Constructing bent functions from permutations and involutions

发布时间：2024-01-04 作者：浏览次数：

Speaker:	屈龙江	DateTime:	2024年1月8日（周一）下午16:30-17:30
Brief Introduction to Speaker: 屈龙江，国防科技大学理学院副院长，教授、博导。现任教育部科技委数理学部委员，密码学报、AMC编委。从事密码中的数学理论研究，主持国家优青、173课题等科研项目，在美密、IEEE TIT等发表论文百余篇，入选教育部新世纪优秀人才计划。		Place:	三楼M323学术报告厅
Abstract:Bent functions are extremal combinatorial objects with several applications, such as coding theory, cryptography, etc. In this talk, we introduce and further study two approaches to constructing bent functions from permutations. The first one is by composing a Boolean function with a permutation introduced by Hou and Langevin in 1997. In this part, some new classes of bent functions from quadratic permutations and permutations with Niho exponents are proposed. The second approach is by employing three permutations satisfying a special algebraic property (Am) proposed by Mesnager in 2014. In this part, we construct some triples of permutations satisfying the property (Am) from vectorial functions, trace functions and linearized polynomials, and then obtain some bent functions by them. These works are jointed with Tor Helleseth, Chunlei Li, Kangquan Li, Yubo Li and Sihem Mesnager.