Excluding some weak keys in the mceliece cryptosystem

J. A. Ryan
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引用次数: 3

Abstract

A Goppa code which has a non trivial automorphism group is a weak key for the McEliece cryptosystem. A quasicyclic code clearly has a non trivial automorphism group. Hence any quasicyclic code is a weak key. Some new classes of quasicyclic irreducible Goppa codes have recently been established and it is conjectured that, in the binary case, these new classes contain all binary quasicyclic ireducible Goppa codes. Using simple numerical conditions on the parameters of a Goppa code, we show that if we adopt the parameters as suggested by McEliece himself for choosing Goppa codes in the implementation of his cryptosystem, then some such codes are weak keys. We suggest other parameters which we claim would reduce the probability of choosing a weak key.
排除mcelelece密码系统中的一些弱密钥
具有非平凡自同构群的Goppa码是McEliece密码系统的弱密钥。准循环码显然有一个非平凡的自同构群。因此,任何准循环代码都是弱密钥。最近建立了一些新的拟循环不可约Goppa码类,并推测在二进制情况下,这些新类包含了所有的二进制拟循环不可约Goppa码。利用Goppa码参数的简单数值条件,我们证明了如果我们在实现他的密码系统时采用McEliece自己建议的参数来选择Goppa码,那么一些这样的码是弱密钥。我们建议使用其他参数来降低选择弱密钥的概率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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