Abstract
Let p be a prime and let a and b be integers modulo p. The inversive congruential generator (ICG) is a sequence (u n ) of pseudorandom numbers defined by the relation \(U_{n+1}\equiv au{^{-1}_{n}}+b {\rm mod} p\).We show that if b and sufficiently many of the most significant bits of three consecutive values u n of the ICG are given, one can recover in polynomial time the initial value u 0 (even in the case where the coefficient a is unknown) provided that the initial value u 0 does not lie in a certain small subset of exceptional values.
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Blackburn, S.R., Gomez-Perez, D., Gutierrez, J., Shparlinski, I.E. (2003). Predicting the Inversive Generator. In: Paterson, K.G. (eds) Cryptography and Coding. Cryptography and Coding 2003. Lecture Notes in Computer Science, vol 2898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40974-8_21
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DOI: https://doi.org/10.1007/978-3-540-40974-8_21
Publisher Name: Springer, Berlin, Heidelberg
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