Abstract
Let p be a prime and let a and c be integers modulo p. The quadratic congruential generator (QCG) is a sequence (v n ) of pseudorandom numbers defined by the relation \(v_{n+1}\equiv av^{2}_{n}+c mod p\). We show that if sufficiently many of the most significant bits of several consecutive values v n of the QCG are given, one can recover in polynomial time the initial value v 0 (even in the case where the coefficient c is unknown), provided that the initial value v 0 does not lie in a certain small subset of exceptional values.
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Gomez, D., Gutierrez, J., Ibeas, A. (2005). Cryptanalysis of the Quadratic Generator. In: Maitra, S., Veni Madhavan, C.E., Venkatesan, R. (eds) Progress in Cryptology - INDOCRYPT 2005. INDOCRYPT 2005. Lecture Notes in Computer Science, vol 3797. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11596219_10
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DOI: https://doi.org/10.1007/11596219_10
Publisher Name: Springer, Berlin, Heidelberg
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