Constructions of 1‐resilient Boolean functions on odd number of variables with a high nonlinearity
Fengrong Zhang, Yupu Hu, Min Xie, Yongzhuang Wei · Security and Communication Networks · 2011
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 2 n + 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 © 2011 John Wiley & Sons, Ltd.