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1 | /* -*-c-*- |
2 | * |
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3 | * $Id: mprand.c,v 1.4 2001/05/07 17:31:19 mdw Exp $ |
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4 | * |
5 | * Generate a random multiprecision integer |
6 | * |
7 | * (c) 1999 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: mprand.c,v $ |
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33 | * Revision 1.4 2001/05/07 17:31:19 mdw |
34 | * Fix off-by one bug in mprand_range. Probably security critical: the old |
35 | * code generated numbers between zero and the highest power of 2 less than |
36 | * the given range. |
37 | * |
d34decd2 |
38 | * Revision 1.3 2000/06/17 11:45:09 mdw |
39 | * Major memory management overhaul. Added arena support. Use the secure |
40 | * arena for secret integers. Replace and improve the MP management macros |
41 | * (e.g., replace MP_MODIFY by MP_DEST). |
42 | * |
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43 | * Revision 1.2 1999/12/22 15:55:33 mdw |
44 | * Modify `mprand' slightly. Add `mprand_range'. |
45 | * |
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46 | * Revision 1.1 1999/12/10 23:23:05 mdw |
47 | * Support for generating random large integers. |
48 | * |
49 | */ |
50 | |
51 | /*----- Header files ------------------------------------------------------*/ |
52 | |
53 | #include <mLib/alloc.h> |
54 | |
55 | #include "grand.h" |
56 | #include "mp.h" |
57 | #include "mprand.h" |
58 | |
59 | /*----- Main code ---------------------------------------------------------*/ |
60 | |
61 | /* --- @mprand@ --- * |
62 | * |
63 | * Arguments: @mp *d@ = destination integer |
64 | * @unsigned b@ = number of bits |
65 | * @grand *r@ = pointer to random number source |
66 | * @mpw or@ = mask to OR with low-order bits |
67 | * |
68 | * Returns: A random integer with the requested number of bits. |
69 | * |
70 | * Use: Constructs an arbitrarily large pseudorandom integer. |
71 | * Assuming that the generator @r@ is good, the result is |
72 | * uniformly distributed in the interval %$[2^{b - 1}, 2^b)$%. |
73 | * The result is then ORred with the given @or@ value. This |
74 | * will often be 1, to make the result odd. |
75 | */ |
76 | |
77 | mp *mprand(mp *d, unsigned b, grand *r, mpw or) |
78 | { |
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79 | size_t sz = (b + 7) >> 3; |
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80 | arena *a = (d && (d->f & MP_BURN)) ? arena_secure : arena_global; |
81 | octet *v = x_alloc(a, sz); |
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82 | unsigned m; |
83 | |
84 | /* --- Fill buffer with random data --- */ |
85 | |
86 | r->ops->fill(r, v, sz); |
87 | |
88 | /* --- Force into the correct range --- * |
89 | * |
90 | * This is slightly tricky. Oh, well. |
91 | */ |
92 | |
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93 | b = (b - 1) & 7; |
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94 | m = (1 << b); |
95 | v[0] = (v[0] & (m - 1)) | m; |
96 | |
97 | /* --- Mask, load and return --- */ |
98 | |
99 | d = mp_loadb(d, v, sz); |
100 | d->v[0] |= or; |
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101 | memset(v, 0, sz); |
102 | x_free(a, v); |
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103 | return (d); |
104 | } |
105 | |
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106 | /* --- @mprand_range@ --- * |
107 | * |
108 | * Arguments: @mp *d@ = destination integer |
109 | * @mp *l@ = limit for random number |
110 | * @grand *r@ = random number source |
111 | * @mpw or@ = mask for low-order bits |
112 | * |
113 | * Returns: A pseudorandom integer, unformly distributed over the |
114 | * interval %$[0, l)$%. |
115 | * |
116 | * Use: Generates a uniformly-distributed pseudorandom number in the |
117 | * appropriate range. |
118 | */ |
119 | |
120 | mp *mprand_range(mp *d, mp *l, grand *r, mpw or) |
121 | { |
122 | size_t b = mp_bits(l); |
123 | size_t sz = (b + 7) >> 3; |
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124 | arena *a = (d && (d->f & MP_BURN)) ? arena_secure : arena_global; |
125 | octet *v = x_alloc(a, sz); |
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126 | unsigned m; |
127 | |
128 | /* --- The algorithm --- * |
129 | * |
130 | * Rather simpler than most. Find the number of bits in the number %$l$% |
131 | * (i.e., the integer %$b$% such that %$2^{b - 1} \le l < 2^b$%), and |
132 | * generate pseudorandom integers with %$n$% bits (but not, unlike in the |
133 | * function above, with the top bit forced to 1). If the integer is |
134 | * greater than or equal to %$l$%, try again. |
135 | * |
136 | * This is similar to the algorithms used in @lcrand_range@ and friends, |
137 | * except that I've forced the `raw' range of the random numbers such that |
138 | * %$l$% itself is the largest multiple of %$l$% in the range (since, by |
139 | * the inequality above, %$2^b \le 2l$%). This removes the need for costly |
140 | * division and remainder operations. |
141 | * |
142 | * As usual, the number of iterations expected is two. |
143 | */ |
144 | |
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145 | b = ((b - 1) & 7) + 1; |
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146 | m = (1 << b) - 1; |
147 | do { |
148 | r->ops->fill(r, v, sz); |
149 | v[0] &= m; |
150 | d = mp_loadb(d, v, sz); |
151 | d->v[0] |= or; |
152 | } while (MP_CMP(d, >=, l)); |
153 | |
154 | /* --- Done --- */ |
155 | |
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156 | memset(v, 0, sz); |
157 | x_free(a, v); |
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158 | return (d); |
159 | } |
160 | |
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161 | /*----- That's all, folks -------------------------------------------------*/ |