void fp2_mulc_low(dv2_t c, fp2_t a, fp2_t b) {
align dig_t t0[2 * FP_DIGS], t1[2 * FP_DIGS], t2[2 * FP_DIGS];
/* Karatsuba algorithm. */
/* t0 = a_0 + a_1, t1 = b_0 + b_1. */
fp_addn_low(t0, a[0], a[1]);
fp_addn_low(t1, b[0], b[1]);
/* c_0 = a_0 * b_0, c_1 = a_1 * b_1, t2 = (a_0 + a_1) * (b_0 + b_1). */
fp_muln_low(c[0], a[0], b[0]);
fp_muln_low(c[1], a[1], b[1]);
fp_muln_low(t2, t0, t1);
/* t0 = (a_0 * b_0) + (a_1 * b_1). */
fp_addd_low(t0, c[0], c[1]);
/* c_0 = (a_0 * b_0) + u^2 * (a_1 * b_1). */
fp_subd_low(c[0], c[0], c[1]);
#ifndef FP_QNRES
/* t1 = u^2 * (a_1 * b_1). */
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_subd_low(c[0], c[0], c[1]);
}
#endif
/* c_1 = (t2 - t0). */
fp_subd_low(c[1], t2, t0);
/* c_0 = c_0 + 2^N * p/4. */
bn_lshb_low(c[0] + FP_DIGS - 1, c[0] + FP_DIGS - 1, FP_DIGS + 1, 2);
fp_addn_low(c[0] + FP_DIGS, c[0] + FP_DIGS, fp_prime_get());
bn_rshb_low(c[0] + FP_DIGS - 1, c[0] + FP_DIGS - 1, FP_DIGS + 1, 2);
}
void fp_subc_low(dig_t *c, const dig_t *a, const dig_t *b) {
dig_t carry = fp_subd_low(c, a, b);
if (carry) {
fp_addn_low(c + FP_DIGS, c + FP_DIGS, fp_prime_get());
}
}
void fp2_muln_low(dv2_t c, fp2_t a, fp2_t b) {
align dig_t t0[2 * FP_DIGS], t1[2 * FP_DIGS], t2[2 * FP_DIGS];
/* Karatsuba algorithm. */
/* t0 = a_0 + a_1, t1 = b_0 + b_1. */
#ifdef FP_SPACE
fp_addn_low(t0, a[0], a[1]);
fp_addn_low(t1, b[0], b[1]);
#else
fp_addm_low(t0, a[0], a[1]);
fp_addm_low(t1, b[0], b[1]);
#endif
/* c_0 = a_0 * b_0, c_1 = a_1 * b_1. */
fp_muln_low(c[0], a[0], b[0]);
fp_muln_low(c[1], a[1], b[1]);
/* t2 = (a_0 + a_1) * (b_0 + b_1). */
fp_muln_low(t2, t0, t1);
/* t0 = (a_0 * b_0) + (a_1 * b_1). */
#ifdef FP_SPACE
fp_addd_low(t0, c[0], c[1]);
#else
fp_addc_low(t0, c[0], c[1]);
#endif
/* c_0 = (a_0 * b_0) + u^2 * (a_1 * b_1). */
fp_subc_low(c[0], c[0], c[1]);
#ifndef FP_QNRES
/* t1 = u^2 * (a_1 * b_1). */
for (int i = -1; i > fp_prime_get_qnr(); i--) {
fp_subc_low(c[0], c[0], c[1]);
}
for (int i = 0; i <= fp_prime_get_qnr(); i++) {
fp_addc_low(c[0], c[0], c[1]);
}
#endif
/* c_1 = t2 - t0. */
#ifdef FP_SPACE
fp_subd_low(c[1], t2, t0);
#else
fp_subc_low(c[1], t2, t0);
#endif
}
void fp2_subd_low(dv2_t c, dv2_t a, dv2_t b) {
fp_subd_low(c[0], a[0], b[0]);
fp_subd_low(c[1], a[1], b[1]);
}
void fp2_norh_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);
#ifdef 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[1], a[1], 2 * FP_DIGS);
fp_addd_low(c[1], a[0], a[1]);
/* c_0 = c_0 + 2^N * p/2. */
dv_copy(t[0], a[0], 2 * FP_DIGS);
bn_lshb_low(t[0] + FP_DIGS - 1, t[0] + FP_DIGS - 1, FP_DIGS + 1, 1);
fp_addn_low(t[0] + FP_DIGS, t[0] + FP_DIGS, fp_prime_get());
bn_rshb_low(t[0] + FP_DIGS - 1, t[0] + FP_DIGS - 1, FP_DIGS + 1, 1);
fp_subd_low(c[0], t[0], t[1]);
#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 1:
case 5:
/* If p = 1,5 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 + u) is a QNR/CNR. */
fp2_addc_low(t, a, a);
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);
}
}
