void
poly_starmultiply(fmpz_poly_t c,
const fmpz_poly_t a,
const fmpz_poly_t b,
const ntru_params *params,
uint32_t modulus)
{
fmpz_poly_t a_tmp;
fmpz_t c_coeff_k;
fmpz_poly_init(a_tmp);
fmpz_init(c_coeff_k);
/* avoid side effects */
fmpz_poly_set(a_tmp, a);
fmpz_poly_zero(c);
for (int k = params->N - 1; k >= 0; k--) {
int j;
j = k + 1;
fmpz_set_si(c_coeff_k, 0);
for (int i = params->N - 1; i >= 0; i--) {
fmpz *a_tmp_coeff_i,
*b_coeff_j;
if (j == (int)(params->N))
j = 0;
a_tmp_coeff_i = fmpz_poly_get_coeff_ptr(a_tmp, i);
b_coeff_j = fmpz_poly_get_coeff_ptr(b, j);
if (fmpz_cmp_si_n(a_tmp_coeff_i, 0) &&
fmpz_cmp_si_n(b_coeff_j, 0)) {
fmpz_t fmpz_tmp;
fmpz_init(fmpz_tmp);
fmpz_mul(fmpz_tmp, a_tmp_coeff_i, b_coeff_j);
fmpz_add(fmpz_tmp, fmpz_tmp, c_coeff_k);
fmpz_mod_ui(c_coeff_k, fmpz_tmp, modulus);
fmpz_poly_set_coeff_fmpz(c, k, c_coeff_k);
fmpz_clear(fmpz_tmp);
}
j++;
}
fmpz_clear(c_coeff_k);
}
fmpz_poly_clear(a_tmp);
}
int
main(void)
{
int iter;
FLINT_TEST_INIT(state);
flint_printf("sgn_eval_at_half....");
fflush(stdout);
/* Check aliasing */
for (iter = 0; iter < 1000 * flint_test_multiplier(); iter++)
{
fmpz_t a;
fmpz_poly_t f, g;
long i, d;
int s1, s2;
fmpz_init(a);
fmpz_poly_init(f);
fmpz_poly_init(g);
fmpz_poly_randtest(f, state, n_randint(state, 100), 200);
s1 = fmpz_poly_sgn_eval_at_half(f);
fmpz_poly_set(g, f);
d = fmpz_poly_degree(g);
for (i = 0; i <= d; i++)
{
fmpz_mul_2exp(fmpz_poly_get_coeff_ptr(g, i),
fmpz_poly_get_coeff_ptr(g, i), d - i);
}
fmpz_one(a);
fmpz_poly_evaluate_fmpz(a, g, a);
s2 = fmpz_sgn(a);
if (s1 != s2)
{
flint_printf("FAIL:\n");
fmpz_poly_print(f); printf("\n\n");
printf("s1 = %d, s2 = %d\n\n", s1, s2);
abort();
}
fmpz_clear(a);
fmpz_poly_clear(f);
fmpz_poly_clear(g);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
string *
bin_poly_to_ascii(const fmpz_poly_t poly,
const ntru_params *params)
{
string *result_string = ntru_malloc(sizeof(*result_string));
char *binary_rep = ntru_malloc(CHAR_SIZE * (params->N));
uint32_t i = 0;
for (i = 0; i < params->N; i++) {
fmpz *coeff = fmpz_poly_get_coeff_ptr(poly, i);
if (coeff) {
if (!fmpz_cmp_si(coeff, 1))
binary_rep[i] = '1';
else if (!fmpz_cmp_si(coeff, -1))
binary_rep[i] = '0';
} else {
break;
}
}
result_string->ptr = binary_rep;
result_string->len = i;
return result_string;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("get_coeff_ptr....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_poly_t A;
fmpz_t a;
slong n = n_randint(state, 100);
fmpz_poly_init(A);
fmpz_poly_randtest(A, state, n_randint(state, 100), 100);
fmpz_init(a);
fmpz_poly_get_coeff_fmpz(a, A, n);
result = n < fmpz_poly_length(A) ?
fmpz_equal(a, fmpz_poly_get_coeff_ptr(A, n)) :
fmpz_poly_get_coeff_ptr(A, n) == NULL;
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("A = "), fmpz_poly_print(A), flint_printf("\n\n");
flint_printf("a = "), fmpz_print(a), flint_printf("\n\n");
flint_printf("n = %wd\n\n", n);
abort();
}
fmpz_poly_clear(A);
fmpz_clear(a);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
bool
poly_inverse_poly_p(fmpz_poly_t Fp,
const fmpz_poly_t a,
const ntru_params *params)
{
bool retval = false;
int k = 0,
j = 0;
fmpz *b_last;
fmpz_poly_t a_tmp,
b,
c,
f,
g;
/* general initialization of temp variables */
fmpz_poly_init(b);
fmpz_poly_set_coeff_ui(b, 0, 1);
fmpz_poly_init(c);
fmpz_poly_init(f);
fmpz_poly_set(f, a);
/* set g(x) = x^N − 1 */
fmpz_poly_init(g);
fmpz_poly_set_coeff_si(g, 0, -1);
fmpz_poly_set_coeff_si(g, params->N, 1);
/* avoid side effects */
fmpz_poly_init(a_tmp);
fmpz_poly_set(a_tmp, a);
fmpz_poly_zero(Fp);
while (1) {
while (fmpz_poly_get_coeff_ptr(f, 0) &&
fmpz_is_zero(fmpz_poly_get_coeff_ptr(f, 0))) {
for (uint32_t i = 1; i <= params->N; i++) {
fmpz *f_coeff = fmpz_poly_get_coeff_ptr(f, i);
fmpz *c_coeff = fmpz_poly_get_coeff_ptr(c, params->N - i);
/* f(x) = f(x) / x */
fmpz_poly_set_coeff_fmpz_n(f, i - 1,
f_coeff);
/* c(x) = c(x) * x */
fmpz_poly_set_coeff_fmpz_n(c, params->N + 1 - i,
c_coeff);
}
fmpz_poly_set_coeff_si(f, params->N, 0);
fmpz_poly_set_coeff_si(c, 0, 0);
k++;
if (fmpz_poly_degree(f) == -1)
goto cleanup;
}
if (fmpz_poly_is_zero(g) == 1)
goto cleanup;
if (fmpz_poly_degree(f) == 0)
break;
if (fmpz_poly_degree(f) < fmpz_poly_degree(g)) {
/* exchange f and g and exchange b and c */
fmpz_poly_swap(f, g);
fmpz_poly_swap(b, c);
}
{
fmpz_poly_t c_tmp,
g_tmp;
fmpz_t u,
mp_tmp;
fmpz_init(u);
fmpz_zero(u);
fmpz_init_set(mp_tmp, fmpz_poly_get_coeff_ptr(f, 0));
fmpz_poly_init(g_tmp);
fmpz_poly_set(g_tmp, g);
fmpz_poly_init(c_tmp);
fmpz_poly_set(c_tmp, c);
/* u = f[0] * g[0]^(-1) mod p */
/* = (f[0] mod p) * (g[0] inverse mod p) mod p */
fmpz_invmod_ui(u,
fmpz_poly_get_coeff_ptr(g, 0),
params->p);
fmpz_mod_ui(mp_tmp, mp_tmp, params->p);
fmpz_mul(u, mp_tmp, u);
fmpz_mod_ui(u, u, params->p);
/* f = f - u * g mod p */
fmpz_poly_scalar_mul_fmpz(g_tmp, g_tmp, u);
fmpz_poly_sub(f, f, g_tmp);
fmpz_poly_mod_unsigned(f, params->p);
/* b = b - u * c mod p */
fmpz_poly_scalar_mul_fmpz(c_tmp, c_tmp, u);
fmpz_poly_sub(b, b, c_tmp);
fmpz_poly_mod_unsigned(b, params->p);
fmpz_clear(u);
fmpz_poly_clear(g_tmp);
fmpz_poly_clear(c_tmp);
}
}
k = k % params->N;
b_last = fmpz_poly_get_coeff_ptr(b, params->N);
if (fmpz_cmp_si_n(b_last, 0))
goto cleanup;
/* Fp(x) = x^(N-k) * b(x) */
for (int i = params->N - 1; i >= 0; i--) {
fmpz *b_i;
/* b(X) = f[0]^(-1) * b(X) (mod p) */
{
fmpz_t mp_tmp;
fmpz_init(mp_tmp);
fmpz_invmod_ui(mp_tmp,
fmpz_poly_get_coeff_ptr(f, 0),
params->p);
if (fmpz_poly_get_coeff_ptr(b, i)) {
fmpz_mul(fmpz_poly_get_coeff_ptr(b, i),
fmpz_poly_get_coeff_ptr(b, i),
mp_tmp);
fmpz_mod_ui(fmpz_poly_get_coeff_ptr(b, i),
fmpz_poly_get_coeff_ptr(b, i),
params->p);
}
}
j = i - k;
if (j < 0)
j = j + params->N;
b_i = fmpz_poly_get_coeff_ptr(b, i);
fmpz_poly_set_coeff_fmpz_n(Fp, j, b_i);
}
/* check if the f * Fp = 1 (mod p) condition holds true */
fmpz_poly_set(a_tmp, a);
poly_starmultiply(a_tmp, a_tmp, Fp, params, params->p);
if (fmpz_poly_is_one(a_tmp))
retval = true;
else
fmpz_poly_zero(Fp);
cleanup:
fmpz_poly_clear(a_tmp);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
fmpz_poly_clear(f);
fmpz_poly_clear(g);
return retval;
}
bool
poly_inverse_poly_q(fmpz_poly_t Fq,
const fmpz_poly_t a,
const ntru_params *params)
{
bool retval = false;
int k = 0,
j = 0;
fmpz *b_last;
fmpz_poly_t a_tmp,
b,
c,
f,
g;
/* general initialization of temp variables */
fmpz_poly_init(b);
fmpz_poly_set_coeff_ui(b, 0, 1);
fmpz_poly_init(c);
fmpz_poly_init(f);
fmpz_poly_set(f, a);
/* set g(x) = x^N − 1 */
fmpz_poly_init(g);
fmpz_poly_set_coeff_si(g, 0, -1);
fmpz_poly_set_coeff_si(g, params->N, 1);
/* avoid side effects */
fmpz_poly_init(a_tmp);
fmpz_poly_set(a_tmp, a);
fmpz_poly_zero(Fq);
while (1) {
while (fmpz_poly_get_coeff_ptr(f, 0) &&
fmpz_is_zero(fmpz_poly_get_coeff_ptr(f, 0))) {
for (uint32_t i = 1; i <= params->N; i++) {
fmpz *f_coeff = fmpz_poly_get_coeff_ptr(f, i);
fmpz *c_coeff = fmpz_poly_get_coeff_ptr(c, params->N - i);
/* f(x) = f(x) / x */
fmpz_poly_set_coeff_fmpz_n(f, i - 1,
f_coeff);
/* c(x) = c(x) * x */
fmpz_poly_set_coeff_fmpz_n(c, params->N + 1 - i,
c_coeff);
}
fmpz_poly_set_coeff_si(f, params->N, 0);
fmpz_poly_set_coeff_si(c, 0, 0);
k++;
if (fmpz_poly_degree(f) == -1)
goto cleanup;
}
if (fmpz_poly_is_zero(g) == 1)
goto cleanup;
if (fmpz_poly_degree(f) == 0)
break;
if (fmpz_poly_degree(f) < fmpz_poly_degree(g)) {
fmpz_poly_swap(f, g);
fmpz_poly_swap(b, c);
}
fmpz_poly_add(f, g, f);
fmpz_poly_mod_unsigned(f, 2);
fmpz_poly_add(b, c, b);
fmpz_poly_mod_unsigned(b, 2);
}
k = k % params->N;
b_last = fmpz_poly_get_coeff_ptr(b, params->N);
if (fmpz_cmp_si_n(b_last, 0))
goto cleanup;
/* Fq(x) = x^(N-k) * b(x) */
for (int i = params->N - 1; i >= 0; i--) {
fmpz *b_i;
j = i - k;
if (j < 0)
j = j + params->N;
b_i = fmpz_poly_get_coeff_ptr(b, i);
fmpz_poly_set_coeff_fmpz_n(Fq, j, b_i);
}
poly_mod2_to_modq(Fq, a_tmp, params);
/* check if the f * Fq = 1 (mod p) condition holds true */
fmpz_poly_set(a_tmp, a);
poly_starmultiply(a_tmp, a_tmp, Fq, params, params->q);
if (fmpz_poly_is_one(a_tmp))
retval = true;
else
fmpz_poly_zero(Fq);
cleanup:
fmpz_poly_clear(a_tmp);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
fmpz_poly_clear(f);
fmpz_poly_clear(g);
return retval;
}