if (s != NULL) {
fp_copy(s, t1);
}
/* t2 = t1^2. */
fp_sqr(t2, t1);
/* x3 = t1^2 - 2 * x1. */
fp_dbl(t0, p->x);
fp_sub(t0, t2, t0);
/* y3 = t1 * (x1 - x3) - y1. */
fp_sub(t2, p->x, t0);
fp_mul(t1, t1, t2);
fp_sub(r->y, t1, p->y);
fp_copy(r->x, t0);
fp_copy(r->z, p->z);
r->norm = 1;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp_free(t0);
fp_free(t1);
fp_free(t2);
}
}