报告专家:屈龙江
专家所在单位:国防科学技术大学
报告时间:2021年7月21日上午
报告地点:永利集团88304官网201学术报告厅
专家简介:屈龙江,国防科技大学数学学科教授、博导。国家自然科学优秀青年基金获得者,入选教育部新世纪优秀人才计划,获中国密码学会优秀青年奖。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 J. Dis. Math.》等国内外著名学术期刊和CRYPTO、FSE等国内外高水平学术会议上发表学术论文70余篇,其中SCI 50余篇,在科学出版社合作出版密码学方面的教材和专著各1部。
报告摘要:Planar functions, Almost perfect nonlinear (APN) functions and functions with boomerang uniformity 4 over $F_{2^n} are interesting classes of functions, which has important applications in cryptography, coding theory, combinatorics, etc. In this talk, we will recall recent advances in these functions, with emphasis on the work of our group. First, we recall known constructions of PN functions over $F_{2^n}$, and also give a complete characterization for a class of functions. Second, we give a complete characterization on a class of functions to be APN, then we recall recent constructions of new APN functions. Lastly, we give an equivalent definition of boomerang uniformity, and show new constructions of functions with boomerang uniformity 4.
邀请人: 郑大彬
(审核:郑大彬)