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,  

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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.