Table of Contents Author Guidelines Submit a Manuscript
Security and Communication Networks
Volume 2017, Article ID 6268230, 9 pages
Research Article

1-Resilient Boolean Functions on Even Variables with Almost Perfect Algebraic Immunity

1School of Electronics and Information, Northwestern Polytechnical University, Shaanxi, China
2Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China
3Westone Cryptologic Research Center, Beijing, China
4Department of Computer Science and Technology, East China Normal University, Shanghai, China
5National Engineering Laboratory for Wireless Security, Xi’an University of Posts and Telecommunications, Xi’an, China

Correspondence should be addressed to Yu Yu; kh.uyuy@uyuy and Xiangxue Li;

Received 15 November 2016; Accepted 12 June 2017; Published 14 September 2017

Academic Editor: Pedro García-Teodoro

Copyright © 2017 Gang Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Several factors (e.g., balancedness, good correlation immunity) are considered as important properties of Boolean functions for using in cryptographic primitives. A Boolean function is perfect algebraic immune if it is with perfect immunity against algebraic and fast algebraic attacks. There is an increasing interest in construction of Boolean function that is perfect algebraic immune combined with other characteristics, like resiliency. A resilient function is a balanced correlation-immune function. This paper uses bivariate representation of Boolean function and theory of finite field to construct a generalized and new class of Boolean functions on even variables by extending the Carlet-Feng functions. We show that the functions generated by this construction support cryptographic properties of 1-resiliency and (sub)optimal algebraic immunity and further propose the sufficient condition of achieving optimal algebraic immunity. Compared experimentally with Carlet-Feng functions and the functions constructed by the method of first-order concatenation existing in the literature on even (from 6 to 16) variables, these functions have better immunity against fast algebraic attacks. Implementation results also show that they are almost perfect algebraic immune functions.