void ep2_mul_sim_joint(ep2_t r, ep2_t p, bn_t k, ep2_t q, bn_t l) {
ep2_t t[5];
int u_i, len, offset;
int8_t jsf[4 * (FP_BITS + 1)];
int i;
ep2_null(t[0]);
ep2_null(t[1]);
ep2_null(t[2]);
ep2_null(t[3]);
ep2_null(t[4]);
TRY {
for (i = 0; i < 5; i++) {
ep2_new(t[i]);
}
ep2_set_infty(t[0]);
ep2_copy(t[1], q);
ep2_copy(t[2], p);
ep2_add(t[3], p, q);
ep2_sub(t[4], p, q);
len = 4 * (FP_BITS + 1);
bn_rec_jsf(jsf, &len, k, l);
ep2_set_infty(r);
i = bn_bits(k);
offset = MAX(i, bn_bits(l)) + 1;
for (i = len - 1; i >= 0; i--) {
ep2_dbl(r, r);
if (jsf[i] != 0 && jsf[i] == -jsf[i + offset]) {
u_i = jsf[i] * 2 + jsf[i + offset];
if (u_i < 0) {
ep2_sub(r, r, t[4]);
} else {
ep2_add(r, r, t[4]);
}
} else {
u_i = jsf[i] * 2 + jsf[i + offset];
if (u_i < 0) {
ep2_sub(r, r, t[-u_i]);
} else {
ep2_add(r, r, t[u_i]);
}
}
}
ep2_norm(r, r);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
for (i = 0; i < 5; i++) {
ep2_free(t[i]);
}
}
}
/**
* Multiplies a point on a Barreto-Lynn-Soctt curve by the cofactor.
*
* @param[out] r - the result.
* @param[in] p - the point to multiply.
*/
void ep2_mul_cof_b12(ep2_t r, ep2_t p) {
bn_t x;
ep2_t t0, t1, t2, t3;
ep2_null(t0);
ep2_null(t1);
ep2_null(t2);
ep2_null(t3);
bn_null(x);
TRY {
ep2_new(t0);
ep2_new(t1);
ep2_new(t2);
ep2_new(t3);
bn_new(x);
fp_param_get_var(x);
/* Compute t0 = xP. */
ep2_mul(t0, p, x);
if (bn_sign(x) == BN_NEG) {
ep2_neg(t0, t0);
}
/* Compute t1 = [x^2]P. */
ep2_mul(t1, t0, x);
if (bn_sign(x) == BN_NEG) {
ep2_neg(t1, t1);
}
/* t2 = (x^2 - x - 1)P = x^2P - x*P - P. */
ep2_sub(t2, t1, t0);
ep2_sub(t2, t2, p);
/* t3 = \psi(x - 1)P. */
ep2_sub(t3, t0, p);
ep2_norm(t3, t3);
ep2_frb(t3, t3, 1);
ep2_add(t2, t2, t3);
/* t3 = \psi^2(2P). */
ep2_dbl(t3, p);
ep2_norm(t3, t3);
ep2_frb(t3, t3, 2);
ep2_add(t2, t2, t3);
ep2_norm(r, t2);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
ep2_free(t0);
ep2_free(t1);
ep2_free(t2);
ep2_free(t3);
bn_free(x);
}
}
/**
* Multiplies a binary elliptic curve point by an integer using the w-NAF
* method.
*
* @param[out] r - the result.
* @param[in] p - the point to multiply.
* @param[in] k - the integer.
*/
static void ep2_mul_fix_ordin(ep2_t r, ep2_t *table, bn_t k) {
int len, i, n;
int8_t naf[2 * RLC_FP_BITS + 1], *t;
if (bn_is_zero(k)) {
ep2_set_infty(r);
return;
}
/* Compute the w-TNAF representation of k. */
len = 2 * RLC_FP_BITS + 1;
bn_rec_naf(naf, &len, k, EP_DEPTH);
t = naf + len - 1;
ep2_set_infty(r);
for (i = len - 1; i >= 0; i--, t--) {
ep2_dbl(r, r);
n = *t;
if (n > 0) {
ep2_add(r, r, table[n / 2]);
}
if (n < 0) {
ep2_sub(r, r, table[-n / 2]);
}
}
/* Convert r to affine coordinates. */
ep2_norm(r, r);
if (bn_sign(k) == RLC_NEG) {
ep2_neg(r, r);
}
}
void ep2_mul_fix_nafwi(ep2_t r, ep2_t *t, bn_t k) {
int i, j, l, d, m;
ep2_t a;
int8_t naf[2 * FP_BITS + 1];
char w;
ep2_null(a);
TRY {
ep2_new(a);
ep2_set_infty(r);
ep2_set_infty(a);
l = 2 * FP_BITS + 1;
bn_rec_naf(naf, &l, k, 2);
d = ((l % EP_DEPTH) == 0 ? (l / EP_DEPTH) : (l / EP_DEPTH) + 1);
for (i = 0; i < d; i++) {
w = 0;
for (j = EP_DEPTH - 1; j >= 0; j--) {
if (i * EP_DEPTH + j < l) {
w = (char)(w << 1);
w = (char)(w + naf[i * EP_DEPTH + j]);
}
}
naf[i] = w;
}
if (EP_DEPTH % 2 == 0) {
m = ((1 << (EP_DEPTH + 1)) - 2) / 3;
} else {
m = ((1 << (EP_DEPTH + 1)) - 1) / 3;
}
for (j = m; j >= 1; j--) {
for (i = 0; i < d; i++) {
if (naf[i] == j) {
ep2_add(a, a, t[i]);
}
if (naf[i] == -j) {
ep2_sub(a, a, t[i]);
}
}
ep2_add(r, r, a);
}
ep2_norm(r, r);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
ep2_free(a);
}
}
static void ep2_mul_sim_plain(ep2_t r, ep2_t p, bn_t k, ep2_t q, bn_t l,
ep2_t *t) {
int len, l0, l1, i, n0, n1, w, gen;
int8_t naf0[2 * FP_BITS + 1], naf1[2 * FP_BITS + 1], *_k, *_m;
ep2_t t0[1 << (EP_WIDTH - 2)];
ep2_t t1[1 << (EP_WIDTH - 2)];
for (i = 0; i < (1 << (EP_WIDTH - 2)); i++) {
ep2_null(t0[i]);
ep2_null(t1[i]);
}
TRY {
gen = (t == NULL ? 0 : 1);
if (!gen) {
for (i = 0; i < (1 << (EP_WIDTH - 2)); i++) {
ep2_new(t0[i]);
}
ep2_tab(t0, p, EP_WIDTH);
t = (ep2_t *)t0;
}
/* Prepare the precomputation table. */
for (i = 0; i < (1 << (EP_WIDTH - 2)); i++) {
ep2_new(t1[i]);
}
/* Compute the precomputation table. */
ep2_tab(t1, q, EP_WIDTH);
/* Compute the w-TNAF representation of k. */
if (gen) {
w = EP_DEPTH;
} else {
w = EP_WIDTH;
}
l0 = l1 = 2 * FP_BITS + 1;
bn_rec_naf(naf0, &l0, k, w);
bn_rec_naf(naf1, &l1, l, EP_WIDTH);
len = MAX(l0, l1);
_k = naf0 + len - 1;
_m = naf1 + len - 1;
for (i = l0; i < len; i++)
naf0[i] = 0;
for (i = l1; i < len; i++)
naf1[i] = 0;
ep2_set_infty(r);
for (i = len - 1; i >= 0; i--, _k--, _m--) {
ep2_dbl(r, r);
n0 = *_k;
n1 = *_m;
if (n0 > 0) {
ep2_add(r, r, t[n0 / 2]);
}
if (n0 < 0) {
ep2_sub(r, r, t[-n0 / 2]);
}
if (n1 > 0) {
ep2_add(r, r, t1[n1 / 2]);
}
if (n1 < 0) {
ep2_sub(r, r, t1[-n1 / 2]);
}
}
/* Convert r to affine coordinates. */
ep2_norm(r, r);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
/* Free the precomputation tables. */
if (!gen) {
for (i = 0; i < (1 << (EP_WIDTH - 2)); i++) {
ep2_free(t0[i]);
}
}
for (i = 0; i < (1 << (EP_WIDTH - 2)); i++) {
ep2_free(t1[i]);
}
}
}
static void ep2_mul_sim_ordin(ep2_t r, ep2_t p, bn_t k, ep2_t q, bn_t l, int gen) {
int len, l0, l1, i, n0, n1, w;
signed char naf0[FP_BITS + 1], naf1[FP_BITS + 1], *t0, *t1;
ep2_t table0[1 << (EP_WIDTH - 2)];
ep2_t table1[1 << (EP_WIDTH - 2)];
ep2_t *t = NULL;
for (i = 0; i < (1 << (EP_WIDTH - 2)); i++) {
ep2_null(table0[i]);
ep2_null(table1[i]);
}
if (gen) {
#if defined(EP_PRECO)
t = ep2_curve_get_tab();
#endif
} else {
for (i = 0; i < (1 << (EP_WIDTH - 2)); i++) {
ep2_new(table0[i]);
}
ep2_tab(table0, p, EP_WIDTH);
t = table0;
}
/* Prepare the precomputation table. */
for (i = 0; i < (1 << (EP_WIDTH - 2)); i++) {
ep2_new(table1[i]);
}
/* Compute the precomputation table. */
ep2_tab(table1, q, EP_WIDTH);
/* Compute the w-TNAF representation of k. */
if (gen) {
w = EP_DEPTH;
} else {
w = EP_WIDTH;
}
l0 = l1 = FP_BITS + 1;
bn_rec_naf(naf0, &l0, k, w);
bn_rec_naf(naf1, &l1, l, EP_WIDTH);
len = MAX(l0, l1);
t0 = naf0 + len - 1;
t1 = naf1 + len - 1;
for (i = l0; i < len; i++)
naf0[i] = 0;
for (i = l1; i < len; i++)
naf1[i] = 0;
ep2_set_infty(r);
for (i = len - 1; i >= 0; i--, t0--, t1--) {
ep2_dbl(r, r);
n0 = *t0;
n1 = *t1;
if (n0 > 0) {
ep2_add(r, r, t[n0 / 2]);
}
if (n0 < 0) {
ep2_sub(r, r, t[-n0 / 2]);
}
if (n1 > 0) {
ep2_add(r, r, table1[n1 / 2]);
}
if (n1 < 0) {
ep2_sub(r, r, table1[-n1 / 2]);
}
}
/* Convert r to affine coordinates. */
ep2_norm(r, r);
/* Free the precomputation table. */
for (i = 0; i < 1 << (EP_WIDTH - 2); i++) {
ep2_free(table0[i]);
ep2_free(table1[i]);
}
}
