1-Resilient Boolean Functions on Even Variables with Almost Perfect Algebraic Immunity
1-Resilient Boolean Functions on Even Variables with Almost Perfect Algebraic Immunity
复制标题
1-偶数变量上的弹性布尔函数具有几乎完美的代数免疫性
DOI：
10.1155/2017/6268230
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发表时间：
2017
影响因子：
--
通讯作者：
Li Hui
中科院分区：
文献类型：
--
作者：
Han Gang;Yu Yu;Li Xiangxue;Zhou Qifeng;Zheng Dong;Li Hui
有几个因素(如平衡性、良好的相关免疫性)被认为是用于密码原语的布尔函数的重要性质。布尔函数是完全代数免疫的，如果它对代数攻击和快速代数攻击具有完美免疫力。布尔函数的构造越来越受到人们的关注，它是一种完美的代数免疫与其他性质相结合的函数，如弹性。弹性函数是一种平衡的相关免疫函数。利用布尔函数的二元表示和有限域理论，通过推广Carlet-Feng函数，构造了一类广义的新的偶变量布尔函数。我们证明了这种构造产生的函数支持1-弹性和(次)最优代数免疫的密码学性质，并进一步给出了实现最优代数免疫的充分条件。实验结果表明，与Carlet-Fung函数和文献中用一阶级联方法构造的偶(6~16)元函数相比，这些函数对快速代数攻击具有更好的免疫力。实现结果还表明，它们是几乎完美的代数免疫函数。
Several factors (e.g., balancedness, good correlation immunity) are considered as important properties of Boolean functions for using in cryptographic primitives. A Boolean function is perfect algebraic immune if it is with perfect immunity against algebraic and fast algebraic attacks. There is an increasing interest in construction of Boolean function that is perfect algebraic immune combined with other characteristics, like resiliency. A resilient function is a balanced correlation-immune function. This paper uses bivariate representation of Boolean function and theory of finite field to construct a generalized and new class of Boolean functions on even variables by extending the Carlet-Feng functions. We show that the functions generated by this construction support cryptographic properties of 1-resiliency and (sub)optimal algebraic immunity and further propose the sufficient condition of achieving optimal algebraic immunity. Compared experimentally with Carlet-Feng functions and the functions constructed by the method of first-order concatenation existing in the literature on even (from 6 to 16) variables, these functions have better immunity against fast algebraic attacks. Implementation results also show that they are almost perfect algebraic immune functions.