Geodesic
Some properties of sequences generated by the GEA-1 encryption algorithm
Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 75-78

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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. 
@article{PDMA_2024_17_a16,
     author = {A. D. Bugrov and O. V. Kamlovskii and V. V. Mizerov},
     title = {Some properties of sequences generated by the {GEA-1} encryption algorithm},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {75--78},
     publisher = {mathdoc},
     number = {17},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2024_17_a16/}
}
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A. D. Bugrov; O. V. Kamlovskii; V. V. Mizerov. Some properties of sequences generated by the GEA-1 encryption algorithm. Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 75-78. http://geodesic.mathdoc.fr/item/PDMA_2024_17_a16/