| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * $Id: mpmont-exp.c,v 1.1 2004/04/01 12:50:09 mdw Exp $ |
| 4 | * |
| 5 | * Modular exponentiation with Montgomery reduction |
| 6 | * |
| 7 | * (c) 2004 Straylight/Edgeware |
| 8 | */ |
| 9 | |
| 10 | /*----- Licensing notice --------------------------------------------------* |
| 11 | * |
| 12 | * This file is part of Catacomb. |
| 13 | * |
| 14 | * Catacomb is free software; you can redistribute it and/or modify |
| 15 | * it under the terms of the GNU Library General Public License as |
| 16 | * published by the Free Software Foundation; either version 2 of the |
| 17 | * License, or (at your option) any later version. |
| 18 | * |
| 19 | * Catacomb is distributed in the hope that it will be useful, |
| 20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 22 | * GNU Library General Public License for more details. |
| 23 | * |
| 24 | * You should have received a copy of the GNU Library General Public |
| 25 | * License along with Catacomb; if not, write to the Free |
| 26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| 27 | * MA 02111-1307, USA. |
| 28 | */ |
| 29 | |
| 30 | /*----- Revision history --------------------------------------------------* |
| 31 | * |
| 32 | * $Log: mpmont-exp.c,v $ |
| 33 | * Revision 1.1 2004/04/01 12:50:09 mdw |
| 34 | * Add cyclic group abstraction, with test code. Separate off exponentation |
| 35 | * functions for better static linking. Fix a buttload of bugs on the way. |
| 36 | * Generally ensure that negative exponents do inversion correctly. Add |
| 37 | * table of standard prime-field subgroups. (Binary field subgroups are |
| 38 | * currently unimplemented but easy to add if anyone ever finds a good one.) |
| 39 | * |
| 40 | */ |
| 41 | |
| 42 | /*----- Header files ------------------------------------------------------*/ |
| 43 | |
| 44 | #include "mp.h" |
| 45 | #include "mpmont.h" |
| 46 | #include "mpmont-exp.h" |
| 47 | |
| 48 | /*----- Exponentiation ----------------------------------------------------*/ |
| 49 | |
| 50 | /* --- @mpmont_expr@ --- * |
| 51 | * |
| 52 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
| 53 | * @mp *d@ = fake destination |
| 54 | * @mp *a@ = base |
| 55 | * @mp *e@ = exponent |
| 56 | * |
| 57 | * Returns: Result, %$(a R^{-1})^e R \bmod m$%. |
| 58 | */ |
| 59 | |
| 60 | mp *mpmont_expr(mpmont *mm, mp *d, mp *a, mp *e) |
| 61 | { |
| 62 | mp *x = MP_COPY(mm->r); |
| 63 | mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW; |
| 64 | |
| 65 | MP_COPY(a); |
| 66 | MP_SHRINK(e); |
| 67 | if (e->f & MP_NEG) { |
| 68 | mp *g = MP_NEW; |
| 69 | a = mpmont_reduce(mm, a, a); |
| 70 | mp_gcd(&g, 0, &a, mm->m, a); |
| 71 | assert(MP_EQ(g, MP_ONE)); |
| 72 | a = mpmont_mul(mm, a, a, mm->r2); |
| 73 | mp_drop(g); |
| 74 | } |
| 75 | if (MP_LEN(e) == 0) |
| 76 | ; |
| 77 | else if (MP_LEN(e) < EXP_THRESH) |
| 78 | EXP_SIMPLE(x, a, e); |
| 79 | else |
| 80 | EXP_WINDOW(x, a, e); |
| 81 | mp_drop(d); |
| 82 | mp_drop(spare); |
| 83 | mp_drop(a); |
| 84 | return (x); |
| 85 | } |
| 86 | |
| 87 | /* --- @mpmont_exp@ --- * |
| 88 | * |
| 89 | * Arguments: @mpmont *mm@ = pointer to Montgomery reduction context |
| 90 | * @mp *d@ = fake destination |
| 91 | * @mp *a@ = base |
| 92 | * @mp *e@ = exponent |
| 93 | * |
| 94 | * Returns: Result, %$a^e \bmod m$%. |
| 95 | */ |
| 96 | |
| 97 | mp *mpmont_exp(mpmont *mm, mp *d, mp *a, mp *e) |
| 98 | { |
| 99 | e = MP_COPY(e); |
| 100 | d = mpmont_mul(mm, d, a, mm->r2); |
| 101 | d = mpmont_expr(mm, d, d, e); |
| 102 | d = mpmont_reduce(mm, d, d); |
| 103 | MP_DROP(e); |
| 104 | return (d); |
| 105 | } |
| 106 | |
| 107 | /*----- Test rig ----------------------------------------------------------*/ |
| 108 | |
| 109 | #ifdef TEST_RIG |
| 110 | |
| 111 | static int texp(dstr *v) |
| 112 | { |
| 113 | mp *m = *(mp **)v[0].buf; |
| 114 | mp *a = *(mp **)v[1].buf; |
| 115 | mp *b = *(mp **)v[2].buf; |
| 116 | mp *r = *(mp **)v[3].buf; |
| 117 | mp *mr; |
| 118 | int ok = 1; |
| 119 | |
| 120 | mpmont mm; |
| 121 | mpmont_create(&mm, m); |
| 122 | |
| 123 | mr = mpmont_exp(&mm, MP_NEW, a, b); |
| 124 | |
| 125 | if (!MP_EQ(mr, r)) { |
| 126 | fputs("\n*** montgomery modexp failed", stderr); |
| 127 | fputs("\n m = ", stderr); mp_writefile(m, stderr, 10); |
| 128 | fputs("\n a = ", stderr); mp_writefile(a, stderr, 10); |
| 129 | fputs("\n e = ", stderr); mp_writefile(b, stderr, 10); |
| 130 | fputs("\n r = ", stderr); mp_writefile(r, stderr, 10); |
| 131 | fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10); |
| 132 | fputc('\n', stderr); |
| 133 | ok = 0; |
| 134 | } |
| 135 | |
| 136 | MP_DROP(m); |
| 137 | MP_DROP(a); |
| 138 | MP_DROP(b); |
| 139 | MP_DROP(r); |
| 140 | MP_DROP(mr); |
| 141 | mpmont_destroy(&mm); |
| 142 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
| 143 | return ok; |
| 144 | } |
| 145 | |
| 146 | |
| 147 | static test_chunk tests[] = { |
| 148 | { "exp", texp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
| 149 | { 0, 0, { 0 } }, |
| 150 | }; |
| 151 | |
| 152 | int main(int argc, char *argv[]) |
| 153 | { |
| 154 | sub_init(); |
| 155 | test_run(argc, argv, tests, SRCDIR "/tests/mpmont"); |
| 156 | return (0); |
| 157 | } |
| 158 | |
| 159 | #endif |
| 160 | |
| 161 | /*----- That's all, folks -------------------------------------------------*/ |