Abstract
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
for integers m and αj, and integer functions Φ j, j= 1,...,k. Our predictors are efficient, provided that the functions Φ 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 α 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.
This research was supported by grant No. 86-00301 from the United States - Israel Binational Science Foundation (BSF), Jerusalem, Israel.
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Krawczyk, H. (1990). How to Predict Congruential Generators. In: Brassard, G. (eds) Advances in Cryptology — CRYPTO’ 89 Proceedings. CRYPTO 1989. Lecture Notes in Computer Science, vol 435. Springer, New York, NY. https://doi.org/10.1007/0-387-34805-0_14
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DOI: https://doi.org/10.1007/0-387-34805-0_14
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