| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Key length conversions |
| 4 | * |
| 5 | * (c) 2007 Straylight/Edgeware |
| 6 | */ |
| 7 | |
| 8 | /*----- Licensing notice --------------------------------------------------* |
| 9 | * |
| 10 | * This file is part of Catacomb. |
| 11 | * |
| 12 | * Catacomb is free software; you can redistribute it and/or modify |
| 13 | * it under the terms of the GNU Library General Public License as |
| 14 | * published by the Free Software Foundation; either version 2 of the |
| 15 | * License, or (at your option) any later version. |
| 16 | * |
| 17 | * Catacomb is distributed in the hope that it will be useful, |
| 18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 20 | * GNU Library General Public License for more details. |
| 21 | * |
| 22 | * You should have received a copy of the GNU Library General Public |
| 23 | * License along with Catacomb; if not, write to the Free |
| 24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| 25 | * MA 02111-1307, USA. |
| 26 | */ |
| 27 | |
| 28 | /*----- Header files ------------------------------------------------------*/ |
| 29 | |
| 30 | #include <math.h> |
| 31 | |
| 32 | #include "keysz.h" |
| 33 | |
| 34 | /*----- Main code ---------------------------------------------------------*/ |
| 35 | |
| 36 | /* --- Primitive conversions --- */ |
| 37 | |
| 38 | static double fromnfs(double nbits) |
| 39 | { |
| 40 | /* --- Magic taken from P1363 --- */ |
| 41 | #define LOG2 0.6931471805599453094172321214581765680755 |
| 42 | #define MAGIC 8.567936 /* = 17.135872 / 2 */ |
| 43 | double z = log(nbits * LOG2)/LOG2; |
| 44 | return 4.0/3.0 * pow(3 * nbits * z*z, 1.0/3.0) - MAGIC; |
| 45 | } |
| 46 | |
| 47 | static double tonfs(double nbits) |
| 48 | { |
| 49 | double hi, lo, mid, val; |
| 50 | |
| 51 | /* --- Find upper and lower bounds --- */ |
| 52 | |
| 53 | for (hi = nbits; fromnfs(hi) < nbits; hi *= 2); |
| 54 | for (lo = nbits; fromnfs(lo) > nbits; lo /= 2); |
| 55 | |
| 56 | /* --- Bisect the interval until we get an answer --- */ |
| 57 | |
| 58 | #define THRESH 0.01 |
| 59 | for (;;) { |
| 60 | mid = (hi + lo)/2; |
| 61 | val = fromnfs(mid); |
| 62 | if (fabs(val - nbits) < THRESH) |
| 63 | return (mid); |
| 64 | else if (val < nbits) |
| 65 | lo = mid; |
| 66 | else |
| 67 | hi = mid; |
| 68 | } |
| 69 | } |
| 70 | |
| 71 | static double torho(double nbits) { return 2*nbits; } |
| 72 | static double fromrho(double nbits) { return nbits/2; } |
| 73 | |
| 74 | /* --- @keysz_fromdl@, @_fromschnorr@, @_fromif@, @_fromec@ --- * |
| 75 | * |
| 76 | * Arguments: @double nbits@ = key size |
| 77 | * |
| 78 | * Returns: Equivalent symmetric key size. |
| 79 | * |
| 80 | * Use: Converts key lengths of various kinds of reference problems |
| 81 | * to (roughly) equivalent symmetric key sizes. |
| 82 | * |
| 83 | * * Given the bit length of %$p$%, @keysz_fromdl@ returns a |
| 84 | * key size representing the difficulty of computing |
| 85 | * discrete logarithms in %$\gf{p}$%, for %$p$% prime or a |
| 86 | * small power of a prime. |
| 87 | * |
| 88 | * * Given the bit length of %$r$%, @keysz_fromschnorr@ |
| 89 | * returns a key size representing the difficulty of |
| 90 | * computing discrete logarithms in a subgroup of %$\gf{q}$% |
| 91 | * of order %$r$%. |
| 92 | * |
| 93 | * * Given the bit length of %$n$%, @keysz_fromif@ returns a |
| 94 | * key size representing the difficulty of factoring a |
| 95 | * `hard' number %$n = p q$%, where %$p$% and %$q$% are |
| 96 | * primes of (near enough) the same length. |
| 97 | * |
| 98 | * * Given the bit length of %$r$%, @keysz_fromec@ returns a |
| 99 | * key size representing the difficulty of computing |
| 100 | * discrete logarithms in a subgroup of order-%$r$% of an |
| 101 | * elliptic curve over a finite field. |
| 102 | * |
| 103 | * These functions take and return @double@ rather than an |
| 104 | * integer type in order to preserve precision between |
| 105 | * conversions. |
| 106 | */ |
| 107 | |
| 108 | #define CONVERSIONS(_) \ |
| 109 | _(dl, nfs) \ |
| 110 | _(schnorr, rho) \ |
| 111 | _(if, nfs) \ |
| 112 | _(ec, rho) |
| 113 | |
| 114 | #define DEFINE_FROM(what, how) \ |
| 115 | double keysz_from##what(double nbits) { return from##how(nbits); } |
| 116 | |
| 117 | CONVERSIONS(DEFINE_FROM) |
| 118 | |
| 119 | /* --- @keysz_todl@, @_toschnorr@, @_toif@, @_toec@ --- * |
| 120 | * |
| 121 | * Arguments: @unsigned long nbits@ = symmetric key size |
| 122 | * |
| 123 | * Returns: Equivalent key size. |
| 124 | * |
| 125 | * Use: Converts symmetric key sizes to (roughly) equivalent key |
| 126 | * sizes for various kinds of reference problems. These are the |
| 127 | * approximate inverses of the functions above. |
| 128 | */ |
| 129 | |
| 130 | #define DEFINE_TO(what, how) \ |
| 131 | double keysz_to##what(double nbits) { return to##how(nbits); } |
| 132 | |
| 133 | CONVERSIONS(DEFINE_TO) |
| 134 | |
| 135 | /*----- Interactive mode for testing --------------------------------------*/ |
| 136 | |
| 137 | #ifdef TEST_RIG |
| 138 | |
| 139 | #include <stdio.h> |
| 140 | #include <stdlib.h> |
| 141 | #include <string.h> |
| 142 | |
| 143 | static const struct entry { |
| 144 | const char *name; |
| 145 | double (*func)(double); |
| 146 | } tab[] = { |
| 147 | #define ENTRY_FROM(what, how) { "from" #what, keysz_from##what }, |
| 148 | #define ENTRY_TO(what, how) { "to" #what, keysz_to##what }, |
| 149 | CONVERSIONS(ENTRY_FROM) |
| 150 | CONVERSIONS(ENTRY_TO) |
| 151 | { 0 } |
| 152 | }; |
| 153 | |
| 154 | int main(int argc, char *argv[]) |
| 155 | { |
| 156 | const struct entry *e; |
| 157 | double d; |
| 158 | |
| 159 | if (!argv[1]) { |
| 160 | fprintf(stderr, "conversions:"); |
| 161 | for (e = tab; e->name; e++) fprintf(stderr, " %s", e->name); |
| 162 | putc('\n', stderr); |
| 163 | return (1); |
| 164 | } |
| 165 | for (e = tab; e->name && strcmp(e->name, argv[1]); e++); |
| 166 | if (!e) { |
| 167 | fprintf(stderr, "unknown conversion `%s'\n", argv[1]); |
| 168 | return (1); |
| 169 | } |
| 170 | for (argv += 2; *argv; argv++) { |
| 171 | d = strtod(*argv, 0); |
| 172 | printf("%s(%g) = %g\n", e->name, d, e->func(d)); |
| 173 | } |
| 174 | return (0); |
| 175 | } |
| 176 | |
| 177 | #endif |
| 178 | |
| 179 | /*----- That's all, folks -------------------------------------------------*/ |