On the lower bounds of the second order nonlinearities of some Boolean functions
On the lower bounds of the second order nonlinearities of some Boolean functions
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DOI：
10.1016/j.ins.2009.09.006
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
S. Gangopadhyay;Sumanta Sarkar;R. Telang
中科院分区：
文献类型：
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作者：
S. Gangopadhyay;Sumanta Sarkar;R. Telang
布尔函数的r阶非线性度是分析流密码和分组密码安全性的一个重要密码学判据。它在编码理论中也很重要，因为它与Reed-Muller码R（r，n）的覆盖半径有关。本文导出了下列两类布尔函数的二阶非线性度的下界：对于某一λ，第一类布尔函数是Bent函数，而第二类布尔函数都是Bent函数，即，它们具有最大的一阶非线性。结果表明，在某些情况下，我们的界比之前获得的界更好。
The rth order nonlinearity of a Boolean function is an important cryptographic criterion in analyzing the security of stream as well as block ciphers. It is also important in coding theory as it is related to the covering radius of the Reed–Muller code R(r,n). In this paper we deduce the lower bounds of the second order nonlinearities of the following two types of Boolean functions: For some λ, the functions of the first type are bent functions, whereas Boolean functions of the second type are all bent functions, i.e., they possess the maximum first order nonlinearity. It is demonstrated that in some cases our bounds are better than the previously obtained bounds.