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Diskr. Mat., 2011, Volume 23, Issue 1, Pages 51–71 (Mi dm1130)  

On properties of the Klimov–Shamir generator of pseudorandom numbers

S. V. Rykov


Abstract: The pseudorandom number generator (PRNG) based on the transformation
$$ F_c(x)=x+(x^2\vee c)\pmod{2^n} $$
was suggested by Klimov and Shamir in 2002. The function $F_c(x)$ is transitive modulo $2^n$ if and only if either $c\equiv5\pmod8$ or $c\equiv7\pmod8$.
We consider properties of the distribution of the pairs $(x_i, F_c(x_i))$ for various $c\in\mathbf Z/2^n\mathbf Z$ and demonstrate that their statistical properties are unsatisfactory, most notably for $c\geq2^{n/3}$.
We show that in the case $n=32$, at most 9 distinct pairs $(x_i, F_c(x_i))$ are needed to find the value of $c$ with probability $P\geq0,999$.

DOI: https://doi.org/10.4213/dm1130

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English version:
Discrete Mathematics and Applications, 2011, 21:2, 179–202

Bibliographic databases:

UDC: 519.7
Received: 16.04.2010

Citation: S. V. Rykov, “On properties of the Klimov–Shamir generator of pseudorandom numbers”, Diskr. Mat., 23:1 (2011), 51–71; Discrete Math. Appl., 21:2 (2011), 179–202

Citation in format AMSBIB
\Bibitem{Ryk11}
\by S.~V.~Rykov
\paper On properties of the Klimov--Shamir generator of pseudorandom numbers
\jour Diskr. Mat.
\yr 2011
\vol 23
\issue 1
\pages 51--71
\mathnet{http://mi.mathnet.ru/dm1130}
\crossref{https://doi.org/10.4213/dm1130}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2830697}
\elib{http://elibrary.ru/item.asp?id=20730372}
\transl
\jour Discrete Math. Appl.
\yr 2011
\vol 21
\issue 2
\pages 179--202
\crossref{https://doi.org/10.1515/DMA.2011.011}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79960020664}


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