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 Model. Anal. Inform. Sist., 2018, Volume 25, Number 3, Pages 276–290 (Mi mais628)

Cryptosystems

The support splitting algorithm for induced codes

Yu. V. Kosolapov, A. N. Shigaev

South Federal University,105/42 Bolshaya Sadovaya Str., Rostov-on-Don, 344006, Russia

Abstract: In the paper, the analysis of the stability of the McEliece-type cryptosystem on induced codes for key attacks is examined. In particular, a model is considered when the automorphism group is trivial for the base code $C$, on the basis of which the induced code $\mathbb{F}^l_q \otimes C$ is constructed. In this case, as shown by N. Sendrier in 2000, there exists such a mapping, called a complete discriminant, by means of which a secret permutation that is part of the secret key of a McEliece-type cryptosystem can be effectively found. The automorphism group of the code $\mathbb{F}^l_q \otimes C$ is nontrivial, therefore there is no complete discriminant for this code. This suggests a potentially high resistance of the McEliece-type cryptosystem on the code $\mathbb{F}^l_q \otimes C$. The algorithm for splitting the support for the code $\mathbb{F}^l_q \otimes C$ is constructed and the efficiency of this algorithm is compared with the existing attack on the key of the McElice type cryptosystem based on the code $\mathbb{F}^l_q \otimes C$.

Keywords: group codes, induced group codes, support splitting algorithm, the McEliece cryptosystem.

DOI: https://doi.org/10.18255/1818-1015-2018-3-276-290

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UDC: 517.9

Citation: Yu. V. Kosolapov, A. N. Shigaev, “The support splitting algorithm for induced codes”, Model. Anal. Inform. Sist., 25:3 (2018), 276–290

Citation in format AMSBIB
\Bibitem{KosShi18} \by Yu.~V.~Kosolapov, A.~N.~Shigaev \paper The support splitting algorithm for induced codes \jour Model. Anal. Inform. Sist. \yr 2018 \vol 25 \issue 3 \pages 276--290 \mathnet{http://mi.mathnet.ru/mais628} \crossref{https://doi.org/10.18255/1818-1015-2018-3-276-290} \elib{http://elibrary.ru/item.asp?id=35144410}