A New Construction of Boolean Functions with Maximum Algebraic Immunity

Authors:
Deshuai Dong;Shaojing Fu;Longjiang Qu;Chao Li
Affiliations:
Department of Mathematics and System Science, National University of Defence Technology, Changsha, China 410073;Department of Mathematics and System Science, National University of Defence Technology, Changsha, China 410073;Department of Mathematics and System Science, National University of Defence Technology, Changsha, China 410073 and State Key Laboratory of Mobile Communication, Southeast University, Nanjing, Chi ...;Department of Mathematics and System Science, National University of Defence Technology, Changsha, China 410073 and State Key Laboratory of Mobile Communication, Southeast University, Nanjing, Chi ...
Venue:
ISC '09 Proceedings of the 12th International Conference on Information Security
Year:
2009

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Abstract

Because of the algebraic attacks, a high algebraic immunity is now an important criteria for Boolean functions used in stream ciphers. In this paper, we study the construction of Boolean functions with maximum algebraic immunity. We first present a new method to construct Boolean functions, in any number of variables, with maximum algebraic immunity(AI), and we also improve our algorithm to construct balanced functions with optimum algebraic immunity for any even number of variables. Furthermore, the enumeration and algebraic degree of the constructed Boolean functions are investigated.