How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
A simple unpredictable pseudo random number generator
SIAM Journal on Computing
Theory of linear and integer programming
Theory of linear and integer programming
Realistic analysis of some randomized algorithms
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
RSA and Rabin functions: certain parts are as hard as the whole
SIAM Journal on Computing - Special issue on cryptography
Reconstructing truncated integer variables satisfying linear congruences
SIAM Journal on Computing - Special issue on cryptography
Unique extrapolation of polynomial recurrences
SIAM Journal on Computing - Special issue on cryptography
Inferring sequences produced by pseudo-random number generators
Journal of the ACM (JACM)
On the power of two-point based sampling
Journal of Complexity
Pseudo-random generation from one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Inferring sequences produced by pseudo-random number generators
Inferring sequences produced by pseudo-random number generators
Inferring a sequence generated by a linear congruence
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Secret linear congruential generators are not cryptographically secure
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Efficient And Secure Pseudo-Random Number Generation
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
On the existence of pseudorandom generators
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
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In this paper we show how to predict a large class of pseudorandom number generators. We consider congruential generators which output a sequence of integers s0, s1,... where si is computed by the recurrence si 驴 驴j=1k 驴j 驴j(s0,s1,...si-1) (mod m) for integers m and 驴j and integer functions 驴j, j=1...,k. Our predictors are efficient, provided that the functions 驴j are computable (over the integers) in polynomial time. These predictors have access to the elements of the sequence prior to the element being predicted, but they do not know the modulus m or the coefficients 驴j the generator actually works with. This extends previous results about the predictability of such generators. In particular, we prove that multivariate polynomial generators, i.e. generators where si, = P(si-n,...,si-1) (mod m), for a polynomial P of fixed degree in n variables, are efficiently predictable.