Almost perfect algebraic immune functions with good nonlinearity
Almost perfect algebraic immune functions with good nonlinearity
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DOI：
10.1109/isit.2014.6875151
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发表时间：
2014-08
期刊：
影响因子：
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通讯作者：
Meicheng Liu;D. Lin
中科院分区：
文献类型：
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作者：
Meicheng Liu;D. Lin
在本文中，事实证明，一个2K可变性的布尔功能，包括Tang等人最近构建的功能。 k≥3。更确切地说，它们达到了最佳的代数免疫力，几乎可以对快速代数攻击进行完美的免疫力根据Tang等人的工作，获得了其非线性，这比巡回赛函数的工作要好。在该家族的某些功能中，有些非线性比唐等人的功能略大，而在已知的功能中，该家族的某些功能甚至略大。快速代数攻击，该家族的功能在非线性的确切值和下限之间取决于权衡。
In this paper, it is proven that a family of 2k-variable Boolean functions, including the function recently constructed by Tang et al. [IEEE TIT 59(1): 653-664, 2013], are almost perfect algebraic immune for any integer k ≥ 3. More exactly, they achieve optimal algebraic immunity and almost perfect immunity to fast algebraic attacks. The functions of such family are balanced and have optimal algebraic degree. A lower bound on their nonlinearity is obtained based on the work of Tang et al., which is better than that of Carlet-Feng function. It is also checked for 3 ≤ k ≤ 9 that the exact nonlinearity of such functions is very good, which is slightly smaller than that of Carlet-Feng function, and some functions of this family even have a slightly larger nonlinearity than Tang et al.'s function. To sum up, among the known functions with provable good immunity against fast algebraic attacks, the functions of this family make a trade-off between the exact value and the lower bound of nonlinearity.