void set_identity_tw_extensible(struct tw_extensible_t* a) {
p448_set_ui(&a->x, 0);
p448_set_ui(&a->y, 1);
p448_set_ui(&a->z, 1);
p448_set_ui(&a->t, 0);
p448_set_ui(&a->u, 0);
}
void deserialize_montgomery(struct montgomery_t* a, const struct p448_t* sbz) {
p448_sqr(&a->z0, sbz);
p448_set_ui(&a->xd, 1);
p448_set_ui(&a->zd, 0);
p448_set_ui(&a->xa, 1);
p448_copy(&a->za, &a->z0);
}
void
set_identity_affine (
struct affine_t* a
) {
p448_set_ui( &a->x, 0 );
p448_set_ui( &a->y, 1 );
}
void twist_even(struct tw_extensible_t* b, const struct extensible_t* a) {
mask_t L0, L1;
p448_sqr(&b->y, &a->z);
p448_sqr(&b->z, &a->x);
p448_sub(&b->u, &b->y, &b->z);
p448_bias(&b->u, 2);
p448_weak_reduce(&b->u);
p448_sub(&b->z, &a->z, &a->x);
p448_bias(&b->z, 2);
p448_weak_reduce(&b->z);
p448_mul(&b->y, &b->z, &a->y);
p448_sub(&b->z, &a->z, &a->y);
p448_bias(&b->z, 2);
p448_weak_reduce(&b->z);
p448_mul(&b->x, &b->z, &b->y);
p448_mul(&b->t, &b->x, &b->u);
p448_mul(&b->y, &b->x, &b->t);
p448_isr(&b->t, &b->y);
p448_mul(&b->u, &b->x, &b->t);
p448_sqr(&b->x, &b->t);
p448_mul(&b->t, &b->y, &b->x);
p448_mul(&b->x, &a->x, &b->u);
p448_mul(&b->y, &a->y, &b->u);
L1 = p448_is_zero(&b->z);
L0 = -L1;
p448_addw(&b->y, L0);
p448_weak_reduce(&b->y);
p448_set_ui(&b->z, 1);
p448_copy(&b->t, &b->x);
p448_copy(&b->u, &b->y);
}
void convert_affine_to_extensible(struct extensible_t* b, const struct affine_t* a) {
p448_copy(&b->x, &a->x);
p448_copy(&b->y, &a->y);
p448_set_ui(&b->z, 1);
p448_copy(&b->t, &a->x);
p448_copy(&b->u, &a->y);
}
void convert_tw_niels_to_tw_extensible(struct tw_extensible_t* e,
const struct tw_niels_t* d) {
p448_add(&e->y, &d->b, &d->a);
p448_weak_reduce(&e->y);
p448_sub(&e->x, &d->b, &d->a);
p448_bias(&e->x, 2);
p448_weak_reduce(&e->x);
p448_set_ui(&e->z, 1);
p448_copy(&e->t, &e->x);
p448_copy(&e->u, &e->y);
}
void
test_only_twist (
struct tw_extensible_t* b,
const struct extensible_t* a
) {
mask_t L2, L3;
struct p448_t L0, L1;
p448_sqr ( &b->u, &a->z );
p448_sqr ( &b->y, &a->x );
p448_sub ( &b->z, &b->u, &b->y );
p448_bias ( &b->z, 2 );
p448_add ( &b->y, &b->z, &b->z );
p448_add ( &b->u, &b->y, &b->y );
IF32( p448_weak_reduce( &b->u ) );
p448_sub ( &b->y, &a->z, &a->x );
p448_bias ( &b->y, 2 );
IF32( p448_weak_reduce( &b->y ) );
p448_mul ( &b->x, &b->y, &a->y );
p448_sub ( &b->z, &a->z, &a->y );
p448_bias ( &b->z, 2 );
IF32( p448_weak_reduce( &b->z ) );
p448_mul ( &b->t, &b->z, &b->x );
p448_mul ( &L1, &b->t, &b->u );
p448_mul ( &b->x, &b->t, &L1 );
p448_isr ( &L0, &b->x );
p448_mul ( &b->u, &b->t, &L0 );
p448_sqr ( &L1, &L0 );
p448_mul ( &b->t, &b->x, &L1 );
p448_add ( &L1, &a->y, &a->x );
IF32( p448_weak_reduce( &L1 ) );
p448_sub ( &L0, &a->x, &a->y );
p448_bias ( &L0, 2 );
IF32( p448_weak_reduce( &L0 ) );
p448_mul ( &b->x, &b->t, &L0 );
p448_add ( &L0, &b->x, &L1 );
p448_sub ( &b->t, &L1, &b->x );
p448_bias ( &b->t, 2 );
IF32( p448_weak_reduce( &b->t ) );
p448_mul ( &b->x, &L0, &b->u );
L2 = p448_is_zero( &b->y );
L3 = - L2;
p448_addw ( &b->x, L3 );
p448_weak_reduce( &b->x );
p448_mul ( &b->y, &b->t, &b->u );
L2 = p448_is_zero( &b->z );
L3 = - L2;
p448_addw ( &b->y, L3 );
p448_weak_reduce( &b->y );
L3 = p448_is_zero( &a->y );
L2 = L3 + 1;
p448_set_ui( &b->z, L2 );
p448_copy ( &b->t, &b->x );
p448_copy ( &b->u, &b->y );
}
mask_t
deserialize_and_twist_approx (
struct tw_extensible_t* a,
const struct p448_t* sdm1,
const struct p448_t* sz
) {
struct p448_t L0, L1;
p448_sqr ( &a->z, sz );
p448_copy ( &a->y, &a->z );
p448_addw ( &a->y, 1 );
p448_sqr ( &a->x, &a->y );
p448_mulw ( &a->y, &a->x, 39082 );
p448_neg ( &a->x, &a->y );
p448_add ( &a->y, &a->z, &a->z );
p448_bias ( &a->y, 1 );
p448_add ( &a->u, &a->y, &a->y );
p448_add ( &a->y, &a->u, &a->x );
IF32( p448_weak_reduce( &a->y ) );
p448_sqr ( &a->x, &a->z );
p448_subw ( &a->x, 1 );
p448_neg ( &a->u, &a->x );
p448_bias ( &a->u, 2 );
IF32( p448_weak_reduce( &a->u ) );
p448_mul ( &a->x, sdm1, &a->u );
p448_mul ( &L0, &a->x, &a->y );
p448_mul ( &a->t, &L0, &a->y );
p448_mul ( &a->u, &a->x, &a->t );
p448_mul ( &a->t, &a->u, &L0 );
p448_mul ( &a->y, &a->x, &a->t );
p448_isr ( &L0, &a->y );
p448_mul ( &a->y, &a->u, &L0 );
p448_sqr ( &L1, &L0 );
p448_mul ( &a->u, &a->t, &L1 );
p448_mul ( &a->t, &a->x, &a->u );
p448_add ( &a->x, sz, sz );
p448_mul ( &L0, &a->u, &a->x );
p448_copy ( &a->x, &a->z );
p448_subw ( &a->x, 1 );
p448_neg ( &L1, &a->x );
p448_bias ( &L1, 2 );
IF32( p448_weak_reduce( &L1 ) );
p448_mul ( &a->x, &L1, &L0 );
p448_mul ( &L0, &a->u, &a->y );
p448_addw ( &a->z, 1 );
p448_mul ( &a->y, &a->z, &L0 );
p448_subw ( &a->t, 1 );
p448_bias ( &a->t, 1 );
mask_t ret = p448_is_zero( &a->t );
p448_set_ui( &a->z, 1 );
p448_copy ( &a->t, &a->x );
p448_copy ( &a->u, &a->y );
return ret;
}
void convert_tw_affine_to_tw_pniels(struct tw_pniels_t* b, const struct tw_affine_t* a) {
p448_sub(&b->n.a, &a->y, &a->x);
p448_bias(&b->n.a, 2);
p448_weak_reduce(&b->n.a);
p448_add(&b->n.b, &a->x, &a->y);
p448_weak_reduce(&b->n.b);
p448_mul(&b->n.c, &a->y, &a->x);
p448_mulw(&b->z, &b->n.c, 78164);
p448_neg(&b->n.c, &b->z);
p448_bias(&b->n.c, 2);
p448_weak_reduce(&b->n.c);
p448_set_ui(&b->z, 2);
}
void test_only_twist(struct tw_extensible_t* b, const struct extensible_t* a) {
mask_t L0, L1;
struct p448_t L2, L3;
p448_sqr(&b->u, &a->z);
p448_sqr(&b->y, &a->x);
p448_sub(&b->z, &b->u, &b->y);
p448_bias(&b->z, 2);
p448_add(&b->y, &b->z, &b->z);
p448_add(&b->u, &b->y, &b->y);
p448_sub(&b->y, &a->z, &a->x);
p448_bias(&b->y, 2);
p448_mul(&b->x, &b->y, &a->y);
p448_sub(&b->z, &a->z, &a->y);
p448_bias(&b->z, 2);
p448_mul(&b->t, &b->z, &b->x);
p448_mul(&L3, &b->t, &b->u);
p448_mul(&b->x, &b->t, &L3);
p448_isr(&L2, &b->x);
p448_mul(&b->u, &b->t, &L2);
p448_sqr(&L3, &L2);
p448_mul(&b->t, &b->x, &L3);
p448_add(&L3, &a->y, &a->x);
p448_sub(&L2, &a->x, &a->y);
p448_bias(&L2, 2);
p448_mul(&b->x, &b->t, &L2);
p448_add(&L2, &b->x, &L3);
p448_sub(&b->t, &L3, &b->x);
p448_bias(&b->t, 2);
p448_mul(&b->x, &L2, &b->u);
L0 = p448_is_zero(&b->y);
L1 = -L0;
p448_addw(&b->x, L1);
p448_weak_reduce(&b->x);
p448_mul(&b->y, &b->t, &b->u);
L0 = p448_is_zero(&b->z);
L1 = -L0;
p448_addw(&b->y, L1);
p448_weak_reduce(&b->y);
L1 = p448_is_zero(&a->y);
L0 = L1 + 1;
p448_set_ui(&b->z, L0);
p448_copy(&b->t, &b->x);
p448_copy(&b->u, &b->y);
}
