From 5ee4c8931f0cd48cfe38cfc82cdd853f72e60e35 Mon Sep 17 00:00:00 2001 From: mdw Date: Mon, 22 Nov 1999 20:51:19 +0000 Subject: [PATCH] Add support for solving Chinese Remainder Theorem problems. --- mpcrt.c | 262 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ mpcrt.h | 132 ++++++++++++++++++++++++++++++ tests/mpcrt | 21 +++++ 3 files changed, 415 insertions(+) create mode 100644 mpcrt.c create mode 100644 mpcrt.h create mode 100644 tests/mpcrt diff --git a/mpcrt.c b/mpcrt.c new file mode 100644 index 0000000..3b1ee22 --- /dev/null +++ b/mpcrt.c @@ -0,0 +1,262 @@ +/* -*-c-*- + * + * $Id: mpcrt.c,v 1.1 1999/11/22 20:50:57 mdw Exp $ + * + * Chinese Remainder Theorem computations (Gauss's algorithm) + * + * (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. + */ + +/*----- Revision history --------------------------------------------------* + * + * $Log: mpcrt.c,v $ + * Revision 1.1 1999/11/22 20:50:57 mdw + * Add support for solving Chinese Remainder Theorem problems. + * + */ + +/*----- Header files ------------------------------------------------------*/ + +#include "mp.h" +#include "mpcrt.h" +#include "mpmont.h" + +/*----- Main code ---------------------------------------------------------*/ + +/* --- @mpcrt_create@ --- * + * + * Arguments: @mpcrt *c@ = pointer to CRT context + * @mpcrt_mod *v@ = pointer to vector of moduli + * @size_t k@ = number of moduli + * @mp *n@ = product of all moduli (@MP_NEW@ if unknown) + * + * Returns: --- + * + * Use: Initializes a context for solving Chinese Remainder Theorem + * problems. The vector of moduli can be incomplete. Omitted + * items must be left as null pointers. Not all combinations of + * missing things can be coped with, even if there is + * technically enough information to cope. For example, if @n@ + * is unspecified, all the @m@ values must be present, even if + * there is one modulus with both @m@ and @n@ (from which the + * product of all moduli could clearly be calculated). + */ + +void mpcrt_create(mpcrt *c, mpcrt_mod *v, size_t k, mp *n) +{ + mp *x = MP_NEW, *y = MP_NEW; + size_t i; + + /* --- Simple initialization things --- */ + + c->k = k; + c->v = v; + + /* --- Work out @n@ if I don't have it already --- */ + + if (n == MP_NEW) { + n = MP_COPY(v[0].m); + for (i = 1; i < k; i++) { + mp *d = mp_mul(x, n, v[i].m); + x = n; + n = d; + } + } + + /* --- Set up the Montgomery context --- */ + + mpmont_create(&c->mm, n); + + /* --- Walk through filling in @n@, @ni@ and @nnir@ --- */ + + for (i = 0; i < k; i++) { + if (!v[i].n) + mp_div(&v[i].n, 0, n, v[i].m); + if (!v[i].ni) + mp_gcd(0, &v[i].ni, 0, v[i].n, v[i].m); + if (!v[i].nnir) { + x = mpmont_mul(&c->mm, x, v[i].n, c->mm.r2); + y = mpmont_mul(&c->mm, y, v[i].ni, c->mm.r2); + v[i].nnir = mpmont_mul(&c->mm, MP_NEW, x, y); + } + } + + /* --- Done --- */ + + if (x) + mp_drop(x); + if (y) + mp_drop(y); +} + +/* --- @mpcrt_destroy@ --- * + * + * Arguments: @mpcrt *c@ - pointer to CRT context + * + * Returns: --- + * + * Use: Destroys a CRT context, releasing all the resources it holds. + */ + +void mpcrt_destroy(mpcrt *c) +{ + size_t i; + + for (i = 0; i < c->k; i++) { + if (c->v[i].m) mp_drop(c->v[i].m); + if (c->v[i].n) mp_drop(c->v[i].n); + if (c->v[i].ni) mp_drop(c->v[i].ni); + if (c->v[i].nnir) mp_drop(c->v[i].nnir); + } + mpmont_destroy(&c->mm); +} + +/* --- @mpcrt_solve@ --- * + * + * Arguments: @mpcrt *c@ = pointer to CRT context + * @mp **v@ = array of residues + * + * Returns: The unique solution modulo the product of the individual + * moduli, which leaves the given residues. + * + * Use: Constructs a result given its residue modulo an array of + * coprime integers. This can be used to improve performance of + * RSA encryption or Blum-Blum-Shub generation if the factors + * of the modulus are known, since results can be computed mod + * each of the individual factors and then combined at the end. + * This is rather faster than doing the full-scale modular + * exponentiation. + */ + +mp *mpcrt_solve(mpcrt *c, mp **v) +{ + mp *a = MP_ZERO; + mp *x = MP_NEW; + size_t i; + + for (i = 0; i < c->k; i++) { + x = mpmont_mul(&c->mm, x, c->v[i].nnir, v[i]); + a = mp_add(a, a, x); + } + if (x) + mp_drop(x); + if (MP_CMP(a, >=, c->mm.m)) + mp_div(0, &a, a, c->mm.m); + return (a); +} + +/*----- Test rig ----------------------------------------------------------*/ + +#ifdef TEST_RIG + +static int verify(size_t n, dstr *v) +{ + mpcrt_mod *m = xmalloc(n * sizeof(mpcrt_mod)); + mp **r = xmalloc(n * sizeof(mp *)); + mpcrt c; + mp *a, *b; + size_t i; + int ok = 1; + + for (i = 0; i < n; i++) { + r[i] = *(mp **)v[2 * i].buf; + m[i].m = *(mp **)v[2 * i + 1].buf; + m[i].n = 0; + m[i].ni = 0; + m[i].nnir = 0; + } + a = *(mp **)v[2 * n].buf; + + mpcrt_create(&c, m, n, 0); + b = mpcrt_solve(&c, r); + + if (MP_CMP(a, !=, b)) { + fputs("\n*** failed\n", stderr); + fputs("n = ", stderr); + mp_writefile(c.mm.m, stderr, 10); + for (i = 0; i < n; i++) { + fprintf(stderr, "\nr[%u] = ", i); + mp_writefile(r[i], stderr, 10); + fprintf(stderr, "\nm[%u] = ", i); + mp_writefile(m[i].m, stderr, 10); + fprintf(stderr, "\nN[%u] = ", i); + mp_writefile(m[i].n, stderr, 10); + fprintf(stderr, "\nM[%u] = ", i); + mp_writefile(m[i].ni, stderr, 10); + } + fputs("\nresult = ", stderr); + mp_writefile(b, stderr, 10); + fputs("\nexpect = ", stderr); + mp_writefile(a, stderr, 10); + fputc('\n', stderr); + ok = 0; + } + + mp_drop(a); + mp_drop(b); + mpcrt_destroy(&c); + free(m); + free(r); + return (ok); +} + +static int crt1(dstr *v) { return verify(1, v); } +static int crt2(dstr *v) { return verify(2, v); } +static int crt3(dstr *v) { return verify(3, v); } +static int crt4(dstr *v) { return verify(4, v); } +static int crt5(dstr *v) { return verify(5, v); } + +static test_chunk tests[] = { + { "crt-1", crt1, { &type_mp, &type_mp, + &type_mp, 0 } }, + { "crt-2", crt2, { &type_mp, &type_mp, + &type_mp, &type_mp, + &type_mp, 0 } }, + { "crt-3", crt3, { &type_mp, &type_mp, + &type_mp, &type_mp, + &type_mp, &type_mp, + &type_mp, 0 } }, + { "crt-4", crt4, { &type_mp, &type_mp, + &type_mp, &type_mp, + &type_mp, &type_mp, + &type_mp, &type_mp, + &type_mp, 0 } }, + { "crt-5", crt5, { &type_mp, &type_mp, + &type_mp, &type_mp, + &type_mp, &type_mp, + &type_mp, &type_mp, + &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/mpcrt"); + return (0); +} + +#endif + +/*----- That's all, folks -------------------------------------------------*/ diff --git a/mpcrt.h b/mpcrt.h new file mode 100644 index 0000000..5474a92 --- /dev/null +++ b/mpcrt.h @@ -0,0 +1,132 @@ +/* -*-c-*- + * + * $Id: mpcrt.h,v 1.1 1999/11/22 20:50:57 mdw Exp $ + * + * Chinese Remainder Theorem computations (Gauss's algorithm) + * + * (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. + */ + +/*----- Revision history --------------------------------------------------* + * + * $Log: mpcrt.h,v $ + * Revision 1.1 1999/11/22 20:50:57 mdw + * Add support for solving Chinese Remainder Theorem problems. + * + */ + +#ifndef MPCRT_H +#define MPCRT_H + +#ifdef __cplusplus + extern "C" { +#endif + +/*----- Header files ------------------------------------------------------*/ + +#include + +#ifndef MP_H +# include "mp.h" +#endif + +#ifndef MPMONT_H +# include "mpmont.h" +#endif + +/*----- Data structures ---------------------------------------------------*/ + +typedef struct mpcrt_mod { + mp *m; /* %$n_i$% -- the modulus */ + mp *n; /* %$N_i = n / n_i$% */ + mp *ni; /* %$M_i = N_i^{-1} \bmod n_i$% */ + mp *nnir; /* %$N_i M_i R \bmod m$% */ +} mpcrt_mod; + +typedef struct mpcrt { + size_t k; /* Number of distinct moduli */ + mpmont mm; /* Montgomery context for product */ + mpcrt_mod *v; /* Vector of information for each */ +} mpcrt; + +/*----- Functions provided ------------------------------------------------*/ + +/* --- @mpcrt_create@ --- * + * + * Arguments: @mpcrt *c@ = pointer to CRT context + * @mpcrt_mod *v@ = pointer to vector of moduli + * @size_t k@ = number of moduli + * @mp *n@ = product of all moduli (@MP_NEW@ if unknown) + * + * Returns: --- + * + * Use: Initializes a context for solving Chinese Remainder Theorem + * problems. The vector of moduli can be incomplete. Omitted + * items must be left as null pointers. Not all combinations of + * missing things can be coped with, even if there is + * technically enough information to cope. For example, if @n@ + * is unspecified, all the @m@ values must be present, even if + * there is one modulus with both @m@ and @n@ (from which the + * product of all moduli could clearly be calculated). + */ + +extern void mpcrt_create(mpcrt */*c*/, mpcrt_mod */*v*/, + size_t /*k*/, mp */*n*/); + +/* --- @mpcrt_destroy@ --- * + * + * Arguments: @mpcrt *c@ - pointer to CRT context + * + * Returns: --- + * + * Use: Destroys a CRT context, releasing all the resources it holds. + */ + +extern void mpcrt_destroy(mpcrt */*c*/); + +/* --- @mpcrt_solve@ --- * + * + * Arguments: @mpcrt *c@ = pointer to CRT context + * @mp **v@ = array of residues + * + * Returns: The unique solution modulo the product of the individual + * moduli, which leaves the given residues. + * + * Use: Constructs a result given its residue modulo an array of + * coprime integers. This can be used to improve performance of + * RSA encryption or Blum-Blum-Shub generation if the factors + * of the modulus are known, since results can be computed mod + * each of the individual factors and then combined at the end. + * This is rather faster than doing the full-scale modular + * exponentiation. + */ + +extern mp *mpcrt_solve(mpcrt */*c*/, mp **/*v*/); + +/*----- That's all, folks -------------------------------------------------*/ + +#ifdef __cplusplus + } +#endif + +#endif diff --git a/tests/mpcrt b/tests/mpcrt new file mode 100644 index 0000000..4d08d90 --- /dev/null +++ b/tests/mpcrt @@ -0,0 +1,21 @@ +# Test vectors for Chinese Remainder Theorem solution (Gauss's algorithm) +# +# $Id: mpcrt,v 1.1 1999/11/22 20:51:19 mdw Exp $ + +crt-1 { + 1 5 1; + 3498243289823 4534543545463431 3498243289823; +} + +crt-2 { + 3 7 7 13 59; + 39845 435435221 43534545 32423423467 13736097689153284731; + + 2200541929485233317342398 498459898455435345676576793 + 13046769915260439091721075347560767438958354488807168684311588308214063361125238823412234206191582332588 40831929843180254171317254073271577309351168965431122042755102715326515941762786951037109689522493526197 + 14756532044160797319048143986538019326281096778844833416304858521742332925502855547148214406728673769162624068049034315018936294558; +} + +crt-4 { + 2 5 1 7 3 11 8 13 2192; +} \ No newline at end of file -- 2.11.0