void eb_sub_basic(eb_t r, const eb_t p, const eb_t q) {
eb_t t;
eb_null(t);
if (p == q) {
eb_set_infty(r);
return;
}
TRY {
eb_new(t);
eb_neg_basic(t, q);
eb_add_basic(r, p, t);
r->norm = 1;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
eb_free(t);
}
}
void eb_norm(eb_t r, const eb_t p) {
if (eb_is_infty(p)) {
eb_set_infty(r);
return;
}
if (p->norm == 1) {
/* If the point is represented in affine coordinates, we just copy it. */
eb_copy(r, p);
return;
}
if (p->norm == 2) {
eb_norm_halve(r, p);
return;
}
#if EB_ADD == PROJC || !defined(STRIP)
#if defined(EB_SUPER)
if (eb_curve_is_super()) {
eb_norm_super(r, p, 0);
return;
}
#endif /* EB_SUPER */
#if defined(EB_ORDIN) || defined(EB_KBLTZ)
eb_norm_ordin(r, p, 0);
#endif /* EB_ORDIN || EB_KBLTZ */
#endif /* EB_ADD == PROJC */
}
void eb_mul_pre_combs(eb_t *t, eb_t p) {
int i, j, l;
bn_t ord;
bn_null(ord);
TRY {
bn_new(ord);
eb_curve_get_ord(ord);
l = bn_bits(ord);
l = ((l % EB_DEPTH) == 0 ? (l / EB_DEPTH) : (l / EB_DEPTH) + 1);
eb_set_infty(t[0]);
eb_copy(t[1], p);
for (j = 1; j < EB_DEPTH; j++) {
eb_dbl(t[1 << j], t[1 << (j - 1)]);
for (i = 1; i < l; i++) {
eb_dbl(t[1 << j], t[1 << j]);
}
for (i = 1; i < (1 << j); i++) {
eb_add(t[(1 << j) + i], t[1 << j], t[i]);
}
}
eb_norm_sim(t + 2, t + 2, EB_TABLE_COMBS - 2);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(ord);
}
}
void eb_dbl_basic(eb_t r, const eb_t p) {
if (eb_is_infty(p)) {
eb_set_infty(r);
return;
}
eb_dbl_basic_imp(r, p);
}
void eb_mul_pre_combd(eb_t *t, eb_t p) {
bn_t n;
bn_null(n);
TRY {
int i, j, d, e;
bn_new(n);
eb_curve_get_ord(n);
d = bn_bits(n);
d = ((d % EB_DEPTH) == 0 ? (d / EB_DEPTH) : (d / EB_DEPTH) + 1);
e = (d % 2 == 0 ? (d / 2) : (d / 2) + 1);
eb_set_infty(t[0]);
eb_copy(t[1], p);
for (j = 1; j < EB_DEPTH; j++) {
eb_dbl(t[1 << j], t[1 << (j - 1)]);
for (i = 1; i < d; i++) {
eb_dbl(t[1 << j], t[1 << j]);
}
for (i = 1; i < (1 << j); i++) {
eb_add(t[(1 << j) + i], t[1 << j], t[i]);
}
}
eb_set_infty(t[1 << EB_DEPTH]);
for (j = 1; j < (1 << EB_DEPTH); j++) {
eb_dbl(t[(1 << EB_DEPTH) + j], t[j]);
for (i = 1; i < e; i++) {
eb_dbl(t[(1 << EB_DEPTH) + j], t[(1 << EB_DEPTH) + j]);
}
}
eb_norm_sim(t + 2, t + 2, (1 << EB_DEPTH) - 2);
eb_norm_sim(t + (1 << EB_DEPTH) + 1, t + (1 << EB_DEPTH) + 1, (1 << EB_DEPTH) - 1);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(n);
}
}
void eb_mul_fix_combd(eb_t r, eb_t *t, bn_t k) {
int i, j, d, e, w0, w1, n0, p0, p1;
bn_t n;
bn_null(n);
TRY {
bn_new(n);
eb_curve_get_ord(n);
d = bn_bits(n);
d = ((d % EB_DEPTH) == 0 ? (d / EB_DEPTH) : (d / EB_DEPTH) + 1);
e = (d % 2 == 0 ? (d / 2) : (d / 2) + 1);
eb_set_infty(r);
n0 = bn_bits(k);
p1 = (e - 1) + (EB_DEPTH - 1) * d;
for (i = e - 1; i >= 0; i--) {
eb_dbl(r, r);
w0 = 0;
p0 = p1;
for (j = EB_DEPTH - 1; j >= 0; j--, p0 -= d) {
w0 = w0 << 1;
if (p0 < n0 && bn_test_bit(k, p0)) {
w0 = w0 | 1;
}
}
w1 = 0;
p0 = p1-- + e;
for (j = EB_DEPTH - 1; j >= 0; j--, p0 -= d) {
w1 = w1 << 1;
if (i + e < d && p0 < n0 && bn_test_bit(k, p0)) {
w1 = w1 | 1;
}
}
eb_add(r, r, t[w0]);
eb_add(r, r, t[(1 << EB_DEPTH) + w1]);
}
eb_norm(r, r);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(n);
}
}
void eb_neg_basic(eb_t r, const eb_t p) {
if (eb_is_infty(p)) {
eb_set_infty(r);
return;
}
if (r != p) {
fb_copy(r->x, p->x);
fb_copy(r->z, p->z);
}
fb_add(r->y, p->x, p->y);
r->norm = 1;
}
void eb_read_bin(eb_t a, const uint8_t *bin, int len) {
if (len == 1) {
if (bin[0] == 0) {
eb_set_infty(a);
return;
} else {
THROW(ERR_NO_BUFFER);
return;
}
}
if (len != (FB_BYTES + 1) && len != (2 * FB_BYTES + 1)) {
THROW(ERR_NO_BUFFER);
return;
}
a->norm = 1;
fb_set_dig(a->z, 1);
fb_read_bin(a->x, bin + 1, FB_BYTES);
if (len == FB_BYTES + 1) {
switch(bin[0]) {
case 2:
fb_zero(a->y);
break;
case 3:
fb_zero(a->y);
fb_set_bit(a->y, 0, 1);
break;
default:
THROW(ERR_NO_VALID);
break;
}
eb_upk(a, a);
}
if (len == 2 * FB_BYTES + 1) {
if (bin[0] == 4) {
fb_read_bin(a->y, bin + FB_BYTES + 1, FB_BYTES);
} else {
THROW(ERR_NO_VALID);
}
}
}
void eb_neg_projc(eb_t r, const eb_t p) {
fb_t t;
fb_null(t);
if (eb_is_infty(p)) {
eb_set_infty(r);
return;
}
if (p->norm) {
if (r != p) {
fb_copy(r->x, p->x);
fb_copy(r->z, p->z);
}
fb_add(r->y, p->x, p->y);
r->norm = 1;
return;
}
TRY {
fb_new(t);
fb_mul(t, p->x, p->z);
fb_add(r->y, p->y, t);
if (r != p) {
fb_copy(r->z, p->z);
fb_copy(r->x, p->x);
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(t);
}
}
void eb_neg_basic(eb_t r, const eb_t p) {
if (eb_is_infty(p)) {
eb_set_infty(r);
return;
}
if (r != p) {
fb_copy(r->x, p->x);
fb_copy(r->z, p->z);
}
#if defined(EB_SUPER)
if (eb_curve_is_super()) {
switch (eb_curve_opt_c()) {
case OPT_ZERO:
fb_copy(r->y, p->y);
break;
case OPT_ONE:
fb_add_dig(r->y, p->y, (dig_t)1);
break;
case OPT_DIGIT:
fb_add_dig(r->y, p->y, eb_curve_get_c()[0]);
break;
default:
fb_add(r->y, p->y, eb_curve_get_c());
break;
}
r->norm = 1;
return;
}
#endif
fb_add(r->y, p->x, p->y);
r->norm = 1;
}
void eb_mul_sim_trick(eb_t r, const eb_t p, const bn_t k, const eb_t q,
const bn_t m) {
eb_t t0[1 << (EB_WIDTH / 2)], t1[1 << (EB_WIDTH / 2)], t[1 << EB_WIDTH];
bn_t n;
int l0, l1, w = EB_WIDTH / 2;
uint8_t w0[CEIL(FB_BITS, 2)], w1[CEIL(FB_BITS, w)];
bn_null(n);
for (int i = 0; i < 1 << EB_WIDTH; i++) {
eb_null(t[i]);
}
for (int i = 0; i < 1 << (EB_WIDTH / 2); i++) {
eb_null(t0[i]);
eb_null(t1[i]);
}
TRY {
bn_new(n);
eb_curve_get_ord(n);
for (int i = 0; i < (1 << w); i++) {
eb_new(t0[i]);
eb_new(t1[i]);
}
for (int i = 0; i < (1 << EB_WIDTH); i++) {
eb_new(t[i]);
}
eb_set_infty(t0[0]);
for (int i = 1; i < (1 << w); i++) {
eb_add(t0[i], t0[i - 1], p);
}
eb_set_infty(t1[0]);
for (int i = 1; i < (1 << w); i++) {
eb_add(t1[i], t1[i - 1], q);
}
for (int i = 0; i < (1 << w); i++) {
for (int j = 0; j < (1 << w); j++) {
eb_add(t[(i << w) + j], t0[i], t1[j]);
}
}
#if EB_WIDTH > 2 && defined(EB_MIXED)
eb_norm_sim(t + 1, (const eb_t *)(t + 1), (1 << EB_WIDTH) - 1);
#endif
l0 = l1 = CEIL(FB_BITS, w);
bn_rec_win(w0, &l0, k, w);
bn_rec_win(w1, &l1, m, w);
for (int i = l0; i < l1; i++) {
w0[i] = 0;
}
for (int i = l1; i < l0; i++) {
w1[i] = 0;
}
eb_set_infty(r);
for (int i = MAX(l0, l1) - 1; i >= 0; i--) {
for (int j = 0; j < w; j++) {
eb_dbl(r, r);
}
eb_add(r, r, t[(w0[i] << w) + w1[i]]);
}
eb_norm(r, r);
} CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(n);
for (int i = 0; i < (1 << w); i++) {
eb_free(t0[i]);
eb_free(t1[i]);
}
for (int i = 0; i < (1 << EB_WIDTH); i++) {
eb_free(t[i]);
}
}
}
/**
* Multiplies and adds two binary elliptic curve points simultaneously,
* optionally choosing the first point as the generator depending on an optional
* table of precomputed points.
*
* @param[out] r - the result.
* @param[in] p - the first point to multiply.
* @param[in] k - the first integer.
* @param[in] q - the second point to multiply.
* @param[in] m - the second integer.
* @param[in] t - the pointer to a precomputed table.
*/
static void eb_mul_sim_plain(eb_t r, const eb_t p, const bn_t k, const eb_t q,
const bn_t m, const eb_t *t) {
int l, l0, l1, i, n0, n1, w, g;
int8_t naf0[FB_BITS + 1], naf1[FB_BITS + 1], *_k, *_m;
eb_t t0[1 << (EB_WIDTH - 2)];
eb_t t1[1 << (EB_WIDTH - 2)];
for (i = 0; i < (1 << (EB_WIDTH - 2)); i++) {
eb_null(t0[i]);
eb_null(t1[i]);
}
TRY {
g = (t == NULL ? 0 : 1);
if (!g) {
for (i = 0; i < (1 << (EB_WIDTH - 2)); i++) {
eb_new(t0[i]);
}
eb_tab(t0, p, EB_WIDTH);
t = (const eb_t *)t0;
}
/* Prepare the precomputation table. */
for (i = 0; i < (1 << (EB_WIDTH - 2)); i++) {
eb_new(t1[i]);
}
/* Compute the precomputation table. */
eb_tab(t1, q, EB_WIDTH);
/* Compute the w-NAF representation of k. */
if (g) {
w = EB_DEPTH;
} else {
w = EB_WIDTH;
}
l0 = l1 = FB_BITS + 1;
bn_rec_naf(naf0, &l0, k, w);
bn_rec_naf(naf1, &l1, m, EB_WIDTH);
l = MAX(l0, l1);
_k = naf0 + l - 1;
_m = naf1 + l - 1;
for (i = l0; i < l; i++) {
naf0[i] = 0;
}
for (i = l1; i < l; i++) {
naf1[i] = 0;
}
eb_set_infty(r);
for (i = l - 1; i >= 0; i--, _k--, _m--) {
eb_dbl(r, r);
n0 = *_k;
n1 = *_m;
if (n0 > 0) {
eb_add(r, r, t[n0 / 2]);
}
if (n0 < 0) {
eb_sub(r, r, t[-n0 / 2]);
}
if (n1 > 0) {
eb_add(r, r, t1[n1 / 2]);
}
if (n1 < 0) {
eb_sub(r, r, t1[-n1 / 2]);
}
}
/* Convert r to affine coordinates. */
eb_norm(r, r);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
/* Free the precomputation tables. */
if (!g) {
for (i = 0; i < 1 << (EB_WIDTH - 2); i++) {
eb_free(t0[i]);
}
}
for (i = 0; i < 1 << (EB_WIDTH - 2); i++) {
eb_free(t1[i]);
}
}
}
void eb_mul_sim_trick(eb_t r, const eb_t p, const bn_t k, const eb_t q,
const bn_t m) {
eb_t t0[1 << (EB_WIDTH / 2)], t1[1 << (EB_WIDTH / 2)], t[1 << EB_WIDTH];
int l0, l1, w = EB_WIDTH / 2;
uint8_t *w0 = RLC_ALLOCA(uint8_t, RLC_CEIL(RLC_FB_BITS, w));
uint8_t *w1 = RLC_ALLOCA(uint8_t, RLC_CEIL(RLC_FB_BITS, w));
bn_t n;
bn_null(n);
if (bn_is_zero(k) || eb_is_infty(p)) {
eb_mul(r, q, m);
return;
}
if (bn_is_zero(m) || eb_is_infty(q)) {
eb_mul(r, p, k);
return;
}
TRY {
bn_new(n);
eb_curve_get_ord(n);
for (int i = 0; i < (1 << w); i++) {
eb_null(t0[i]);
eb_null(t1[i]);
eb_new(t0[i]);
eb_new(t1[i]);
}
for (int i = 0; i < (1 << EB_WIDTH); i++) {
eb_null(t[i]);
eb_new(t[i]);
}
eb_set_infty(t0[0]);
eb_copy(t0[1], p);
if (bn_sign(k) == RLC_NEG) {
eb_neg(t0[1], t0[1]);
}
for (int i = 2; i < (1 << w); i++) {
eb_add(t0[i], t0[i - 1], t0[1]);
}
eb_set_infty(t1[0]);
eb_copy(t1[1], q);
if (bn_sign(m) == RLC_NEG) {
eb_neg(t1[1], t1[1]);
}
for (int i = 2; i < (1 << w); i++) {
eb_add(t1[i], t1[i - 1], t1[1]);
}
for (int i = 0; i < (1 << w); i++) {
for (int j = 0; j < (1 << w); j++) {
eb_add(t[(i << w) + j], t0[i], t1[j]);
}
}
#if EB_WIDTH > 2 && defined(EB_MIXED)
eb_norm_sim(t + 1, (const eb_t *)(t + 1), (1 << EB_WIDTH) - 1);
#endif
l0 = l1 = RLC_CEIL(RLC_FB_BITS + 1, w);
bn_rec_win(w0, &l0, k, w);
bn_rec_win(w1, &l1, m, w);
for (int i = l0; i < l1; i++) {
w0[i] = 0;
}
for (int i = l1; i < l0; i++) {
w1[i] = 0;
}
eb_set_infty(r);
for (int i = RLC_MAX(l0, l1) - 1; i >= 0; i--) {
for (int j = 0; j < w; j++) {
eb_dbl(r, r);
}
eb_add(r, r, t[(w0[i] << w) + w1[i]]);
}
eb_norm(r, r);
} CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
bn_free(n);
for (int i = 0; i < (1 << w); i++) {
eb_free(t0[i]);
eb_free(t1[i]);
}
for (int i = 0; i < (1 << EB_WIDTH); i++) {
eb_free(t[i]);
}
}
}
void eb_tab(eb_t *t, const eb_t p, int w) {
int u;
#if defined(EB_PLAIN)
if (!eb_curve_is_kbltz()) {
if (w > 2) {
eb_dbl(t[0], p);
#if defined(EB_MIXED)
eb_norm(t[0], t[0]);
#endif
eb_add(t[1], t[0], p);
for (int i = 2; i < (1 << (w - 2)); i++) {
eb_add(t[i], t[i - 1], t[0]);
}
#if defined(EB_MIXED)
eb_norm_sim(t + 1, (const eb_t *)t + 1, (1 << (w - 2)) - 1);
#endif
}
eb_copy(t[0], p);
}
#endif /* EB_PLAIN */
#if defined(EB_KBLTZ)
if (eb_curve_is_kbltz()) {
u = (eb_curve_opt_a() == OPT_ZERO ? -1 : 1);
/* Prepare the precomputation table. */
for (int i = 0; i < 1 << (w - 2); i++) {
eb_set_infty(t[i]);
fb_set_dig(t[i]->z, 1);
t[i]->norm = 1;
}
#if defined(EB_MIXED)
eb_norm(t[0], p);
#else
eb_copy(t[0], p);
#endif
switch (w) {
#if EB_DEPTH == 3 || EB_WIDTH == 3
case 3:
eb_frb(t[1], t[0]);
if (u == 1) {
eb_sub(t[1], t[0], t[1]);
} else {
eb_add(t[1], t[0], t[1]);
}
break;
#endif
#if EB_DEPTH == 4 || EB_WIDTH == 4
case 4:
eb_frb(t[3], t[0]);
eb_frb(t[3], t[3]);
eb_sub(t[1], t[3], p);
eb_add(t[2], t[3], p);
eb_frb(t[3], t[3]);
if (u == 1) {
eb_neg(t[3], t[3]);
}
eb_sub(t[3], t[3], p);
break;
#endif
#if EB_DEPTH == 5 || EB_WIDTH == 5
case 5:
eb_frb(t[3], t[0]);
eb_frb(t[3], t[3]);
eb_sub(t[1], t[3], p);
eb_add(t[2], t[3], p);
eb_frb(t[3], t[3]);
eb_frb(t[7], t[3]);
eb_sub(t[7], t[7], p);
if (u == 1) {
eb_neg(t[3], t[3]);
}
eb_sub(t[3], t[3], p);
eb_frb(t[4], t[2]);
eb_frb(t[4], t[4]);
eb_neg(t[4], t[4]);
eb_sub(t[5], t[4], p);
eb_add(t[6], t[4], p);
eb_frb(t[4], t[4]);
if (u == -1) {
eb_neg(t[4], t[4]);
}
eb_add(t[4], t[4], p);
break;
#endif
#if EB_DEPTH == 6 || EB_WIDTH == 6
case 6:
eb_frb(t[0], t[0]);
eb_frb(t[0], t[0]);
eb_neg(t[14], t[0]);
eb_sub(t[13], t[14], p);
eb_add(t[14], t[14], p);
eb_frb(t[0], t[0]);
eb_frb(t[8], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[11], t[0], p);
eb_add(t[12], t[0], p);
eb_frb(t[0], t[12]);
eb_frb(t[0], t[0]);
eb_sub(t[1], t[0], p);
eb_add(t[2], t[0], p);
eb_frb(t[15], t[8]);
if (u == -1) {
eb_neg(t[15], t[15]);
}
eb_sub(t[15], t[15], p);
eb_frb(t[0], t[13]);
eb_frb(t[0], t[0]);
eb_sub(t[5], t[0], p);
eb_add(t[6], t[0], p);
eb_sub(t[7], t[8], p);
eb_add(t[8], t[8], p);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[3], t[0], p);
eb_add(t[4], t[0], p);
eb_frb(t[0], t[1]);
eb_frb(t[0], t[0]);
eb_neg(t[9], t[0]);
eb_sub(t[9], t[9], p);
eb_frb(t[0], t[14]);
eb_frb(t[0], t[0]);
eb_add(t[10], t[0], p);
eb_copy(t[0], p);
break;
#endif
#if EB_DEPTH == 7 || EB_WIDTH == 7
/**
* Formulas from http://eprint.iacr.org/2012/519
*/
case 7:
eb_frb(t[0], t[0]);
eb_frb(t[0], t[0]);
eb_sub(t[17], t[0], p);
eb_add(t[18], t[0], p);
eb_frb(t[0], t[0]);
if (u == 1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[19], t[0], p);
eb_add(t[20], t[0], p);
eb_frb(t[0], t[19]);
eb_frb(t[0], t[0]);
eb_frb(t[11], t[0]);
if (u == 1) {
eb_neg(t[11], t[11]);
}
eb_add(t[12], t[11], p);
eb_sub(t[11], t[11], p);
eb_neg(t[0], t[0]);
eb_sub(t[1], t[0], p);
eb_add(t[2], t[0], p);
eb_frb(t[0], t[17]);
eb_frb(t[0], t[0]);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[3], t[0], p);
eb_frb(t[0], t[1]);
eb_frb(t[0], t[0]);
eb_add(t[9], t[0], p);
eb_neg(t[9], t[9]);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_add(t[4], t[0], p);
eb_frb(t[0], t[18]);
eb_frb(t[0], t[0]);
eb_sub(t[7], t[0], t[18]);
eb_sub(t[25], t[0], p);
eb_add(t[26], t[0], p);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[27], t[0], p);
eb_add(t[28], t[0], p);
eb_frb(t[0], t[17]);
eb_frb(t[0], t[0]);
eb_add(t[8], t[0], t[18]);
eb_neg(t[0], t[0]);
eb_add(t[10], t[0], p);
eb_frb(t[0], t[7]);
eb_frb(t[0], t[0]);
eb_sub(t[13], t[0], p);
eb_frb(t[0], t[8]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_add(t[14], t[0], p);
eb_frb(t[0], t[19]);
eb_frb(t[0], t[0]);
eb_add(t[15], t[0], t[17]);
eb_add(t[16], t[0], t[18]);
eb_frb(t[0], t[26]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_sub(t[5], t[0], p);
eb_add(t[6], t[0], p);
eb_add(t[23], t[0], t[17]);
eb_add(t[24], t[0], t[18]);
eb_frb(t[0], t[25]);
eb_frb(t[0], t[0]);
eb_sub(t[21], t[0], p);
eb_add(t[22], t[0], p);
eb_frb(t[0], t[20]);
eb_frb(t[0], t[0]);
eb_add(t[29], t[0], p);
eb_neg(t[29], t[29]);
eb_frb(t[0], t[27]);
eb_frb(t[0], t[0]);
eb_add(t[30], t[0], p);
eb_frb(t[0], t[7]);
eb_frb(t[0], t[0]);
eb_add(t[31], t[0], t[17])
eb_copy(t[0], p);
break;
#endif
#if EB_DEPTH == 8 || EB_WIDTH == 8
/**
* Formulas from http://eprint.iacr.org/2012/519
*/
case 8:
eb_frb(t[0], t[0]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_sub(t[45], t[0], p);
eb_add(t[46], t[0], p);
eb_frb(t[0], t[0]);
if (u == 1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[43], t[0], p);
eb_add(t[44], t[0], p);
eb_frb(t[0], t[44]);
eb_frb(t[0], t[0]);
eb_sub(t[1], t[0], p);
eb_add(t[2], t[0], p);
eb_add(t[47], t[0], t[45]);
eb_add(t[48], t[0], t[46]);
eb_frb(t[0], t[46]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_sub(t[7], t[0], t[46]);
eb_sub(t[8], t[0], t[45]);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[3], t[0], p);
eb_frb(t[0], t[1]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_add(t[55], t[0], t[45]);
eb_add(t[56], t[0], t[46]);
eb_sub(t[9], t[0], p);
eb_add(t[10], t[0], p);
eb_frb(t[0], t[0]);
if (u == 1) {
eb_neg(t[0], t[0]);
}
eb_add(t[4], t[0], p);
eb_frb(t[0], t[47]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_sub(t[17], t[0], p);
eb_add(t[18], t[0], p);
eb_frb(t[0], t[8]);
eb_frb(t[0], t[0]);
eb_add(t[31], t[0], t[45]);
eb_add(t[32], t[0], t[46]);
eb_neg(t[0], t[0]);
eb_sub(t[13], t[0], p);
eb_add(t[14], t[0], p);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[19], t[0], p);
eb_frb(t[0], t[7]);
eb_frb(t[0], t[0]);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_add(t[20], t[0], p);
eb_frb(t[0], t[9]);
eb_frb(t[0], t[0]);
eb_sub(t[21], t[0], p);
eb_add(t[22], t[0], p);
eb_frb(t[0], t[2]);
eb_frb(t[0], t[0]);
eb_sub(t[25], t[0], p);
eb_add(t[26], t[0], p);
eb_frb(t[0], t[43]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_sub(t[33], t[0], p);
eb_add(t[34], t[0], p);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_add(t[12], t[0], p);
eb_frb(t[0], t[45]);
eb_frb(t[0], t[0]);
eb_sub(t[37], t[0], p);
eb_add(t[38], t[0], p);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[35], t[0], p);
eb_add(t[36], t[0], p);
eb_frb(t[0], t[38]);
eb_frb(t[0], t[0]);
eb_sub(t[41], t[0], p);
eb_add(t[42], t[0], p);
eb_neg(t[0], t[0]);
eb_sub(t[39], t[0], t[46]);
eb_sub(t[40], t[0], t[45]);
eb_frb(t[0], t[37]);
eb_frb(t[0], t[0]);
eb_sub(t[5], t[0], p);
eb_add(t[6], t[0], p);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_add(t[15], t[0], t[43]);
eb_add(t[16], t[0], t[44]);
eb_neg(t[0], t[0]);
eb_sub(t[27], t[0], p);
eb_add(t[28], t[0], p);
eb_frb(t[0], t[36]);
eb_frb(t[0], t[0]);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[11], t[0], p);
eb_frb(t[0], t[39]);
eb_frb(t[0], t[0]);
eb_add(t[0], t[0], p);
eb_neg(t[49], t[0]);
eb_frb(t[0], t[7]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_add(t[50], t[0], p);
eb_frb(t[0], t[44]);
eb_frb(t[0], t[0]);
eb_frb(t[0], t[0]);
if (u == 1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[51], t[0], p);
eb_add(t[52], t[0], p);
eb_frb(t[0], t[46]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_sub(t[53], t[0], p);
eb_add(t[54], t[0], p);
eb_frb(t[0], t[54]);
eb_frb(t[0], t[0]);
eb_add(t[23], t[0], t[45]);
eb_add(t[24], t[0], t[46]);
eb_frb(t[0], t[42]);
eb_frb(t[0], t[0]);
eb_sub(t[57], t[0], p);
eb_frb(t[0], t[53]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_add(t[58], t[0], p);
eb_frb(t[0], t[38]);
eb_frb(t[0], t[0]);
eb_frb(t[0], t[0]);
if (u == -1) {
eb_neg(t[0], t[0]);
}
eb_sub(t[59], t[0], p);
eb_add(t[60], t[0], p);
eb_frb(t[0], t[35]);
eb_frb(t[0], t[0]);
eb_sub(t[61], t[0], p);
eb_add(t[62], t[0], p);
eb_frb(t[0], t[47]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_add(t[63], t[0], t[45]);
eb_frb(t[0], t[36]);
eb_frb(t[0], t[0]);
eb_neg(t[0], t[0]);
eb_sub(t[29], t[0], p);
eb_add(t[30], t[0], p);
eb_copy(t[0], p);
break;
#endif
}
#if defined(EB_MIXED)
if (w > 2) {
eb_norm_sim(t + 1, (const eb_t *)t + 1, (1 << (w - 2)) - 1);
}
#endif
}
#endif /* EB_KBLTZ */
}
/**
* Adds a point represented in affine coordinates to a point represented in
* projective coordinates.
*
* @param r - the result.
* @param p - the affine point.
* @param q - the projective point.
*/
static void eb_add_projc_ordin_mix(eb_t r, eb_t p, eb_t q) {
fb_t t0, t1, t2, t3, t4, t5;
fb_null(t0);
fb_null(t1);
fb_null(t2);
fb_null(t3);
fb_null(t4);
fb_null(t5);
TRY {
fb_new(t0);
fb_new(t1);
fb_new(t2);
fb_new(t3);
fb_new(t4);
fb_new(t5);
if (!p->norm) {
/* A = y1 + y2 * z1^2. */
fb_sqr(t0, p->z);
fb_mul(t0, t0, q->y);
fb_add(t0, t0, p->y);
/* B = x1 + x2 * z1. */
fb_mul(t1, p->z, q->x);
fb_add(t1, t1, p->x);
} else {
/* t0 = A = y1 + y2. */
fb_add(t0, p->y, q->y);
/* t1 = B = x1 + x2. */
fb_add(t1, p->x, q->x);
}
if (fb_is_zero(t1)) {
if (fb_is_zero(t0)) {
/* If t0 = 0 and t1 = 0, p = q, should have doubled! */
eb_dbl_projc(r, p);
} else {
/* If t0 = 0, r is infinity. */
eb_set_infty(r);
}
} else {
if (!p->norm) {
/* t2 = C = B * z1. */
fb_mul(t2, p->z, t1);
/* z3 = C^2. */
fb_sqr(r->z, t2);
/* t1 = B^2. */
fb_sqr(t1, t1);
/* t1 = A + B^2. */
fb_add(t1, t0, t1);
} else {
/* If z1 = 0, t2 = C = B. */
fb_copy(t2, t1);
/* z3 = B^2. */
fb_sqr(r->z, t1);
/* t1 = A + z3. */
fb_add(t1, t0, r->z);
}
/* t3 = D = x2 * z3. */
fb_mul(t3, r->z, q->x);
/* t4 = (y2 + x2). */
fb_add(t4, q->x, q->y);
/* z3 = A^2. */
fb_sqr(r->x, t0);
/* t1 = A + B^2 + a2 * C. */
switch (eb_curve_opt_a()) {
case OPT_ZERO:
break;
case OPT_ONE:
fb_add(t1, t1, t2);
break;
case OPT_DIGIT:
/* t5 = a2 * C. */
fb_mul_dig(t5, t2, eb_curve_get_a()[0]);
fb_add(t1, t1, t5);
break;
default:
/* t5 = a2 * C. */
fb_mul(t5, eb_curve_get_a(), t2);
fb_add(t1, t1, t5);
break;
}
/* t1 = C * (A + B^2 + a2 * C). */
fb_mul(t1, t1, t2);
/* x3 = A^2 + C * (A + B^2 + a2 * C). */
fb_add(r->x, r->x, t1);
/* t3 = D + x3. */
fb_add(t3, t3, r->x);
/* t2 = A * B. */
fb_mul(t2, t0, t2);
/* y3 = (D + x3) * (A * B + z3). */
fb_add(r->y, t2, r->z);
fb_mul(r->y, r->y, t3);
/* t0 = z3^2. */
fb_sqr(t0, r->z);
/* t0 = (y2 + x2) * z3^2. */
fb_mul(t0, t0, t4);
/* y3 = (D + x3) * (A * B + z3) + (y2 + x2) * z3^2. */
fb_add(r->y, r->y, t0);
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(t0);
fb_free(t1);
fb_free(t2);
fb_free(t3);
fb_free(t4);
fb_free(t5);
}
}
/**
* Adds two points represented in projective coordinates on an ordinary binary
* elliptic curve.
*
* @param r - the result.
* @param p - the first point to add.
* @param q - the second point to add.
*/
static void eb_add_projc_ordin(eb_t r, eb_t p, eb_t q) {
#if defined(EB_MIXED) && defined(STRIP)
eb_add_projc_ordin_mix(r, p, q);
#else /* General addition. */
fb_t t0, t1, t2, t3, t4, t5, t6, t7;
fb_null(t0);
fb_null(t1);
fb_null(t2);
fb_null(t3);
fb_null(t4);
fb_null(t5);
fb_null(t6);
fb_null(t7);
TRY {
fb_new(t0);
fb_new(t1);
fb_new(t2);
fb_new(t3);
fb_new(t4);
fb_new(t5);
fb_new(t6);
fb_new(t7);
if (q->norm) {
eb_add_projc_ordin_mix(r, p, q);
} else {
/* t0 = B = x2 * z1. */
fb_mul(t0, q->x, p->z);
/* A = x1 * z2 */
fb_mul(t1, p->x, q->z);
/* t2 = E = A + B. */
fb_add(t2, t1, t0);
/* t3 = D = B^2. */
fb_sqr(t3, t0);
/* t4 = C = A^2. */
fb_sqr(t4, t1);
/* t5 = F = C + D. */
fb_add(t5, t3, t4);
/* t6 = H = y2 * z1^2. */
fb_sqr(t6, p->z);
fb_mul(t6, t6, q->y);
/* t7 = G = y1 * z2^2. */
fb_sqr(t7, q->z);
fb_mul(t7, t7, p->y);
/* t3 = D + H. */
fb_add(t3, t3, t6);
/* t4 = C + G. */
fb_add(t4, t4, t7);
/* t6 = I = G + H. */
fb_add(t6, t7, t6);
/* If E is zero. */
if (fb_is_zero(t2)) {
if (fb_is_zero(t6)) {
/* If I is zero, p = q, should have doubled. */
eb_dbl_projc(r, p);
} else {
/* If I is not zero, q = -p, r = infinity. */
eb_set_infty(r);
}
} else {
/* t6 = J = I * E. */
fb_mul(t6, t6, t2);
/* z3 = F * z1 * z2. */
fb_mul(r->z, p->z, q->z);
fb_mul(r->z, t5, r->z);
/* t4 = B * (C + G). */
fb_mul(t4, t0, t4);
/* t2 = A * J. */
fb_mul(t2, t1, t6);
/* x3 = A * (D + H) + B * (C + G). */
fb_mul(r->x, t1, t3);
fb_add(r->x, r->x, t4);
/* t7 = F * G. */
fb_mul(t7, t7, t5);
/* Y3 = (A * J + F * G) * F + (J + z3) * x3. */
fb_add(r->y, t2, t7);
fb_mul(r->y, r->y, t5);
/* t7 = (J + z3) * x3. */
fb_add(t7, t6, r->z);
fb_mul(t7, t7, r->x);
fb_add(r->y, r->y, t7);
}
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(t0);
fb_free(t1);
fb_free(t2);
fb_free(t3);
fb_free(t4);
fb_free(t5);
fb_free(t6);
fb_free(t7);
}
#endif
}
/**
* Adds two points represented in affine coordinates on an ordinary binary
* 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 eb_add_basic_imp(eb_t r, const eb_t p, const eb_t q) {
fb_t t0, t1, t2;
fb_null(t0);
fb_null(t1);
fb_null(t2);
TRY {
fb_new(t0);
fb_new(t1);
fb_new(t2);
/* t0 = (y1 + y2). */
fb_add(t0, p->y, q->y);
/* t1 = (x1 + x2). */
fb_add(t1, p->x, q->x);
if (fb_is_zero(t1)) {
if (fb_is_zero(t0)) {
/* If t1 is zero and t0 is zero, p = q, should have doubled. */
eb_dbl_basic(r, p);
} else {
/* If t0 is not zero and t1 is zero, q = -p and r = infinity. */
eb_set_infty(r);
}
} else {
/* t2 = 1/(x1 + x2). */
fb_inv(t2, t1);
/* t0 = lambda = (y1 + y2)/(x1 + x2). */
fb_mul(t0, t0, t2);
/* t2 = lambda^2. */
fb_sqr(t2, t0);
/* t2 = lambda^2 + lambda + x1 + x2 + a. */
fb_add(t2, t2, t0);
fb_add(t2, t2, t1);
switch (eb_curve_opt_a()) {
case OPT_ZERO:
break;
case OPT_ONE:
fb_add_dig(t2, t2, (dig_t)1);
break;
case OPT_DIGIT:
fb_add_dig(t2, t2, eb_curve_get_a()[0]);
break;
default:
fb_add(t2, t2, eb_curve_get_a());
break;
}
/* y3 = lambda*(x3 + x1) + x3 + y1. */
fb_add(t1, t2, p->x);
fb_mul(t1, t1, t0);
fb_add(t1, t1, t2);
fb_add(r->y, p->y, t1);
/* x3 = lambda^2 + lambda + x1 + x2 + a. */
fb_copy(r->x, t2);
fb_copy(r->z, p->z);
r->norm = 1;
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(t0);
fb_free(t1);
fb_free(t2);
}
}
void eb_mul_sim_joint(eb_t r, const eb_t p, const bn_t k, const eb_t q,
const bn_t m) {
eb_t t[5];
int u_i, len, offset;
int8_t jsf[2 * (FB_BITS + 1)];
int i;
eb_null(t[0]);
eb_null(t[1]);
eb_null(t[2]);
eb_null(t[3]);
eb_null(t[4]);
TRY {
for (i = 0; i < 5; i++) {
eb_new(t[i]);
}
eb_set_infty(t[0]);
eb_copy(t[1], q);
eb_copy(t[2], p);
eb_add(t[3], p, q);
eb_sub(t[4], p, q);
#if defined(EB_MIXED)
eb_norm_sim(t + 3, (const eb_t*)(t + 3), 2);
#endif
len = 2 * (FB_BITS + 1);
bn_rec_jsf(jsf, &len, k, m);
eb_set_infty(r);
offset = MAX(bn_bits(k), bn_bits(m)) + 1;
for (i = len - 1; i >= 0; i--) {
eb_dbl(r, r);
if (jsf[i] != 0 && jsf[i] == -jsf[i + offset]) {
u_i = jsf[i] * 2 + jsf[i + offset];
if (u_i < 0) {
eb_sub(r, r, t[4]);
} else {
eb_add(r, r, t[4]);
}
} else {
u_i = jsf[i] * 2 + jsf[i + offset];
if (u_i < 0) {
eb_sub(r, r, t[-u_i]);
} else {
eb_add(r, r, t[u_i]);
}
}
}
eb_norm(r, r);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
for (i = 0; i < 5; i++) {
eb_free(t[i]);
}
}
}
void eb_neg_projc(eb_t r, const eb_t p) {
fb_t t;
fb_null(t);
if (eb_is_infty(p)) {
eb_set_infty(r);
return;
}
if (p->norm) {
if (r != p) {
fb_copy(r->x, p->x);
fb_copy(r->z, p->z);
}
#if defined(EB_SUPER)
if (eb_curve_is_super()) {
switch (eb_curve_opt_c()) {
case OPT_ZERO:
fb_copy(r->y, p->y);
break;
case OPT_ONE:
fb_add_dig(r->y, p->y, (dig_t)1);
break;
case OPT_DIGIT:
fb_add_dig(r->y, p->y, eb_curve_get_c()[0]);
break;
default:
fb_add(r->y, p->y, eb_curve_get_c());
break;
}
r->norm = 1;
return;
}
#endif
fb_add(r->y, p->x, p->y);
r->norm = 1;
return;
}
#if defined(EB_SUPER)
if (eb_curve_is_super()) {
fb_add(r->y, p->y, p->z);
fb_copy(r->z, p->z);
fb_copy(r->x, p->x);
r->norm = 0;
return;
}
#endif
TRY {
fb_new(t);
fb_mul(t, p->x, p->z);
fb_add(r->y, p->y, t);
if (r != p) {
fb_copy(r->z, p->z);
fb_copy(r->x, p->x);
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(t);
}
}
/**
* Multiplies and adds two binary elliptic curve points simultaneously,
* optionally choosing the first point as the generator depending on an optional
* table of precomputed points.
*
* @param[out] r - the result.
* @param[in] p - the first point to multiply.
* @param[in] k - the first integer.
* @param[in] q - the second point to multiply.
* @param[in] m - the second integer.
* @param[in] t - the pointer to a precomputed table.
*/
static void eb_mul_sim_kbltz(eb_t r, const eb_t p, const bn_t k, const eb_t q,
const bn_t m, const eb_t *t) {
int l0, l1, l, i, n0, n1, w, g;
int8_t u, tnaf0[FB_BITS + 8], tnaf1[FB_BITS + 8], *_k, *_m;
eb_t t0[1 << (EB_WIDTH - 2)];
eb_t t1[1 << (EB_WIDTH - 2)];
bn_t vm, s0, s1;
bn_null(vm);
bn_null(s0);
bn_null(s1);
for (i = 0; i < (1 << (EB_WIDTH - 2)); i++) {
eb_null(t0[i]);
eb_null(t1[i]);
}
TRY {
bn_new(vm);
bn_new(s0);
bn_new(s1);
/* Compute the w-TNAF representation of k. */
if (eb_curve_opt_a() == OPT_ZERO) {
u = -1;
} else {
u = 1;
}
g = (t == NULL ? 0 : 1);
if (!g) {
for (i = 0; i < (1 << (EB_WIDTH - 2)); i++) {
eb_new(t0[i]);
eb_set_infty(t0[i]);
fb_set_bit(t0[i]->z, 0, 1);
t0[i]->norm = 1;
}
eb_tab(t0, p, EB_WIDTH);
t = (const eb_t *)t0;
}
/* Prepare the precomputation table. */
for (i = 0; i < (1 << (EB_WIDTH - 2)); i++) {
eb_new(t1[i]);
eb_set_infty(t1[i]);
fb_set_bit(t1[i]->z, 0, 1);
t1[i]->norm = 1;
}
/* Compute the precomputation table. */
eb_tab(t1, q, EB_WIDTH);
/* Compute the w-TNAF representation of k. */
if (g) {
w = EB_DEPTH;
} else {
w = EB_WIDTH;
}
eb_curve_get_vm(vm);
eb_curve_get_s0(s0);
eb_curve_get_s1(s1);
l0 = l1 = FB_BITS + 8;
bn_rec_tnaf(tnaf0, &l0, k, vm, s0, s1, u, FB_BITS, w);
bn_rec_tnaf(tnaf1, &l1, m, vm, s0, s1, u, FB_BITS, EB_WIDTH);
l = MAX(l0, l1);
_k = tnaf0 + l - 1;
_m = tnaf1 + l - 1;
for (i = l0; i < l; i++)
tnaf0[i] = 0;
for (i = l1; i < l; i++)
tnaf1[i] = 0;
_k = tnaf0 + l - 1;
_m = tnaf1 + l - 1;
eb_set_infty(r);
for (i = l - 1; i >= 0; i--, _k--, _m--) {
eb_frb(r, r);
n0 = *_k;
n1 = *_m;
if (n0 > 0) {
eb_add(r, r, t[n0 / 2]);
}
if (n0 < 0) {
eb_sub(r, r, t[-n0 / 2]);
}
if (n1 > 0) {
eb_add(r, r, t1[n1 / 2]);
}
if (n1 < 0) {
eb_sub(r, r, t1[-n1 / 2]);
}
}
/* Convert r to affine coordinates. */
eb_norm(r, r);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
if (!g) {
for (i = 0; i < (1 << (EB_WIDTH - 2)); i++) {
eb_free(t0[i]);
}
}
for (i = 0; i < (1 << (EB_WIDTH - 2)); i++) {
eb_free(t1[i]);
}
bn_free(vm);
bn_free(s0);
bn_free(s1);
}
}
/**
* Adds a point represented in affine coordinates to a point represented in
* projective coordinates.
*
* @param[out] r - the result.
* @param[in] p - the affine point.
* @param[in] q - the projective point.
*/
static void eb_add_projc_mix(eb_t r, const eb_t p, const eb_t q) {
fb_t t0, t1, t2, t3, t4, t5;
fb_null(t0);
fb_null(t1);
fb_null(t2);
fb_null(t3);
fb_null(t4);
fb_null(t5);
TRY {
fb_new(t0);
fb_new(t1);
fb_new(t2);
fb_new(t3);
fb_new(t4);
fb_new(t5);
/* madd-2005-dl formulas: 7M + 4S + 9add + 1*4 + 3*2. */
/* http://www.hyperelliptic.org/EFD/g12o/auto-shortw-lopezdahab-1.html#addition-madd-2005-dl */
if (!p->norm) {
/* A = y1 + y2 * z1^2. */
fb_sqr(t0, p->z);
fb_mul(t0, t0, q->y);
fb_add(t0, t0, p->y);
/* B = x1 + x2 * z1. */
fb_mul(t1, p->z, q->x);
fb_add(t1, t1, p->x);
} else {
/* t0 = A = y1 + y2. */
fb_add(t0, p->y, q->y);
/* t1 = B = x1 + x2. */
fb_add(t1, p->x, q->x);
}
if (fb_is_zero(t1)) {
if (fb_is_zero(t0)) {
/* If t0 = 0 and t1 = 0, p = q, should have doubled! */
eb_dbl_projc(r, p);
} else {
/* If t0 = 0, r is infinity. */
eb_set_infty(r);
}
} else {
if (!p->norm) {
/* t2 = C = B * z1. */
fb_mul(t2, p->z, t1);
/* z3 = C^2. */
fb_sqr(r->z, t2);
/* t1 = B^2. */
fb_sqr(t1, t1);
/* t1 = A + B^2. */
fb_add(t1, t0, t1);
} else {
/* If z1 = 0, t2 = C = B. */
fb_copy(t2, t1);
/* z3 = B^2. */
fb_sqr(r->z, t1);
/* t1 = A + z3. */
fb_add(t1, t0, r->z);
}
/* t3 = D = x2 * z3. */
fb_mul(t3, r->z, q->x);
/* t4 = (y2 + x2). */
fb_add(t4, q->x, q->y);
/* z3 = A^2. */
fb_sqr(r->x, t0);
/* t1 = A + B^2 + a2 * C. */
switch (eb_curve_opt_a()) {
case OPT_ZERO:
break;
case OPT_ONE:
fb_add(t1, t1, t2);
break;
case OPT_DIGIT:
/* t5 = a2 * C. */
fb_mul_dig(t5, t2, eb_curve_get_a()[0]);
fb_add(t1, t1, t5);
break;
default:
/* t5 = a2 * C. */
fb_mul(t5, eb_curve_get_a(), t2);
fb_add(t1, t1, t5);
break;
}
/* t1 = C * (A + B^2 + a2 * C). */
fb_mul(t1, t1, t2);
/* x3 = A^2 + C * (A + B^2 + a2 * C). */
fb_add(r->x, r->x, t1);
/* t3 = D + x3. */
fb_add(t3, t3, r->x);
/* t2 = A * B. */
fb_mul(t2, t0, t2);
/* y3 = (D + x3) * (A * B + z3). */
fb_add(r->y, t2, r->z);
fb_mul(r->y, r->y, t3);
/* t0 = z3^2. */
fb_sqr(t0, r->z);
/* t0 = (y2 + x2) * z3^2. */
fb_mul(t0, t0, t4);
/* y3 = (D + x3) * (A * B + z3) + (y2 + x2) * z3^2. */
fb_add(r->y, r->y, t0);
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(t0);
fb_free(t1);
fb_free(t2);
fb_free(t3);
fb_free(t4);
fb_free(t5);
}
}