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#include "tommath_private.h"
#ifdef BN_MP_KRONECKER_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* SPDX-License-Identifier: Unlicense
*/
/*
Kronecker symbol (a|p)
Straightforward implementation of algorithm 1.4.10 in
Henri Cohen: "A Course in Computational Algebraic Number Theory"
@book{cohen2013course,
title={A course in computational algebraic number theory},
author={Cohen, Henri},
volume={138},
year={2013},
publisher={Springer Science \& Business Media}
}
*/
int mp_kronecker(const mp_int *a, const mp_int *p, int *c)
{
mp_int a1, p1, r;
int e = MP_OKAY;
int v, k;
static const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1};
if (mp_iszero(p) != MP_NO) {
if ((a->used == 1) && (a->dp[0] == 1u)) {
*c = 1;
return e;
} else {
*c = 0;
return e;
}
}
if ((mp_iseven(a) != MP_NO) && (mp_iseven(p) != MP_NO)) {
*c = 0;
return e;
}
if ((e = mp_init_copy(&a1, a)) != MP_OKAY) {
return e;
}
if ((e = mp_init_copy(&p1, p)) != MP_OKAY) {
goto LBL_KRON_0;
}
v = mp_cnt_lsb(&p1);
if ((e = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) {
goto LBL_KRON_1;
}
if ((v & 0x1) == 0) {
k = 1;
} else {
k = table[a->dp[0] & 7u];
}
if (p1.sign == MP_NEG) {
p1.sign = MP_ZPOS;
if (a1.sign == MP_NEG) {
k = -k;
}
}
if ((e = mp_init(&r)) != MP_OKAY) {
goto LBL_KRON_1;
}
for (;;) {
if (mp_iszero(&a1) != MP_NO) {
if (mp_cmp_d(&p1, 1uL) == MP_EQ) {
*c = k;
goto LBL_KRON;
} else {
*c = 0;
goto LBL_KRON;
}
}
v = mp_cnt_lsb(&a1);
if ((e = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) {
goto LBL_KRON;
}
if ((v & 0x1) == 1) {
k = k * table[p1.dp[0] & 7u];
}
if (a1.sign == MP_NEG) {
/*
* Compute k = (-1)^((a1)*(p1-1)/4) * k
* a1.dp[0] + 1 cannot overflow because the MSB
* of the type mp_digit is not set by definition
*/
if (((a1.dp[0] + 1u) & p1.dp[0] & 2u) != 0u) {
k = -k;
}
} else {
/* compute k = (-1)^((a1-1)*(p1-1)/4) * k */
if ((a1.dp[0] & p1.dp[0] & 2u) != 0u) {
k = -k;
}
}
if ((e = mp_copy(&a1, &r)) != MP_OKAY) {
goto LBL_KRON;
}
r.sign = MP_ZPOS;
if ((e = mp_mod(&p1, &r, &a1)) != MP_OKAY) {
goto LBL_KRON;
}
if ((e = mp_copy(&r, &p1)) != MP_OKAY) {
goto LBL_KRON;
}
}
LBL_KRON:
mp_clear(&r);
LBL_KRON_1:
mp_clear(&p1);
LBL_KRON_0:
mp_clear(&a1);
return e;
}
#endif
/* ref: HEAD -> master, tag: v1.1.0 */
/* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
/* commit time: 2019-01-28 20:32:32 +0100 */
|
