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Construction of Resilient Boolean and Vectorial Boolean Functions with High Nonlinearity

Luyang LI, Dong ZHENG, Qinglan ZHAO

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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.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.10 pp.1397-1401
Publication Date
2019/10/01
Publicized
Online ISSN
1745-1337
DOI
10.1587/transfun.E102.A.1397
Type of Manuscript
LETTER
Category
Cryptography and Information Security

Authors

Luyang LI
  the Xi'an University of Posts and Telecommunications
Dong ZHENG
  the Xi'an University of Posts and Telecommunications
Qinglan ZHAO
  the Xi'an University of Posts and Telecommunications

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