void fp6_inv(fp6_t c, fp6_t a) {
fp2_t v0;
fp2_t v1;
fp2_t v2;
fp2_t t0;
fp2_null(v0);
fp2_null(v1);
fp2_null(v2);
fp2_null(t0);
TRY {
fp2_new(v0);
fp2_new(v1);
fp2_new(v2);
fp2_new(t0);
/* v0 = a_0^2 - E * a_1 * a_2. */
fp2_sqr(t0, a[0]);
fp2_mul(v0, a[1], a[2]);
fp2_mul_nor(v2, v0);
fp2_sub(v0, t0, v2);
/* v1 = E * a_2^2 - a_0 * a_1. */
fp2_sqr(t0, a[2]);
fp2_mul_nor(v2, t0);
fp2_mul(v1, a[0], a[1]);
fp2_sub(v1, v2, v1);
/* v2 = a_1^2 - a_0 * a_2. */
fp2_sqr(t0, a[1]);
fp2_mul(v2, a[0], a[2]);
fp2_sub(v2, t0, v2);
fp2_mul(t0, a[1], v2);
fp2_mul_nor(c[1], t0);
fp2_mul(c[0], a[0], v0);
fp2_mul(t0, a[2], v1);
fp2_mul_nor(c[2], t0);
fp2_add(t0, c[0], c[1]);
fp2_add(t0, t0, c[2]);
fp2_inv(t0, t0);
fp2_mul(c[0], v0, t0);
fp2_mul(c[1], v1, t0);
fp2_mul(c[2], v2, t0);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp2_free(v0);
fp2_free(v1);
fp2_free(v2);
fp2_free(t0);
}
}
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);
}
}
/**
* Computes the constantes required for evaluating Frobenius maps.
*/
static void fp2_calc() {
bn_t e;
fp2_t t0;
fp2_t t1;
ctx_t *ctx = core_get();
bn_null(e);
fp2_null(t0);
fp2_null(t1);
TRY {
bn_new(e);
fp2_new(t0);
fp2_new(t1);
fp2_zero(t0);
fp_set_dig(t0[0], 1);
fp2_mul_nor(t0, t0);
e->used = FP_DIGS;
dv_copy(e->dp, fp_prime_get(), FP_DIGS);
bn_sub_dig(e, e, 1);
bn_div_dig(e, e, 6);
fp2_exp(t0, t0, e);
#if ALLOC == AUTO
fp2_copy(ctx->fp2_p[0], t0);
fp2_sqr(ctx->fp2_p[1], ctx->fp2_p[0]);
fp2_mul(ctx->fp2_p[2], ctx->fp2_p[1], ctx->fp2_p[0]);
fp2_sqr(ctx->fp2_p[3], ctx->fp2_p[1]);
fp2_mul(ctx->fp2_p[4], ctx->fp2_p[3], ctx->fp2_p[0]);
#else
fp_copy(ctx->fp2_p[0][0], t0[0]);
fp_copy(ctx->fp2_p[0][1], t0[1]);
fp2_sqr(t1, t0);
fp_copy(ctx->fp2_p[1][0], t1[0]);
fp_copy(ctx->fp2_p[1][1], t1[1]);
fp2_mul(t1, t1, t0);
fp_copy(ctx->fp2_p[2][0], t1[0]);
fp_copy(ctx->fp2_p[2][1], t1[1]);
fp2_sqr(t1, t0);
fp2_sqr(t1, t1);
fp_copy(ctx->fp2_p[3][0], t1[0]);
fp_copy(ctx->fp2_p[3][1], t1[1]);
fp2_mul(t1, t1, t0);
fp_copy(ctx->fp2_p[4][0], t1[0]);
fp_copy(ctx->fp2_p[4][1], t1[1]);
#endif
fp2_frb(t1, t0, 1);
fp2_mul(t0, t1, t0);
fp_copy(ctx->fp2_p2[0], t0[0]);
fp_sqr(ctx->fp2_p2[1], ctx->fp2_p2[0]);
fp_mul(ctx->fp2_p2[2], ctx->fp2_p2[1], ctx->fp2_p2[0]);
fp_sqr(ctx->fp2_p2[3], ctx->fp2_p2[1]);
for (int i = 0; i < 5; i++) {
fp_mul(ctx->fp2_p3[i][0], ctx->fp2_p2[i % 3], ctx->fp2_p[i][0]);
fp_mul(ctx->fp2_p3[i][1], ctx->fp2_p2[i % 3], ctx->fp2_p[i][1]);
}
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
bn_free(e);
fp2_free(t0);
fp2_free(t1);
}
}
void fp12_sqr_pck_basic(fp12_t c, fp12_t a) {
fp2_t t0, t1, t2, t3, t4, t5, t6;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
fp2_null(t3);
fp2_null(t4);
fp2_null(t5);
fp2_null(t6);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
fp2_new(t3);
fp2_new(t4);
fp2_new(t5);
fp2_new(t6);
fp2_sqr(t0, a[0][1]);
fp2_sqr(t1, a[1][2]);
fp2_add(t5, a[0][1], a[1][2]);
fp2_sqr(t2, t5);
fp2_add(t3, t0, t1);
fp2_sub(t5, t2, t3);
fp2_add(t6, a[1][0], a[0][2]);
fp2_sqr(t3, t6);
fp2_sqr(t2, a[1][0]);
fp2_mul_nor(t6, t5);
fp2_add(t5, t6, a[1][0]);
fp2_dbl(t5, t5);
fp2_add(c[1][0], t5, t6);
fp2_mul_nor(t4, t1);
fp2_add(t5, t0, t4);
fp2_sub(t6, t5, a[0][2]);
fp2_sqr(t1, a[0][2]);
fp2_dbl(t6, t6);
fp2_add(c[0][2], t6, t5);
fp2_mul_nor(t4, t1);
fp2_add(t5, t2, t4);
fp2_sub(t6, t5, a[0][1]);
fp2_dbl(t6, t6);
fp2_add(c[0][1], t6, t5);
fp2_add(t0, t2, t1);
fp2_sub(t5, t3, t0);
fp2_add(t6, t5, a[1][2]);
fp2_dbl(t6, t6);
fp2_add(c[1][2], t5, t6);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
fp2_free(t3);
fp2_free(t4);
fp2_free(t5);
fp2_free(t6);
}
}
void fp12_sqr_cyc_basic(fp12_t c, fp12_t a) {
fp2_t t0, t1, t2, t3, t4, t5, t6;
fp2_null(t0);
fp2_null(t1);
fp2_null(t2);
fp2_null(t3);
fp2_null(t4);
fp2_null(t5);
fp2_null(t6);
TRY {
fp2_new(t0);
fp2_new(t1);
fp2_new(t2);
fp2_new(t3);
fp2_new(t4);
fp2_new(t5);
fp2_new(t6);
/* Define z = sqrt(E) */
/* Now a is seen as (t0,t1) + (t2,t3) * w + (t4,t5) * w^2 */
/* (t0, t1) = (a00 + a11*z)^2. */
fp2_sqr(t2, a[0][0]);
fp2_sqr(t3, a[1][1]);
fp2_add(t1, a[0][0], a[1][1]);
fp2_mul_nor(t0, t3);
fp2_add(t0, t0, t2);
fp2_sqr(t1, t1);
fp2_sub(t1, t1, t2);
fp2_sub(t1, t1, t3);
fp2_sub(c[0][0], t0, a[0][0]);
fp2_add(c[0][0], c[0][0], c[0][0]);
fp2_add(c[0][0], t0, c[0][0]);
fp2_add(c[1][1], t1, a[1][1]);
fp2_add(c[1][1], c[1][1], c[1][1]);
fp2_add(c[1][1], t1, c[1][1]);
fp2_sqr(t0, a[0][1]);
fp2_sqr(t1, a[1][2]);
fp2_add(t5, a[0][1], a[1][2]);
fp2_sqr(t2, t5);
fp2_add(t3, t0, t1);
fp2_sub(t5, t2, t3);
fp2_add(t6, a[1][0], a[0][2]);
fp2_sqr(t3, t6);
fp2_sqr(t2, a[1][0]);
fp2_mul_nor(t6, t5);
fp2_add(t5, t6, a[1][0]);
fp2_dbl(t5, t5);
fp2_add(c[1][0], t5, t6);
fp2_mul_nor(t4, t1);
fp2_add(t5, t0, t4);
fp2_sub(t6, t5, a[0][2]);
fp2_sqr(t1, a[0][2]);
fp2_dbl(t6, t6);
fp2_add(c[0][2], t6, t5);
fp2_mul_nor(t4, t1);
fp2_add(t5, t2, t4);
fp2_sub(t6, t5, a[0][1]);
fp2_dbl(t6, t6);
fp2_add(c[0][1], t6, t5);
fp2_add(t0, t2, t1);
fp2_sub(t5, t3, t0);
fp2_add(t6, t5, a[1][2]);
fp2_dbl(t6, t6);
fp2_add(c[1][2], t5, t6);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp2_free(t0);
fp2_free(t1);
fp2_free(t2);
fp2_free(t3);
fp2_free(t4);
fp2_free(t5);
fp2_free(t6);
}
}
