Constructions of 1-resilient Boolean functions on odd number of variables with a high nonlinearity

  • Authors:

  • Fengrong Zhang;Yupu Hu;Min Xie;Yongzhuang Wei

  • Affiliations:

  • Key Laboratory of Computer Network and Information Security, Ministry of Education, Xidian University, Xi'an, 710071, China;Key Laboratory of Computer Network and Information Security, Ministry of Education, Xidian University, Xi'an, 710071, China;Key Laboratory of Computer Network and Information Security, Ministry of Education, Xidian University, Xi'an, 710071, China;Department of Communication and Information Engineering, Guilin University of Electronic Technology, Guilin, 541004, China

  • Venue:
  • Security and Communication Networks
  • Year:
  • 2012

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Abstract

In this paper, we concentrate on the design of 1-resilient Boolean functions with desirable cryptographic properties. Firstly, we put forward a novel secondary construction to obtain 1-resilient functions. Next, we present the relationships between the properties of these constructed 1-resilient functions and that of the initial functions. Based on the construction and a class of bent functions on n variables, we can obtain a class of (n + 3)-variable 1-resilient non-separable cryptographic functions with a high algebraic immunity, whose nonlinearity is equal to the bent concatenation bound 2n + 2 − 2(n + 2)/2. Furthermore, we propose a set of 1-resilient non-separable functions on odd number of variables with an optimal algebraic degree, a high algebraic immunity, and a high nonlinearity. Copyright © 2012 John Wiley & Sons, Ltd.