报告一：夏永波

报告题目：The Differential Spectrum of the Power Mapping $x^{p^n-3}$

报告人：夏永波 教授 中南民族大学

报告时间：2020年11月30日 14:30–15:30

报告地点：腾讯会议 ID：775 532 368

主持人：李成举

报告摘要：Let $n$ be a positive integer and p a prime. The power mapping $x^{p^n-3}$ over $F_{p^n}$ has desirable differential properties, and a bound for its differential uniformity has been given by Helleseth, Rong and Sandberg in 1999. In this talk, by investigating some equations and certain character sums over $F_{p^n}$ , the differential spectrum of  $x^{p^n-3}$ for any odd prime $p$ is completely determined. This settles a question left open by Helleseth, Rong and Sandberg in 1999.

报告人简介：夏永波，男，教授。2009年6月毕业于湖北大学数学系，获理学博士学位；2013年9月至2014年9月，受留学基金委资助，赴挪威卑尔根大学访学，合作导师为IEEE Fellow、挪威科学院院士Tor Helleseth教授。目前的研究兴趣为：无线通信中的序列设计、编码和密码学。主持国家自然科学基金面上项目和青年项目各1项，湖北省自然科学基金2项，国家民委高等教育教学改革研究项目1项；在《IEEE Transactions on Information Theory》、《Finite Fields and Their Applications》、《Cryptography and Communications》、《Science China Mathematics》等期刊上发表论文20余篇。曾获2018年湖北省自然科学奖二等奖（排名2）、2018年湖北省教学成果奖三等奖（排名3）、2019年国家民委教学成果二等奖（排名1），2019年入选国家民委青年教学标兵，2020年入选国家民委中青年英才。

报告二：唐春明

报告题目：FAI and LCD codes

报告人：唐春明 教授 西华师范大学

报告时间：2020年11月30日 15:30-16:30

报告地点：腾讯会议 ID：775 532 368

主持人：李成举

报告摘要：Nowadays, the resistance against algebraic attacks and fast algebraic attacks are considered as an important cryptographic property for Boolean functions used in stream ciphers. Both attacks are very powerful analysis concepts and can be applied to symmetric cryptographic algorithms used in stream ciphers. The notion of algebraic immunity has received wide attention since it is a powerful tool to measure the resistance of a Boolean function to standard algebraic attacks. Nevertheless, an algebraic tool to handle the resistance to fast algebraic attacks is not clearly identified in the literature. In this talk, we propose a new parameter to measure the resistance of a Boolean function to fast algebraic attack. We also introduce the notion of fast immunity profile and show that it informs both on the resistance to standard and fast algebraic attacks. Further, we evaluate our parameter for two secondary constructions of Boolean functions. Moreover, A coding-theory approach to the characterization of perfect algebraic immune functions is presented. Via this characterization, infinite families of binary linear complementary dual codes (or LCD codes for short) are obtained from perfect algebraic immune functions. The binary LCD codes presented in this paper have applications in armoring implementations against so-called side-channel attacks (SCA) and fault non-invasive attacks, in addition to their applications in communication and data storage systems.

报告人简介：唐春明，男，博士，西华师范大学数学与信息学院教授。2012年博士毕业于北京大学。并先后在巴黎第八大学和香港科技大学从事博士后研究工作。主要研究包括密码、编码及其相关的数学理论。先后主持国家自然科学基金青年项目和面上项目各一项。发表研究论文 60 余篇，其中 EI、SCI 检索论文50 余篇，代表性成果发表在国内外重要学术期刊《IEEE Transactions on Information Theory》、《Finite Fields and Their Applications 》、《Designs, Codes and Cryptography 》、《Science China》和《China Communications》 等上面。曾访问多所国内外知名院校；目前，担任三个国际SCI期刊的编委。

报告三：吴严生

报告题目：Optimal minimal linear codes from posets

报告人：吴严生 教授 南京邮电大学

报告时间：2020年11月30日 16:30-17:30

报告地点：腾讯会议 ID：775 532 368

主持人：李成举

报告摘要：Recently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun et al. In talk, we will first extend this construction method to arbitrary posets. Especially, anti-chains are corresponded to simplicial complexes. Secondly, we will present two constructions of binary linear codes from hierarchical posets of two levels. In particular, we determine the weight distributions of binary linear codes associated with hierarchical posets with two levels. Based on these results, we also obtain some optimal and minimal binary linear codes not satisfying the condition of Ashikhmin-Barg. Moreover, we will also put up many worthwhile questions.

报告人简介：吴严生，现任南京邮电大学教授。欧洲数学会《数学文摘》、美国数学会《数学评论》评论员。以第一作者或通讯作者在IEEE Transactions on Information Theory、IEEE Communications Letters、Designs Codes and Cryptography、Finite Fields and Their Applications、Discrete Applied Mathematics、Discrete Mathematics 等国际期刊上发表 SCI 论文 17 篇。 主要研究方向为代数编码理论、密码函数。