Mathematical Methods of Cryptography

Some properties of sequences generated by the GEA-1 encryption algorithm

A. D. Bugrov^a, O. V. Kamlovskii^b, V. V. Mizerov<sup>c

a</sup> MIREA — Russian Technological University, Moscow
^b Moscow Technical University of Communications and Informatics
^c LLC "Certification Research Center", Moscow

Abstract: We consider distribution properties and autocorrelation coefficients of sequences generated by the GEA-1 encryption algorithm. We use known estimates of exponential sums from linear recurrence sequences. Let $v=(v(i))_{i=0}^{\infty}$ be the keystream sequence of the GEA-1 algorithm. We prove that the period of sequence $v$ equals to $T(v)=(2^{31}-1)(2^{32}-1)(2^{33}-1)$. We also prove that the number of occurrences of elements $z\in \{0,1\}$ in the vector $(v(0),\ldots, v(l-1))$ satisfies the following relations: $N(z, v)=(T(v)-(-1)^z)/{2}$ and $\left|N_l(z,v)-{l}/{2}\right|<1{,}8\cdot 2^{60}$ for all $l\le T(v)$.

Keywords: linear recurrence sequences, filter generators, discrete functions, additive character sums, cross-correlation function.

UDC: 512.552

DOI: 10.17223/2226308X/17/17