报告题目:A New Approach to Constructing Quadratic Pseudo-Planar Functions over GF_2^n

报告时间:2016年4月7日(周四)下午16:30-17:30

报 告 人:屈龙江 教授

工作单位：国防科学技术大学

报告地点: 数学学科楼310办公室

举办单位：万象城官方网站（中国）有限公司

报告摘 要：Planar functions over finite fields give rise to finite projective planes. They were also used in the constructions of DES-like iterated ciphers, error-correcting codes, and codebooks. They were originally defined only in finite fields with odd characteristic, but recently Zhou introduced pesudo-planar functions in even characteristic which yields similar applications. All known pesudo-planar functions are quadratic and hence they give presemifields. In this paper, a new approach to constructing quadratic pseudo-planar functions is given. Then five explicit families of pseudo-planar functions are constructed, one of which is a binomial, two of which are trinomials, and the other two are quadrinomials. All known pesudo-planar functions are revisited, some of which are generalized. These functions not only lead to projective planes, relative difference sets and presemifields, but also give optimal codebooks meeting the Levenstein bound, complete sets of mutually unbiased bases (MUB) and good compressed sensing matrices.

报告人简介: 屈龙江，男，河南新县人，1980年11月生，2002年、2007年在国防科技大学理学院数学与系统科学系分别获理学学士学位和博士学位，后留校任教。现为该系教授，国家自然科学基金通讯评议专家，美国Math Review评论员，IEEE会员，中国密码学会会员，入选教育部新世纪人才计划和国防科技大学首届青年拔尖人才计划。从事编码密码理论及其应用研究，在密码函数的安全性指标分析、对称密码算法安全性分析等方面取得一系列研究成果，在《IEEE Trans. on Inform. Theory》、《SIAM Dis. Math.》、《Designs, Codes and Cryptography》等国内外学术期刊和SETA、ISC等国内外学术会议上发表学术论文60余篇，其中SCI检索35篇，在科学出版社合作出版密码学方面的教材和专著各一部。先后主持国家自然科学基金面上项目、国防科技大学杰出青年基金等近10个项目，担任十余种学术期刊审稿人。