讲座题目：Permutation trinomials and quadrinomials with nontrivial coefficients over finite fields

主办单位：三峡数学研究中心/理学院

报告专家：曾祥勇 教授（湖北大学）

报告时间：2021年12月7日（周二）  下午 15：00

报告地点：腾讯会议（ID： 894 139 129）

专家简介： 曾祥勇，湖北大学二级教授，博士生导师，研究领域为密码学、代数学。现为中国密码学会理事、湖北省重要领域国产密码应用专家、《Cryptography and Communications》编委、《密码学报》编委，先后主持七项国家自然科学基金、两项国家密码发展基金，2017年获湖北省自然科学二等奖一项、2018年获全国教育专业学位教学成果一等奖一项、2018年获国务院政府特殊津贴、2020年获全国密码算法设计竞赛三等奖一项。

报告摘要： Permutation polynomials are important objects in the theory of finite fields, and they have been widely used in cryptography, coding theory and combinatorial design theory. In this talk, we will introduce several classes of permutation trinomials and quadrinomials with nontrivial coefficients over finite fields. Through transforming the permutation problem into studying some low-degree equations over finite fields and utilizing the knowledge of the algebraic curve, as well as some known results on the Kloosterman sum, the necessary and sufficient conditions on coefficients for these trinomials and quadrinomials being permutations are presented. In addition, we also show that one class of the presented permutation quadrinomials has Boomerang uniformity 4.