| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Generate a random multiprecision integer |
| 4 | * |
| 5 | * (c) 1999 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 <mLib/alloc.h> |
| 31 | |
| 32 | #include "grand.h" |
| 33 | #include "mp.h" |
| 34 | #include "mprand.h" |
| 35 | |
| 36 | /*----- Main code ---------------------------------------------------------*/ |
| 37 | |
| 38 | /* --- @mprand@ --- * |
| 39 | * |
| 40 | * Arguments: @mp *d@ = destination integer |
| 41 | * @unsigned b@ = number of bits |
| 42 | * @grand *r@ = pointer to random number source |
| 43 | * @mpw or@ = mask to OR with low-order bits |
| 44 | * |
| 45 | * Returns: A random integer with the requested number of bits. |
| 46 | * |
| 47 | * Use: Constructs an arbitrarily large pseudorandom integer. |
| 48 | * Assuming that the generator @r@ is good, the result is |
| 49 | * uniformly distributed in the interval %$[2^{b - 1}, 2^b)$%. |
| 50 | * The result is then ORred with the given @or@ value. This |
| 51 | * will often be 1, to make the result odd. |
| 52 | * |
| 53 | * The length @b@ may be zero; but %$\texttt{or} \ge 2^b$% is |
| 54 | * not permitted. |
| 55 | */ |
| 56 | |
| 57 | mp *mprand(mp *d, unsigned b, grand *r, mpw or) |
| 58 | { |
| 59 | size_t sz = (b + 7) >> 3; |
| 60 | arena *a = (d && (d->f & MP_BURN)) ? arena_secure : arena_global; |
| 61 | octet *v; |
| 62 | unsigned m; |
| 63 | |
| 64 | assert(b >= MPW_BITS || !(or >> b)); |
| 65 | |
| 66 | /* --- Special case --- */ |
| 67 | |
| 68 | if (!b) return (MP_ZERO); |
| 69 | |
| 70 | /* --- Fill buffer with random data --- */ |
| 71 | |
| 72 | v = x_alloc(a, sz); |
| 73 | r->ops->fill(r, v, sz); |
| 74 | |
| 75 | /* --- Force into the correct range --- * |
| 76 | * |
| 77 | * This is slightly tricky. Oh, well. |
| 78 | */ |
| 79 | |
| 80 | b = (b - 1) & 7; |
| 81 | m = (1 << b); |
| 82 | v[0] = (v[0] & (m - 1)) | m; |
| 83 | |
| 84 | /* --- Mask, load and return --- */ |
| 85 | |
| 86 | d = mp_loadb(d, v, sz); |
| 87 | if (or) { |
| 88 | assert(d->sz); |
| 89 | if (!MP_LEN(d)) d->vl = d->v + 1; |
| 90 | d->v[0] |= or; |
| 91 | } |
| 92 | memset(v, 0, sz); |
| 93 | x_free(a, v); |
| 94 | return (d); |
| 95 | } |
| 96 | |
| 97 | /* --- @mprand_range@ --- * |
| 98 | * |
| 99 | * Arguments: @mp *d@ = destination integer |
| 100 | * @mp *l@ = limit for random number |
| 101 | * @grand *r@ = random number source |
| 102 | * @mpw or@ = mask for low-order bits |
| 103 | * |
| 104 | * Returns: A pseudorandom integer, unformly distributed over the |
| 105 | * interval %$[0, l)$%. |
| 106 | * |
| 107 | * Use: Generates a uniformly-distributed pseudorandom number in the |
| 108 | * appropriate range. We must have %$l > 0$%. |
| 109 | */ |
| 110 | |
| 111 | mp *mprand_range(mp *d, mp *l, grand *r, mpw or) |
| 112 | { |
| 113 | size_t b = mp_bits(l); |
| 114 | size_t sz = (b + 7) >> 3; |
| 115 | arena *a = (d && (d->f & MP_BURN)) ? arena_secure : arena_global; |
| 116 | octet *v = x_alloc(a, sz); |
| 117 | unsigned m; |
| 118 | |
| 119 | /* --- The algorithm --- * |
| 120 | * |
| 121 | * Rather simpler than most. Find the number of bits in the number %$l$% |
| 122 | * (i.e., the integer %$b$% such that %$2^{b - 1} \le l < 2^b$%), and |
| 123 | * generate pseudorandom integers with %$n$% bits (but not, unlike in the |
| 124 | * function above, with the top bit forced to 1). If the integer is |
| 125 | * greater than or equal to %$l$%, try again. |
| 126 | * |
| 127 | * This is similar to the algorithms used in @lcrand_range@ and friends, |
| 128 | * except that I've forced the `raw' range of the random numbers such that |
| 129 | * %$l$% itself is the largest multiple of %$l$% in the range (since, by |
| 130 | * the inequality above, %$2^b \le 2l$%). This removes the need for costly |
| 131 | * division and remainder operations. |
| 132 | * |
| 133 | * As usual, the number of iterations expected is two. |
| 134 | */ |
| 135 | |
| 136 | assert(MP_POSP(l)); |
| 137 | b = ((b - 1) & 7) + 1; |
| 138 | m = (1 << b) - 1; |
| 139 | do { |
| 140 | r->ops->fill(r, v, sz); |
| 141 | v[0] &= m; |
| 142 | d = mp_loadb(d, v, sz); |
| 143 | d->v[0] |= or; |
| 144 | } while (MP_CMP(d, >=, l)); |
| 145 | |
| 146 | /* --- Done --- */ |
| 147 | |
| 148 | memset(v, 0, sz); |
| 149 | x_free(a, v); |
| 150 | return (d); |
| 151 | } |
| 152 | |
| 153 | /*----- That's all, folks -------------------------------------------------*/ |