2005 | OriginalPaper | Buchkapitel
Cryptanalysis of the Quadratic Generator
verfasst von : Domingo Gomez, Jaime Gutierrez, Alvar Ibeas
Erschienen in: Progress in Cryptology - INDOCRYPT 2005
Verlag: Springer Berlin Heidelberg
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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.