四川师范大学
四川师范大学 Sichuan Normal University
学术讲座 您所在的位置:首页 > 信息服务 > 学术讲座

A Generic Construction of Bent Functions and Bent Idempotents with Any Possible Algebraic Degrees

2017年01月03日  来源:  浏览:190次
讲座题目:A Generic Construction of Bent Functions and Bent Idempotents with Any Possible Algebraic Degrees
讲座时间:2017-1-6 15:00:00
讲座地点:狮子山校区6教811
主办单位:数学与软件科学学
主讲人 :周正春 教授
主讲人简介:
周正春,博士,现任西南交通大学教授。主要研究方向为序列设计、代数编码理论和密码函数设计。曾获全国百篇优秀博士学位论文奖(2013年)、教育部自然科学二等奖(2015年,2/4)、上海市自然科学二等奖(2014年,3/4)、四川省杰青(2014年)、中国电子学会信息论分会青年新星(2016年);所负责的研究团队“代数编码理论及其应用”入选2015年四川省教育厅科研创新团队。以第一作者或通讯作者身份发表SCI检索论文40余篇,其中包括IEEE 期刊论文20篇,信息论与代数编码领域旗舰期刊IEEE Transactions on Information Theory 13篇,ESI高被引论文2篇,研究成果共被SCI他引200余次。担任三个国际SCI期刊的编委。



Abstract: As a class of optimal combinatorial objects, bent functions have important applications in cryptography, sequence design, and coding theory. Bent idempotents area subclass of bent functions and of great interest since they can be stored in less space and allow faster computation of the Walsh-Hadamard transform.

The objective of this talk is to present a generic construction of bent functions from known ones. It includes the previous constructions of bent functions as special cases, and produces new bent functions which cannot be produced by earlier ones. In particular, it also generates infinite families of bent idempotents with any possible degree. This together with a recent construction by Su and Tang gives a positive answer to an open problem on bent idempotents proposed by Carlet. In addition, an infinite family of anti-self-dual bent functions is obtained in which the sum of any three distinct functions is again an anti-self-dual bent function in this family. This solves an open problem recently proposed by Mesnager.