一、题目

Permutation trinomials and quadrinomials with nontrivial coefficients over finite fields

二、主讲人

曾祥勇

三、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.

四、主讲人介绍

曾祥勇，湖北大学教授，研究领域为密码学、代数学。现为中国密码学会理事、湖北省工业与应用数学学会副理事长、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。

五、邀请人

王明强 数学学院教授

六、时间

12月20日（周一）9:00

七、地点

腾讯会议ID：580 337 923

八、主办方

山东大学数学学院