applied cryptography - protocols, algorithms, and source code in c

The resulting output sequence is called an m sequence

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Unformatted text preview: a list of good constants for linear congruential generators. They all produce maximal period generators and even more important, pass the spectral test for randomness for dimensions 2, 3, 4, 5, and 6 [385,863]. They are organized by the largest product that does not overflow a specific word length. The advantage of linear congruential generators is that they are fast, requiring few operations per bit. Unfortunately, linear congruential generators cannot be used for cryptography; they are predictable. Linear congruential generators were first broken by Jim Reeds [1294,1295,1296] and then by Joan Boyar [1251]. She also broke quadratic generators: Xn = (aXn-12 + bXn-1 + c) mod m and cubic generators: Xn = (aXn-13 + bXn-12 + cXn-1 + d) mod m Other researchers extended Boyar’s work to break any polynomial congruential generator [923,899,900]. Truncated linear congruential generators were also broken [581,705,580], as were truncated linear congruential generators with unknown parameters [1500,212]. The preponderance of evidence is that congruential generators aren’t useful for cryptography. Table 16.1 Constants for Linear Congruential Generators Overflow At: 220 221 222 223 a 106 211 421 430 936 1366 171 859 419 967 141 625 1541 1741 1291 205 421 1255 281 1093 421 1021 1021 1277 b 1283 1663 1663 2531 1399 1283 11213 2531 6173 3041 28411 6571 2957 2731 4621 29573 17117 6173 28411 18257 54773 24631 25673 24749 m 6075 7875 7875 11979 6655 6075 53125 11979 29282 14406 134456 31104 14000 12960 21870 139968 81000 29282 134456 86436 259200 116640 121500 117128 224 225 226 227 228 229 230 231 232 233 234 235 741 2041 2311 1807 1597 1861 2661 4081 3661 3877 3613 1366 8121 4561 7141 9301 4096 2416 17221 36261 84589 66037 25673 25367 45289 51749 49297 36979 25673 30809 29573 45289 150889 28411 51349 54773 49297 150889 374441 107839 66037 45989 312500 121500 120050 214326 244944 233280 175000 121500 145800 139968 214326 714025 134456 243000 259200 233280 714025 1771875 510300 312500 217728 Previous Table of Contents Next Products | Contact Us | About Us | Privacy | Ad Info | Ho...
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