145 lines
3.1 KiB
C
145 lines
3.1 KiB
C
#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: $Format:%D$ */
|
|
/* git commit: $Format:%H$ */
|
|
/* commit time: $Format:%ai$ */
|