X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/ba6e6b64033b1f9de49feccb5c9cd438354481f7..0f00dc4c8eb47e67bc0f148c2dd109f73a451e0a:/rho.c diff --git a/rho.c b/rho.c deleted file mode 100644 index a02eeba..0000000 --- a/rho.c +++ /dev/null @@ -1,300 +0,0 @@ -/* -*-c-*- - * - * $Id: rho.c,v 1.5 2004/04/08 01:36:15 mdw Exp $ - * - * Pollard's rho algorithm for discrete logs - * - * (c) 2000 Straylight/Edgeware - */ - -/*----- Licensing notice --------------------------------------------------* - * - * This file is part of Catacomb. - * - * Catacomb is free software; you can redistribute it and/or modify - * it under the terms of the GNU Library General Public License as - * published by the Free Software Foundation; either version 2 of the - * License, or (at your option) any later version. - * - * Catacomb is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU Library General Public License for more details. - * - * You should have received a copy of the GNU Library General Public - * License along with Catacomb; if not, write to the Free - * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, - * MA 02111-1307, USA. - */ - -/*----- Header files ------------------------------------------------------*/ - -#include "fibrand.h" -#include "mp.h" -#include "mpmont.h" -#include "mprand.h" -#include "rho.h" - -/*----- Main code ---------------------------------------------------------*/ - -/* --- @rho@ --- * - * - * Arguments: @rho_ctx *cc@ = pointer to the context structure - * @void *x, *y@ = two (equal) base values (try 1) - * @mp *a, *b@ = logs of %$x$% (see below) - * - * Returns: The discrete logarithm %$\log_g a$%, or null if the algorithm - * failed. (This is unlikely, though possible.) - * - * Use: Uses Pollard's rho algorithm to compute discrete logs in the - * group %$G$% generated by %$g$%. - * - * The algorithm works by finding a cycle in a pseudo-random - * walk. The function @ops->split@ should return an element - * from %$\{\,0, 1, 2\,\}$% according to its argument, in order - * to determine the walk. At each step in the walk, we know a - * group element %$x \in G$% together with its representation as - * a product of powers of %$g$% and $%a$% (i.e., we know that - * %$x = g^\alpha a^\beta$% for some %$\alpha$%, %$\beta$%). - * - * Locating a cycle gives us a collision - * - * %$g^{\alpha} a^{\beta} = g^{\alpha'} a^{\beta'}$% - * - * Taking logs of both sides (to base %$g$%) gives us that - * - * %$\log a\equiv\frac{\alpha-\alpha'}{\beta'-\beta}\bmod{n}$% - * - * Good initial values are %$x = y = 1$% (the multiplicative - * identity of %$G$%) and %$\alpha\equiv\beta\equiv0\bmod{n}$%. - * If that doesn't work then start choosing more `interesting' - * values. - * - * Note that the algorithm requires minimal space but - * %$O(\sqrt{n})$% time. Don't do this on large groups, - * particularly if you can find a decent factor base. - * - * Finally, note that this function will free the input values - * when it's finished with them. This probably isn't a great - * problem. - */ - -static void step(rho_ctx *cc, void *x, mp **a, mp **b) -{ - switch (cc->ops->split(x)) { - case 0: - cc->ops->mul(x, cc->g, cc->c); - *a = mp_add(*a, *a, MP_ONE); - if (MP_CMP(*a, >=, cc->n)) - *a = mp_sub(*a, *a, cc->n); - break; - case 1: - cc->ops->sqr(x, cc->c); - *a = mp_lsl(*a, *a, 1); - if (MP_CMP(*a, >=, cc->n)) - *a = mp_sub(*a, *a, cc->n); - *b = mp_lsl(*b, *b, 1); - if (MP_CMP(*b, >=, cc->n)) - *b = mp_sub(*b, *b, cc->n); - break; - case 2: - cc->ops->mul(x, cc->a, cc->c); - *b = mp_add(*b, *b, MP_ONE); - if (MP_CMP(*b, >=, cc->n)) - *b = mp_sub(*b, *b, cc->n); - break; - } -} - -mp *rho(rho_ctx *cc, void *x, void *y, mp *a, mp *b) -{ - mp *aa = MP_COPY(a), *bb = MP_COPY(b); - mp *g; - - /* --- Grind through the random walk until we find a collision --- */ - - do { - step(cc, x, &a, &b); - step(cc, y, &aa, &bb); - step(cc, y, &aa, &bb); - } while (!cc->ops->eq(x, y)); - cc->ops->drop(x); - cc->ops->drop(y); - - /* --- Now sort out the mess --- */ - - aa = mp_sub(aa, a, aa); - bb = mp_sub(bb, bb, b); - g = MP_NEW; - mp_gcd(&g, &bb, 0, bb, cc->n); - if (!MP_EQ(g, MP_ONE)) { - mp_drop(aa); - aa = 0; - } else { - aa = mp_mul(aa, aa, bb); - mp_div(0, &aa, aa, cc->n); - } - - /* --- Done --- */ - - mp_drop(bb); - mp_drop(g); - mp_drop(a); - mp_drop(b); - return (aa); -} - -/* --- @rho_prime@ --- * - * - * Arguments: @mp *g@ = generator for the group - * @mp *a@ = value to find the logarithm of - * @mp *n@ = order of the group - * @mp *p@ = prime size of the underlying prime field - * - * Returns: The discrete logarithm %$\log_g a$%. - * - * Use: Computes discrete logarithms in a subgroup of a prime field. - */ - -static void prime_sqr(void *x, void *c) -{ - mp **p = x; - mp *a = *p; - a = mp_sqr(a, a); - a = mpmont_reduce(c, a, a); - *p = a; -} - -static void prime_mul(void *x, void *y, void *c) -{ - mp **p = x; - mp *a = *p; - a = mpmont_mul(c, a, a, y); - *p = a; -} - -static int prime_eq(void *x, void *y) -{ - return (MP_EQ(*(mp **)x, *(mp **)y)); -} - -static int prime_split(void *x) -{ - /* --- Notes on the splitting function --- * - * - * The objective is to produce a simple pseudorandom mapping from the - * underlying field \gf{p} to \{\,0, 1, 2\,\}$%. This is further - * constrained by the fact that we must not have %$1 \mapsto 1$% (since - * otherwise the stepping function above will loop). - * - * The function we choose is very simple: we take the least significant - * word from the integer, add one (to prevent the %$1 \mapsto 1$% property - * described above) and reduce modulo 3. This is slightly biased against - * the result 2, but this doesn't appear to be relevant. - */ - - return (((*(mp **)x)->v[0] + 1) % 3); -} - -static void prime_drop(void *x) -{ - MP_DROP(*(mp **)x); -} - -static const rho_ops prime_ops = { - prime_sqr, prime_mul, prime_eq, prime_split, prime_drop -}; - -mp *rho_prime(mp *g, mp *a, mp *n, mp *p) -{ - rho_ctx cc; - grand *r = 0; - mpmont mm; - mp *x, *y; - mp *aa, *bb; - mp *l; - - /* --- Initialization --- */ - - mpmont_create(&mm, p); - cc.ops = &prime_ops; - cc.c = &mm; - cc.n = n; - cc.g = mpmont_mul(&mm, MP_NEW, g, mm.r2); - cc.a = mpmont_mul(&mm, MP_NEW, a, mm.r2); - x = MP_COPY(mm.r); - y = MP_COPY(x); - aa = bb = MP_ZERO; - - /* --- The main loop --- */ - - while ((l = rho(&cc, &x, &y, aa, bb)) == 0) { - mp_expfactor f[2]; - - if (!r) - r = fibrand_create(0); - aa = mprand_range(MP_NEW, n, r, 0); - bb = mprand_range(MP_NEW, n, r, 0); - f[0].base = cc.g; f[0].exp = aa; - f[1].base = cc.a; f[1].exp = bb; - x = mpmont_mexpr(&mm, MP_NEW, f, 2); - y = MP_COPY(x); - } - - /* --- Throw everything away now --- */ - - if (r) - r->ops->destroy(r); - mp_drop(cc.g); - mp_drop(cc.a); - mpmont_destroy(&mm); - return (l); -} - -/*----- Test rig ----------------------------------------------------------*/ - -#ifdef TEST_RIG - -#include - -#include "dh.h" - -int main(void) -{ - dh_param dp; - mp *x, *y; - grand *r = fibrand_create(0); - mpmont mm; - mp *l; - int ok; - - fputs("rho: ", stdout); - fflush(stdout); - - dh_gen(&dp, 32, 256, 0, r, pgen_evspin, 0); - x = mprand_range(MP_NEW, dp.q, r, 0); - mpmont_create(&mm, dp.p); - y = mpmont_exp(&mm, MP_NEW, dp.g, x); - mpmont_destroy(&mm); - l = rho_prime(dp.g, y, dp.q, dp.p); - if (MP_EQ(x, l)) { - fputs(". ok\n", stdout); - ok = 1; - } else { - fputs("\n*** rho (discrete logs) failed\n", stdout); - ok = 0; - } - - mp_drop(l); - mp_drop(x); - mp_drop(y); - r->ops->destroy(r); - dh_paramfree(&dp); - assert(mparena_count(MPARENA_GLOBAL) == 0); - - return (ok ? 0 : EXIT_FAILURE); -} - -#endif - -/*----- That's all, folks -------------------------------------------------*/