Maximal values of generalized algebraic immunity
Maximal values of generalized algebraic immunity
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DOI：
10.1007/s10623-008-9228-0
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发表时间：
2009-02
期刊：
影响因子：
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通讯作者：
K. Feng;Qunying Liao;J. Yang
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文献类型：
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作者：
K. Feng;Qunying Liao;J. Yang
布尔函数的代数免疫的概念已经以几种方式推广到向量值函数和/或任意有限域上，并且这种广义代数免疫的合理上界已经在Armknecht和Krause (ICALP学报2006，LNCS，卷4052，页180 - 191,2006)，Ars和Faugere（有限域上函数的代数免疫，INRIA, No report 5532, 2005）和Batten （Canteaut， Viswanathan主编）中得到了证明。密码学进展- indocrypt 2004， LNCS, vol. 3348, pp 84 - 91,2004)。本文利用Reed-Muller码的性质证明了大多数推广的代数免疫的最大值可以达到上界。
The notion of algebraic immunity of Boolean functions has been generalized in several ways to vector-valued functions and/or over arbitrary finite fields and reasonable upper bounds for such generalized algebraic immunities has been proved in Armknecht and Krause (Proceedings of ICALP 2006, LNCS, vol. 4052, pp 180–191, 2006), Ars and Faugere (Algebraic immunity of functions over finite fields, INRIA, No report 5532, 2005) and Batten (Canteaut, Viswanathan (eds.) Progress in Cryptology—INDOCRYPT 2004, LNCS, vol. 3348, pp 84–91, 2004). In this paper we show that the upper bounds can be reached as the maximal values of algebraic immunities for most of generalizations by using properties of Reed–Muller codes.