Construction of rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity

Authors:
Sihong Su;Xiaohu Tang
Affiliations:
Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu, China 610031 and College of Mathematics and Information Scien ...;Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu, China 610031
Venue:
Designs, Codes and Cryptography
Year:
2014

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Abstract

Recent research shows that the class of rotation symmetric Boolean functions is potentially rich in functions of cryptographic significance. In this paper, based on the knowledge of compositions of an integer, we present two new kinds of construction of rotation symmetric Boolean functions having optimal algebraic immunity on either odd variables or even variables. Our new functions are of much better nonlinearity than all the existing theoretical constructions of rotation symmetric Boolean functions with optimal algebraic immunity. Further, the algebraic degree of our rotation symmetric Boolean functions are also high enough.