On the Support Splitting Algorithm for Induced Codes
- Autores: Kosolapov Y.V.1, Shigaev A.N.1
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Afiliações:
- Southern Federal University
- Edição: Volume 53, Nº 7 (2019)
- Páginas: 719-729
- Seção: Article
- URL: https://journals.rcsi.science/0146-4116/article/view/175910
- DOI: https://doi.org/10.3103/S0146411619070125
- ID: 175910
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Resumo
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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Sobre autores
Yu. Kosolapov
Southern Federal University
Autor responsável pela correspondência
Email: itaim@mail.ru
Rússia, Rostov-on-Don, 344016
A. Shigaev
Southern Federal University
Autor responsável pela correspondência
Email: aleksejshig@gmail.com
Rússia, Rostov-on-Don, 344016
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