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SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Linear Congruential Generators Do Not Produce Random Sequences
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Efficient, perfect random number generators
CRYPTO '88 Proceedings on Advances in cryptology
How to predict congruential generators
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This paper discusses the predictability of the sequence given by outputing a constant proportion α of the leading bits of the numbers produced by a linear congruential generator. First, we make the assumption that the modulus of the generator is the only known parameter and we prove that, almost surely, a significant proportion of the bits can be predicted from the previous ones, once the generator has been used K times successively where K is O(√log m). Next, we assume that all parameters of the generator are secret and we show how repeated observations of sequences of outputs of length K will probably allow an opponent to cryptanalyze the full sequence.