Mathematical Methods of Cryptography

On the number of $\ell$-suitable Boolean functions in constructions of filter and combining models of stream ciphers

T. A. Bonich^a, M. A. Panferov^b, N. N. Tokareva<sup>a

a</sup> Novosibirsk State University, Novosibirsk, Russia,
^b Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: It is well known that every stream cipher is based on a good pseudorandom generator. For cryptographic purposes, we are interested in generating pseudorandom sequences with the maximum possible period. A feedback register is one of the most known cryptographic primitives that is used to construct stream ciphers. We consider periodic properties of pseudorandom sequences produced by filter and combiner generators (two known schemes of stream generators based on feedback registers). We analyze functions in these schemes that lead to output sequences of period at least a given number $\ell$. We call such functions $\ell$-suitable and count the exact number of them for an arbitrary $n$.

Keywords: stream cipher, filter generator, combiner generator, Boolean function.

UDC: 519.7

Language: English

DOI: 10.17223/20710410/62/3