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01.12.2019 | Ausgabe 7/2019

On the Support Splitting Algorithm for Induced Codes

Zeitschrift:
Automatic Control and Computer Sciences > Ausgabe 7/2019
Autoren:
Yu. V. Kosolapov, A. N. Shigaev
Wichtige Hinweise
Translated by O. Maslova

Abstract—

As shown by N. Sendrier in 2000, if a $$[n{\text{,}}\,k{\text{,}}\,d]$$-linear code $$C( \subseteq \mathbb{F}_{q}^{n})$$ with length $$n$$, dimensionality $$k$$ and code distance $$d$$ has a trivial group of automorphisms $${\text{PAut}}(C)$$, it allows one to construct a determined support splitting algorithm in order to find a permutation $$\sigma$$ for a code $$D$$, being permutation-equivalent to the code $$C$$, such that $$\sigma (C) = D$$. This algorithm can be used for attacking the McEliece cryptosystem based on the code$$C$$. This work aims the construction and analysis of the support splitting algorithm for the code $$\mathbb{F}_{q}^{l} \otimes C$$, induced by the code $$C$$, $$l \in \mathbb{N}$$. Since the group of automorphisms PAut$$(\mathbb{F}_{q}^{l} \otimes C)$$ is nontrivial even in the case of that trivial for the base code $$C$$, it enables one to assume a potentially high resistance of the McEliece cryptosystem on the code $$\mathbb{F}_{q}^{l} \otimes C$$ to the attack based on a carrier split. The support splitting algorithm is being constructed for the code $$\mathbb{F}_{q}^{l} \otimes C$$ and its efficiency is compared with the attack to a McEliece cryptosystem based on the code $$\mathbb{F}_{q}^{l} \otimes C.$$

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