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Construction of Resilient Boolean and Vectorial Boolean Functions with High Nonlinearity Luyang LI Dong ZHENG Qinglan ZHAO Publication IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Vol.E102-A No.10 pp.1397-1401 Publication Date: 2019/10/01 Online ISSN: 1745-1337 DOI: 10.1587/transfun.E102.A.1397 Type of Manuscript: LETTER Category: Cryptography and Information Security Keyword: Boolean function, vectorial Boolean functions, stream ciphers, nonlinearity, resiliency, algebraic degree, Full Text: PDF>>
Summary: Boolean functions and vectorial Boolean functions are the most important components of stream ciphers. Their cryptographic properties are crucial to the security of the underlying ciphers. And how to construct such functions with good cryptographic properties is a nice problem that worth to be investigated. In this paper, using two small nonlinear functions with t-1 resiliency, we provide a method on constructing t-resilient n variables Boolean functions with strictly almost optimal nonlinearity >2n-1-2n/2 and optimal algebraic degree n-t-1. Based on the method, we give another construction so that a large class of resilient vectorial Boolean functions can be obtained. It is shown that the vectorial Boolean functions also have strictly almost optimal nonlinearity and optimal algebraic degree. | |||||
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