报告题目 (Title)：一类基于Dillon指数的超Bent函数(Hyper-Bent Functions from Dillon Exponents)

报告人 (Speaker)： 唐春明 教授（西南交通大学）

报告时间 (Time)：2023年11月18日(周六) 15：00

报告地点 (Place)：校本部 F309

邀请人(Inviter)：丁洋

主办部门：理学院数学系

报告摘要：Hyper-bent functions are a class of important bent Boolean functions, which achieve maximum distance from all bijective monomial functions, and provide further security towards approximation attacks. Being describled by a stricter definition, hyper-bent functions are much more difficult to characterize than bent functions. In 2008, Charpin and Gong presented a characterization of hyper-bentness of Boolean functions with multiple trace terms obtained via Dillon-like functions with coefficients in the subfield in terms of some exponential sums. In this talk we are interested in the characterization of hyper-bentness of such functions with coefficients in the extension field. By employing Mobius transformation, we give connections among the property of hyper-bentness, the exponential sum involving Dickson polynomials and the number of rational points on some associated hyperelliptic curves. The effectiveness of this new method can be seen from the characterization of a new class of binomial hyper-bent functions with coefficients in extension fields.