void fp12_inv(fp12_t c, fp12_t a) {
fp6_t t0;
fp6_t t1;
fp6_null(t0);
fp6_null(t1);
TRY {
fp6_new(t0);
fp6_new(t1);
fp6_sqr(t0, a[0]);
fp6_sqr(t1, a[1]);
fp6_mul_art(t1, t1);
fp6_sub(t0, t0, t1);
fp6_inv(t0, t0);
fp6_mul(c[0], a[0], t0);
fp6_neg(c[1], a[1]);
fp6_mul(c[1], c[1], t0);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp6_free(t0);
fp6_free(t1);
}
}
void fp12_sqr_basic(fp12_t c, fp12_t a) {
fp6_t t0, t1;
fp6_null(t0);
fp6_null(t1);
TRY {
fp6_new(t0);
fp6_new(t1);
fp6_add(t0, a[0], a[1]);
fp6_mul_art(t1, a[1]);
fp6_add(t1, a[0], t1);
fp6_mul(t0, t0, t1);
fp6_mul(c[1], a[0], a[1]);
fp6_sub(c[0], t0, c[1]);
fp6_mul_art(t1, c[1]);
fp6_sub(c[0], c[0], t1);
fp6_dbl(c[1], c[1]);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp6_free(t0);
fp6_free(t1);
}
}
void fp12_mul_lazyr(fp12_t c, fp12_t a, fp12_t b) {
dv6_t u0, u1, u2, u3;
fp6_t t0, t1;
dv6_null(u0);
dv6_null(u1);
dv6_null(u2);
dv6_null(u3);
fp6_null(t0);
fp6_null(t0);
fp6_null(t1);
TRY {
dv6_new(u0);
dv6_new(u1);
dv6_new(u2);
dv6_new(u3);
fp6_new(t0);
fp6_new(t1);
/* Karatsuba algorithm. */
/* u0 = a_0 * b_0. */
fp6_mul_unr(u0, a[0], b[0]);
/* u1 = a_1 * b_1. */
fp6_mul_unr(u1, a[1], b[1]);
/* t1 = a_0 + a_1. */
fp6_add(t0, a[0], a[1]);
/* t0 = b_0 + b_1. */
fp6_add(t1, b[0], b[1]);
/* u2 = (a_0 + a_1) * (b_0 + b_1) */
fp6_mul_unr(u2, t0, t1);
/* c_1 = u2 - a_0b_0 - a_1b_1. */
for (int i = 0; i < 3; i++) {
fp2_addc_low(u3[i], u0[i], u1[i]);
fp2_subc_low(u2[i], u2[i], u3[i]);
fp2_rdcn_low(c[1][i], u2[i]);
}
/* c_0 = a_0b_0 + v * a_1b_1. */
fp2_nord_low(u2[0], u1[2]);
dv_copy(u2[1][0], u1[0][0], 2 * RLC_FP_DIGS);
dv_copy(u2[1][1], u1[0][1], 2 * RLC_FP_DIGS);
dv_copy(u2[2][0], u1[1][0], 2 * RLC_FP_DIGS);
dv_copy(u2[2][1], u1[1][1], 2 * RLC_FP_DIGS);
for (int i = 0; i < 3; i++) {
fp2_addc_low(u2[i], u0[i], u2[i]);
fp2_rdcn_low(c[0][i], u2[i]);
}
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
dv6_free(u0);
dv6_free(u1);
dv6_free(u2);
dv6_free(u3);
fp6_free(t0);
fp6_free(t1);
}
}
void fp18_inv(fp18_t c, fp18_t a) {
fp6_t v0;
fp6_t v1;
fp6_t v2;
fp6_t t0;
fp6_null(v0);
fp6_null(v1);
fp6_null(v2);
fp6_null(t0);
TRY {
fp6_new(v0);
fp6_new(v1);
fp6_new(v2);
fp6_new(t0);
/* v0 = a_0^2 - E * a_1 * a_2. */
fp6_sqr(t0, a[0]);
fp6_mul(v0, a[1], a[2]);
fp6_mul_art(v2, v0);
fp6_sub(v0, t0, v2);
/* v1 = E * a_2^2 - a_0 * a_1. */
fp6_sqr(t0, a[2]);
fp6_mul_art(v2, t0);
fp6_mul(v1, a[0], a[1]);
fp6_sub(v1, v2, v1);
/* v2 = a_1^2 - a_0 * a_2. */
fp6_sqr(t0, a[1]);
fp6_mul(v2, a[0], a[2]);
fp6_sub(v2, t0, v2);
fp6_mul(t0, a[1], v2);
fp6_mul_art(c[1], t0);
fp6_mul(c[0], a[0], v0);
fp6_mul(t0, a[2], v1);
fp6_mul_art(c[2], t0);
fp6_add(t0, c[0], c[1]);
fp6_add(t0, t0, c[2]);
fp6_inv(t0, t0);
fp6_mul(c[0], v0, t0);
fp6_mul(c[1], v1, t0);
fp6_mul(c[2], v2, t0);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp6_free(v0);
fp6_free(v1);
fp6_free(v2);
fp6_free(t0);
}
}
void fp12_mul_basic(fp12_t c, fp12_t a, fp12_t b) {
fp6_t t0, t1, t2;
fp6_null(t0);
fp6_null(t1);
fp6_null(t2);
TRY {
fp6_new(t0);
fp6_new(t1);
fp6_new(t2);
/* Karatsuba algorithm. */
/* t0 = a_0 * b_0. */
fp6_mul(t0, a[0], b[0]);
/* t1 = a_1 * b_1. */
fp6_mul(t1, a[1], b[1]);
/* t2 = b_0 + b_1. */
fp6_add(t2, b[0], b[1]);
/* c_1 = a_0 + a_1. */
fp6_add(c[1], a[0], a[1]);
/* c_1 = (a_0 + a_1) * (b_0 + b_1) */
fp6_mul(c[1], c[1], t2);
fp6_sub(c[1], c[1], t0);
fp6_sub(c[1], c[1], t1);
/* c_0 = a_0b_0 + v * a_1b_1. */
fp6_mul_art(t1, t1);
fp6_add(c[0], t0, t1);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp6_free(t0);
fp6_free(t1);
fp6_free(t2);
}
}
void fp12_mul_dxs_lazyr(fp12_t c, fp12_t a, fp12_t b) {
fp6_t t0;
dv6_t u0, u1, u2;
fp6_null(t0);
dv6_null(u0);
dv6_null(u1);
dv6_null(u2);
TRY {
fp6_new(t0);
dv6_new(u0);
dv6_new(u1);
dv6_new(u2);
if (ep2_curve_is_twist() == EP_DTYPE) {
#if EP_ADD == BASIC
/* t0 = a_0 * b_0. */
fp_muln_low(u0[0][0], a[0][0][0], b[0][0][0]);
fp_muln_low(u0[0][1], a[0][0][1], b[0][0][0]);
fp_muln_low(u0[1][0], a[0][1][0], b[0][0][0]);
fp_muln_low(u0[1][1], a[0][1][1], b[0][0][0]);
fp_muln_low(u0[2][0], a[0][2][0], b[0][0][0]);
fp_muln_low(u0[2][1], a[0][2][1], b[0][0][0]);
/* t2 = b_0 + b_1. */
fp_add(t0[0][0], b[0][0][0], b[1][0][0]);
fp_copy(t0[0][1], b[1][0][1]);
fp2_copy(t0[1], b[1][1]);
#elif EP_ADD == PROJC
/* t0 = a_0 * b_0. */
#ifdef RLC_FP_ROOM
fp2_mulc_low(u0[0], a[0][0], b[0][0]);
fp2_mulc_low(u0[1], a[0][1], b[0][0]);
fp2_mulc_low(u0[2], a[0][2], b[0][0]);
#else
fp2_muln_low(u0[0], a[0][0], b[0][0]);
fp2_muln_low(u0[1], a[0][1], b[0][0]);
fp2_muln_low(u0[2], a[0][2], b[0][0]);
#endif
/* t2 = b_0 + b_1. */
fp2_add(t0[0], b[0][0], b[1][0]);
fp2_copy(t0[1], b[1][1]);
#endif
/* t1 = a_1 * b_1. */
fp6_mul_dxs_unr_lazyr(u1, a[1], b[1]);
} else {
/* t0 = a_0 * b_0. */
fp6_mul_dxs_unr_lazyr(u0, a[0], b[0]);
#if EP_ADD == BASIC
/* t0 = a_0 * b_0. */
fp_muln_low(u1[1][0], a[1][2][0], b[1][1][0]);
fp_muln_low(u1[1][1], a[1][2][1], b[1][1][0]);
fp2_nord_low(u1[0], u1[1]);
fp_muln_low(u1[1][0], a[1][0][0], b[1][1][0]);
fp_muln_low(u1[1][1], a[1][0][1], b[1][1][0]);
fp_muln_low(u1[2][0], a[1][1][0], b[1][1][0]);
fp_muln_low(u1[2][1], a[1][1][1], b[1][1][0]);
/* t2 = b_0 + b_1. */
fp2_copy(t0[0], b[0][0]);
fp_add(t0[1][0], b[0][1][0], b[1][1][0]);
fp_copy(t0[1][1], b[0][1][1]);
#elif EP_ADD == PROJC
/* t1 = a_1 * b_1. */
fp2_muln_low(u1[1], a[1][2], b[1][1]);
fp2_nord_low(u1[0], u1[1]);
fp2_muln_low(u1[1], a[1][0], b[1][1]);
fp2_muln_low(u1[2], a[1][1], b[1][1]);
/* t2 = b_0 + b_1. */
fp2_copy(t0[0], b[0][0]);
fp2_add(t0[1], b[0][1], b[1][1]);
#endif
}
/* c_1 = a_0 + a_1. */
fp6_add(c[1], a[0], a[1]);
/* c_1 = (a_0 + a_1) * (b_0 + b_1) */
fp6_mul_dxs_unr_lazyr(u2, c[1], t0);
for (int i = 0; i < 3; i++) {
fp2_subc_low(u2[i], u2[i], u0[i]);
fp2_subc_low(u2[i], u2[i], u1[i]);
}
fp2_rdcn_low(c[1][0], u2[0]);
fp2_rdcn_low(c[1][1], u2[1]);
fp2_rdcn_low(c[1][2], u2[2]);
fp2_nord_low(u2[0], u1[2]);
fp2_addc_low(u0[0], u0[0], u2[0]);
fp2_addc_low(u0[1], u0[1], u1[0]);
fp2_addc_low(u0[2], u0[2], u1[1]);
/* c_0 = a_0b_0 + v * a_1b_1. */
fp2_rdcn_low(c[0][0], u0[0]);
fp2_rdcn_low(c[0][1], u0[1]);
fp2_rdcn_low(c[0][2], u0[2]);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp6_free(t0);
dv6_free(u0);
dv6_free(u1);
dv6_free(u2);
}
}
void fp12_mul_dxs_basic(fp12_t c, fp12_t a, fp12_t b) {
fp6_t t0, t1, t2;
fp6_null(t0);
fp6_null(t1);
fp6_null(t2);
TRY {
fp6_new(t0);
fp6_new(t1);
fp6_new(t2);
if (ep2_curve_is_twist() == EP_DTYPE) {
#if EP_ADD == BASIC
/* t0 = a_0 * b_0 */
fp_mul(t0[0][0], a[0][0][0], b[0][0][0]);
fp_mul(t0[0][1], a[0][0][1], b[0][0][0]);
fp_mul(t0[1][0], a[0][1][0], b[0][0][0]);
fp_mul(t0[1][1], a[0][1][1], b[0][0][0]);
fp_mul(t0[2][0], a[0][2][0], b[0][0][0]);
fp_mul(t0[2][1], a[0][2][1], b[0][0][0]);
/* t2 = b_0 + b_1. */
fp_add(t2[0][0], b[0][0][0], b[1][0][0]);
fp_copy(t2[0][1], b[1][0][1]);
fp2_copy(t2[1], b[1][1]);
#elif EP_ADD == PROJC
/* t0 = a_0 * b_0 */
fp2_mul(t0[0], a[0][0], b[0][0]);
fp2_mul(t0[1], a[0][1], b[0][0]);
fp2_mul(t0[2], a[0][2], b[0][0]);
/* t2 = b_0 + b_1. */
fp2_add(t2[0], b[0][0], b[1][0]);
fp2_copy(t2[1], b[1][1]);
#endif
/* t1 = a_1 * b_1. */
fp6_mul_dxs(t1, a[1], b[1]);
} else {
/* t0 = a_0 * b_0. */
fp6_mul_dxs(t0, a[0], b[0]);
#if EP_ADD == BASIC
/* t1 = a_1 * b_1. */
fp_mul(t2[0][0], a[1][2][0], b[1][1][0]);
fp_mul(t2[0][1], a[1][2][1], b[1][1][0]);
fp2_mul_nor(t1[0], t2[0]);
fp_mul(t1[1][0], a[1][0][0], b[1][1][0]);
fp_mul(t1[1][1], a[1][0][1], b[1][1][0]);
fp_mul(t1[2][0], a[1][1][0], b[1][1][0]);
fp_mul(t1[2][1], a[1][1][1], b[1][1][0]);
/* t2 = b_0 + b_1. */
fp2_copy(t2[0], b[0][0]);
fp_add(t2[1][0], b[0][1][0], b[1][1][0]);
fp_copy(t2[1][1], b[0][1][1]);
#elif EP_ADD == PROJC
/* t1 = a_1 * b_1. */
fp2_mul(t2[0], a[1][2], b[1][1]);
fp2_mul_nor(t1[0], t2[0]);
fp2_mul(t1[1], a[1][0], b[1][1]);
fp2_mul(t1[2], a[1][1], b[1][1]);
/* t2 = b_0 + b_1. */
fp2_copy(t2[0], b[0][0]);
fp2_add(t2[1], b[0][1], b[1][1]);
#endif
}
/* c_1 = a_0 + a_1. */
fp6_add(c[1], a[0], a[1]);
/* c_1 = (a_0 + a_1) * (b_0 + b_1) - a_0 * b_0 - a_1 * b_1. */
fp6_mul_dxs(c[1], c[1], t2);
fp6_sub(c[1], c[1], t0);
fp6_sub(c[1], c[1], t1);
/* c_0 = a_0 * b_0 + v * a_1 * b_1. */
fp6_mul_art(t1, t1);
fp6_add(c[0], t0, t1);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fp6_free(t0);
fp6_free(t1);
fp6_free(t2);
}
}