X-Git-Url: https://git.distorted.org.uk/~mdw/catacomb/blobdiff_plain/ba6e6b64033b1f9de49feccb5c9cd438354481f7..0f00dc4c8eb47e67bc0f148c2dd109f73a451e0a:/mp-gcd.c?ds=inline diff --git a/mp-gcd.c b/mp-gcd.c deleted file mode 100644 index 40531c7c..00000000 --- a/mp-gcd.c +++ /dev/null @@ -1,347 +0,0 @@ -/* -*-c-*- - * - * $Id$ - * - * Extended GCD calculation - * - * (c) 1999 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 "mp.h" - -/*----- Main code ---------------------------------------------------------*/ - -/* --- @mp_gcd@ --- * - * - * Arguments: @mp **gcd, **xx, **yy@ = where to write the results - * @mp *a, *b@ = sources (must be nonzero) - * - * Returns: --- - * - * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that - * @ax + by = gcd(a, b)@. This is useful for computing modular - * inverses. - */ - -void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b) -{ - mp *x = MP_ONE, *X = MP_ZERO; - mp *y = MP_ZERO, *Y = MP_ONE; - mp *u, *v; - mp *q = MP_NEW, *t, *spare = MP_NEW; - unsigned f = 0; - -#define f_swap 1u -#define f_aneg 2u -#define f_bneg 4u -#define f_ext 8u - - /* --- Sort out some initial flags --- */ - - if (xx || yy) - f |= f_ext; - - if (MP_NEGP(a)) - f |= f_aneg; - if (MP_NEGP(b)) - f |= f_bneg; - - /* --- Ensure that @a@ is larger than @b@ --- * - * - * Use absolute values here! - */ - - if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { - t = a; a = b; b = t; - f |= f_swap; - } - - /* --- Check for zeroness --- */ - - if (MP_ZEROP(b)) { - - /* --- Store %$|a|$% as the GCD --- */ - - if (gcd) { - if (*gcd) MP_DROP(*gcd); - a = MP_COPY(a); - if (MP_NEGP(a)) { - MP_SPLIT(a); - a->f &= ~MP_NEG; - f |= f_aneg; - } - *gcd = a; - } - - /* --- Store %$1$% and %$0$% in the appropriate bins --- */ - - if (f & f_ext) { - if (f & f_swap) { - mp **tt = xx; xx = yy; yy = tt; - } - if (xx) { - if (*xx) MP_DROP(*xx); - if (MP_EQ(a, MP_ZERO)) - *xx = MP_ZERO; - else if (f & f_aneg) - *xx = MP_MONE; - else - *xx = MP_ONE; - } - if (yy) { - if (*yy) MP_DROP(*yy); - *yy = MP_ZERO; - } - } - return; - } - - /* --- Force the signs on the arguments and take copies --- */ - - a = MP_COPY(a); - b = MP_COPY(b); - - MP_SPLIT(a); a->f &= ~MP_NEG; - MP_SPLIT(b); b->f &= ~MP_NEG; - - u = MP_COPY(a); - v = MP_COPY(b); - - /* --- Main extended Euclidean algorithm --- */ - - while (!MP_ZEROP(v)) { - mp_div(&q, &u, u, v); - if (f & f_ext) { - t = mp_mul(spare, X, q); - t = mp_sub(t, x, t); - spare = x; x = X; X = t; - t = mp_mul(spare, Y, q); - t = mp_sub(t, y, t); - spare = y; y = Y; Y = t; - } - t = u; u = v; v = t; - } - - MP_DROP(q); if (spare) MP_DROP(spare); - if (!gcd) - MP_DROP(u); - else { - if (*gcd) MP_DROP(*gcd); - u->f &= ~MP_NEG; - *gcd = u; - } - - /* --- Perform a little normalization --- * - * - * Ensure that the coefficient returned is positive, if there is only one. - * If there are two, favour @y@. Of course, if the original arguments were - * negative then I'll need to twiddle their signs as well. - */ - - if (f & f_ext) { - - /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */ - - if (f & f_swap) { - t = x; x = y; y = t; - t = a; a = b; b = t; - } - - /* --- Sort out the signs --- * - * - * Note that %$ax + by = a(x - b) + b(y + a)$%. - * - * This is currently bodgy. It needs sorting out at some time. - */ - - if (yy) { - if (MP_NEGP(y)) { - do { - y = mp_add(y, y, a); - x = mp_sub(x, x, b); - } while (MP_NEGP(y)); - } else { - while (MP_CMP(y, >=, a)) { - y = mp_sub(y, y, a); - x = mp_add(x, x, b); - } - } - } else { - if (MP_NEGP(x)) { - do - x = mp_add(x, x, b); - while (MP_NEGP(x)); - } else { - while (MP_CMP(x, >=, b)) - x = mp_sub(x, x, b); - } - } - - /* --- Twiddle the signs --- */ - - if (f & f_aneg) - x->f ^= MP_NEG; - if (f & f_bneg) - y->f ^= MP_NEG; - - /* --- Store the results --- */ - - if (!xx) - MP_DROP(x); - else { - if (*xx) MP_DROP(*xx); - *xx = x; - } - - if (!yy) - MP_DROP(y); - else { - if (*yy) MP_DROP(*yy); - *yy = y; - } - } - - MP_DROP(v); - MP_DROP(X); MP_DROP(Y); - MP_DROP(a); MP_DROP(b); -} - -/* -- @mp_modinv@ --- * - * - * Arguments: @mp *d@ = destination - * @mp *x@ = argument - * @mp *p@ = modulus - * - * Returns: The inverse %$x^{-1} \bmod p$%. - * - * Use: Computes a modular inverse. An assertion fails if %$p$% - * has no inverse. - */ - -mp *mp_modinv(mp *d, mp *x, mp *p) -{ - mp *g = MP_NEW; - mp_gcd(&g, 0, &d, p, x); - assert(MP_EQ(g, MP_ONE)); - mp_drop(g); - return (d); -} - -/*----- Test rig ----------------------------------------------------------*/ - -#ifdef TEST_RIG - -static int modinv(dstr *v) -{ - int ok = 1; - mp *x = *(mp **)v[0].buf; - mp *m = *(mp **)v[1].buf; - mp *r = *(mp **)v[2].buf; - - mp *y = mp_modinv(MP_NEW, x, m); - if (!MP_EQ(y, r)) { - fputs("\n*** mp_modinv failed", stderr); - fputs("\nx = ", stderr); mp_writefile(x, stderr, 10); - fputs("\nm = ", stderr); mp_writefile(m, stderr, 10); - fputs("\nexpect = ", stderr); mp_writefile(r, stderr, 10); - fputs("\nresult = ", stderr); mp_writefile(y, stderr, 10); - ok = 0; - } - MP_DROP(x); MP_DROP(m); MP_DROP(r); MP_DROP(y); - assert(mparena_count(MPARENA_GLOBAL) == 0); - return (ok); -} - -static int gcd(dstr *v) -{ - int ok = 1; - mp *a = *(mp **)v[0].buf; - mp *b = *(mp **)v[1].buf; - mp *g = *(mp **)v[2].buf; - mp *x = *(mp **)v[3].buf; - mp *y = *(mp **)v[4].buf; - - mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW; - mp_gcd(&gg, &xx, &yy, a, b); - if (!MP_EQ(x, xx)) { - fputs("\n*** mp_gcd(x) failed", stderr); - fputs("\na = ", stderr); mp_writefile(a, stderr, 10); - fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); - fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10); - fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10); - fputc('\n', stderr); - ok = 0; - } - if (!MP_EQ(y, yy)) { - fputs("\n*** mp_gcd(y) failed", stderr); - fputs("\na = ", stderr); mp_writefile(a, stderr, 10); - fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); - fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10); - fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10); - fputc('\n', stderr); - ok = 0; - } - - if (!ok) { - mp *ax = mp_mul(MP_NEW, a, xx); - mp *by = mp_mul(MP_NEW, b, yy); - ax = mp_add(ax, ax, by); - if (MP_EQ(ax, gg)) - fputs("\n*** (Alternative result found.)\n", stderr); - MP_DROP(ax); - MP_DROP(by); - } - - if (!MP_EQ(g, gg)) { - fputs("\n*** mp_gcd(gcd) failed", stderr); - fputs("\na = ", stderr); mp_writefile(a, stderr, 10); - fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); - fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10); - fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10); - fputc('\n', stderr); - ok = 0; - } - MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y); - MP_DROP(gg); MP_DROP(xx); MP_DROP(yy); - assert(mparena_count(MPARENA_GLOBAL) == 0); - return (ok); -} - -static test_chunk tests[] = { - { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, - { "modinv", modinv, { &type_mp, &type_mp, &type_mp, 0 } }, - { 0, 0, { 0 } } -}; - -int main(int argc, char *argv[]) -{ - sub_init(); - test_run(argc, argv, tests, SRCDIR "/tests/mp"); - return (0); -} - -#endif - -/*----- That's all, folks -------------------------------------------------*/