mirror of
https://github.com/vale981/arb
synced 2025-03-08 18:51:40 -05:00
133 lines
3.7 KiB
C
133 lines
3.7 KiB
C
/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2016 Pascal Molin
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******************************************************************************/
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#include "dlog.h"
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#include <math.h>
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void
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dlog_rho_init(dlog_rho_t t, ulong a, ulong mod, ulong n)
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{
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t->a = a;
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t->n = n;
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t->mod = mod;
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t->nisprime = n_is_prime(n);
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}
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void
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dlog_rho_clear(dlog_rho_t t)
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{
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return;
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}
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static ulong
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dlog_once(ulong b, ulong a, ulong mod, ulong n)
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{
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if (n < 50)
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{
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int k;
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ulong ak = 1;
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for (k=0; k < n; k++)
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{
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if (ak == b)
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return k;
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ak = (ak * a) % mod;
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}
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flint_printf("FAIL[dlog once]: log(%wu,%wu) mod %wu not found (size %wu)\n",
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b, a, mod, n);
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abort();
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} else {
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dlog_rho_t t;
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dlog_rho_init(t, a, mod, n);
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return dlog_rho(t, b);
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}
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}
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/* solve log knowing equation e = f * log(b) [n] */
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static ulong
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dlog_quotient(const dlog_rho_t t, ulong e, ulong f, ulong g, ulong b)
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{
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ulong r, n, b_ar, an;
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n = t->n;
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if (g == n)
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{
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flint_printf("FAIL[dlog quotient]: trivial relation e = %wu, f = %wu mod %wu\n",
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e, f, n);
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abort();
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}
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n = n / g;
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e = e / g;
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f = f / g;
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f = n_invmod(f, n);
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r = ( e * f ) % n;
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an = n_powmod(t->a, n, t->mod);
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b_ar = (b * n_invmod(n_powmod(t->a, r, t->mod), t->mod)) % t->mod;
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return r + n * dlog_once(b_ar, an, t->mod, g);
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}
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#define RWALK 20
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ulong
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dlog_rho(const dlog_rho_t t, ulong b)
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{
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int j, k, l;
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ulong m[RWALK], n[RWALK], ab[RWALK];
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ulong x[2], e[2], f[2], g;
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flint_rand_t state;
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flint_randinit(state);
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do {
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for (k = 0; k < RWALK; k++)
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{
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m[k] = 1 + n_randint(state, t->n - 1);
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n[k] = 1 + n_randint(state, t->n - 1);
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ab[k] = (n_powmod(t->a, m[k], t->mod) * n_powmod(b, n[k], t->mod)) % t->mod;
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}
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/* x[l] = a^e[l] * b^f[l] */
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x[0] = x[1] = 1;
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e[0] = e[1] = 0;
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f[0] = f[1] = 0;
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do {
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for(j = 0; j < 3; j++)
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{
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l = (j > 0);
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k = floor( (double) RWALK * x[l] / t->mod );
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x[l] = (x[l] * ab[k]) % t->mod;
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e[l] = (e[l] + m[k]) % t->n;
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f[l] = (f[l] + n[k]) % t->n;
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}
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} while (x[0] != x[1]);
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} while (e[0] == e[1] && f[0] == f[1]);
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flint_randclear(state);
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/* e = f * log(b) */
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e[0] = (e[0] > e[1]) ? e[0] - e[1] : e[0] + t->n - e[1];
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f[0] = (f[1] > f[0]) ? f[1] - f[0] : f[1] + t->n - f[0];
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if (!t->nisprime && (g = n_gcd(f[0], t->n)) > 1)
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{
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return dlog_quotient(t, e[0], f[0], g, b);
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}
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else
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{
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f[0] = n_invmod(f[0], t->n);
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return ( e[0] * f[0] ) % t->n;
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}
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}
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