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 \(\mathbb{F}_{q}^{l} \otimes C.\)

中文翻译：

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归纳代码的支持拆分算法

摘要-

如N. Sendrier在2000年所示，如果\（[n {\ text {，}} \，k {\ text {，}} \，d] \）-线性代码\（C（\ subseteq \ mathbb { F} _ {q} ^ {n}）\）的长度为\（n \），维数为\（k \）和代码距离为\（d \）的微不足道的自同构\（{\ text {PAut}} （C）\） ，它允许一个构造确定的支撑分裂算法，以便找到一个置换\（\西格玛\）用于代码\（d \） ，被置换-等效于代码\（C \） ，这样\（\ sigma（C）= D \）。该算法可用于基于代码\（C \）攻击McEliece密码系统。这项工作旨在构建和分析由代码\（C \），\（l \引起的代码\（\ mathbb {F} _ {q} ^ {l} \ otimes C \）的支持拆分算法。在\ mathbb {N} \中）。由于自同构组PAut \（（\ mathbb {F} _ {q} ^ {l} \ otimes C）\）即使对于基码\（C \）来说是微不足道的，也很重要。假设代码\（\ mathbb {F} _ {q} ^ {l} \ otimes C \）上的McEliece密码系统可能对基于载波分裂的攻击具有较高的抵抗力。正在为代码\（\ mathbb {F} _ {q} ^ {l} \ otimes C \）构建支持拆分算法。并将其效率与对基于代码\（\ mathbb {F} _ {q} ^ {l} \ otimes C. \）的McEliece密码系统的攻击进行比较。