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#include "tommath_private.h"
#ifdef BN_MP_PRIME_FROBENIUS_UNDERWOOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
/* SPDX-License-Identifier: Unlicense */
/*
* See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
*/
#ifndef LTM_USE_ONLY_MR
#ifdef MP_8BIT
/*
* floor of positive solution of
* (2^16)-1 = (a+4)*(2*a+5)
* TODO: Both values are smaller than N^(1/4), would have to use a bigint
* for a instead but any a biger than about 120 are already so rare that
* it is possible to ignore them and still get enough pseudoprimes.
* But it is still a restriction of the set of available pseudoprimes
* which makes this implementation less secure if used stand-alone.
*/
#define LTM_FROBENIUS_UNDERWOOD_A 177
#else
#define LTM_FROBENIUS_UNDERWOOD_A 32764
#endif
mp_err mp_prime_frobenius_underwood(const mp_int *N, mp_bool *result)
{
mp_int T1z, T2z, Np1z, sz, tz;
int a, ap2, length, i, j;
mp_err err;
*result = MP_NO;
if ((err = mp_init_multi(&T1z, &T2z, &Np1z, &sz, &tz, NULL)) != MP_OKAY) {
return err;
}
for (a = 0; a < LTM_FROBENIUS_UNDERWOOD_A; a++) {
/* TODO: That's ugly! No, really, it is! */
if ((a==2) || (a==4) || (a==7) || (a==8) || (a==10) ||
(a==14) || (a==18) || (a==23) || (a==26) || (a==28)) {
continue;
}
/* (32764^2 - 4) < 2^31, no bigint for >MP_8BIT needed) */
mp_set_u32(&T1z, (uint32_t)a);
if ((err = mp_sqr(&T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_sub_d(&T1z, 4uL, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_kronecker(&T1z, N, &j)) != MP_OKAY) goto LBL_FU_ERR;
if (j == -1) {
break;
}
if (j == 0) {
/* composite */
goto LBL_FU_ERR;
}
}
/* Tell it a composite and set return value accordingly */
if (a >= LTM_FROBENIUS_UNDERWOOD_A) {
err = MP_ITER;
goto LBL_FU_ERR;
}
/* Composite if N and (a+4)*(2*a+5) are not coprime */
mp_set_u32(&T1z, (uint32_t)((a+4)*((2*a)+5)));
if ((err = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) goto LBL_FU_ERR;
ap2 = a + 2;
if ((err = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) goto LBL_FU_ERR;
mp_set(&sz, 1uL);
mp_set(&tz, 2uL);
length = mp_count_bits(&Np1z);
for (i = length - 2; i >= 0; i--) {
/*
* temp = (sz*(a*sz+2*tz))%N;
* tz = ((tz-sz)*(tz+sz))%N;
* sz = temp;
*/
if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
/* a = 0 at about 50% of the cases (non-square and odd input) */
if (a != 0) {
if ((err = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
}
if ((err = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_add(&sz, &tz, &sz)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_mod(&tz, N, &tz)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_mod(&T1z, N, &sz)) != MP_OKAY) goto LBL_FU_ERR;
if (s_mp_get_bit(&Np1z, (unsigned int)i) == MP_YES) {
/*
* temp = (a+2) * sz + tz
* tz = 2 * tz - sz
* sz = temp
*/
if (a == 0) {
if ((err = mp_mul_2(&sz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
} else {
if ((err = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
}
if ((err = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_mul_2(&tz, &T2z)) != MP_OKAY) goto LBL_FU_ERR;
if ((err = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) goto LBL_FU_ERR;
mp_exch(&sz, &T1z);
}
}
mp_set_u32(&T1z, (uint32_t)((2 * a) + 5));
if ((err = mp_mod(&T1z, N, &T1z)) != MP_OKAY) goto LBL_FU_ERR;
if (MP_IS_ZERO(&sz) && (mp_cmp(&tz, &T1z) == MP_EQ)) {
*result = MP_YES;
}
LBL_FU_ERR:
mp_clear_multi(&tz, &sz, &Np1z, &T2z, &T1z, NULL);
return err;
}
#endif
#endif
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