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);
}
}
void fp2_norm_low(fp2_t c, fp2_t a) {
fp2_t t;
bn_t b;
fp2_null(t);
bn_null(b);
TRY {
fp2_new(t);
bn_new(b);
#if FP_PRIME == 158
fp_dbl(t[0], a[0]);
fp_dbl(t[0], t[0]);
fp_sub(t[0], t[0], a[1]);
fp_dbl(t[1], a[1]);
fp_dbl(t[1], t[1]);
fp_add(c[1], a[0], t[1]);
fp_copy(c[0], t[0]);
#elif defined(FP_QNRES)
/* If p = 3 mod 8, (1 + i) is a QNR/CNR. */
fp_neg(t[0], a[1]);
fp_add(c[1], a[0], a[1]);
fp_add(c[0], t[0], a[0]);
#else
switch (fp_prime_get_mod8()) {
case 3:
/* If p = 3 mod 8, (1 + u) is a QNR/CNR. */
fp_neg(t[0], a[1]);
fp_add(c[1], a[0], a[1]);
fp_add(c[0], t[0], a[0]);
break;
case 5:
/* If p = 5 mod 8, (u) is a QNR/CNR. */
fp2_mul_art(c, a);
break;
case 7:
/* If p = 7 mod 8, we choose (2^(lg_4(b-1)) + u) as QNR/CNR. */
fp2_mul_art(t, a);
fp2_dbl(c, a);
fp_prime_back(b, ep_curve_get_b());
for (int i = 1; i < bn_bits(b) / 2; i++) {
fp2_dbl(c, c);
}
fp2_add(c, c, t);
break;
default:
THROW(ERR_NO_VALID);
break;
}
#endif
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp2_free(t);
bn_free(b);
}
}
void fp2_nord_low(dv2_t c, dv2_t a) {
dv2_t t;
bn_t b;
dv2_null(t);
bn_null(b);
TRY {
dv2_new(t);
bn_new(b);
#if FP_PRIME == 158
fp_addc_low(t[0], a[0], a[0]);
fp_addc_low(t[0], t[0], t[0]);
fp_subc_low(t[0], t[0], a[1]);
fp_addc_low(t[1], a[1], a[1]);
fp_addc_low(t[1], t[1], t[1]);
fp_addc_low(c[1], a[0], t[1]);
dv_copy(c[0], t[0], 2 * FP_DIGS);
#elif defined(FP_QNRES)
/* If p = 3 mod 8, (1 + i) is a QNR/CNR. */
/* (a_0 + a_1 * i) * (1 + i) = (a_0 - a_1) + (a_0 + a_1) * u. */
dv_copy(t[0], a[1], 2 * FP_DIGS);
fp_addc_low(c[1], a[0], a[1]);
fp_subc_low(c[0], a[0], t[0]);
#else
switch (fp_prime_get_mod8()) {
case 3:
/* If p = 3 mod 8, (1 + u) is a QNR, u^2 = -1. */
/* (a_0 + a_1 * u) * (1 + u) = (a_0 - a_1) + (a_0 + a_1) * u. */
dv_copy(t[0], a[1], 2 * FP_DIGS);
fp_addc_low(c[1], a[0], a[1]);
fp_subc_low(c[0], a[0], t[0]);
break;
case 5:
/* If p = 5 mod 8, (u) is a QNR. */
dv_copy(t[0], a[0], 2 * FP_DIGS);
dv_zero(t[1], FP_DIGS);
dv_copy(t[1] + FP_DIGS, fp_prime_get(), FP_DIGS);
fp_subc_low(c[0], t[1], a[1]);
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_subc_low(c[0], c[0], a[1]);
}
dv_copy(c[1], t[0], 2 * FP_DIGS);
break;
case 7:
/* If p = 7 mod 8, (2^lg_4(b-1) + u) is a QNR/CNR. */
/* (a_0 + a_1 * u)(2^lg_4(b-1) + u) =
* (2^lg_4(b-1)a_0 - a_1) + (a_0 + 2^lg_4(b-1)a_1 * u. */
fp2_addc_low(t, a, a);
fp_prime_back(b, ep_curve_get_b());
for (int i = 1; i < bn_bits(b) / 2; i++) {
fp2_addc_low(t, t, t);
}
fp_subc_low(c[0], t[0], a[1]);
fp_addc_low(c[1], t[1], a[0]);
break;
default:
THROW(ERR_NO_VALID);
break;
}
#endif
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
dv2_free(t);
bn_free(b);
}
}
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);
}
}
