A note on two classes of Boolean functions with optimal algebraic immunity

作者：Wu Baofeng^*; Liu Zhuojun; Jin Qingfang; Zhang Xiaoming

来源：Journal of Systems Science and Complexity, 2014, 27(4): 785-794.

DOI：10.1007/s11424-014-2132-y

• Algebraic immunity
• bent function
• Boolean function
• Kloosterman sums
• Walsh transform

Tu and Deng proposed a class of bent functions which are of optimal algebraic immunity under the assumption of a combinatorial conjecture. In this paper, the authors compute the dual of the Tu-Deng functions and then show that they are still of optimal algebraic immunity under the assumption of the same conjecture. For another class of Boolean functions constructed by Tang, et al. which are of optimal algebraic immunity with similar forms to Tu-Deng functions, the authors show that they are not bent functions by using some basic properties of binary complete Kloosterman sums.

• 出版日期2014-8
• 单位中国科学院; 中国科学院数学与系统科学研究院; 中国科学院信息工程研究所