报告题目：Boolean Functions with High (Fast) Algebraic Immunity and Their Applications in Linear Codes
时 间：2021年09月28日（星期二）下午14:30
地 点：腾讯会议（会议号：724 502 052）
主 办：数学与统计学院, 福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：感兴趣的老师和研究生
报告摘要：In the 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, 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. Moreover, two methodologies for constructing minimal binary codes from sets, Boolean functions and vectorial Boolean functions with high algebraic immunity, are proposed. More precisely, a general construction of new minimal codes using minimal codes contained in Reed-Muller codes and sets without nonzero low degree annihilators is presented. The other construction allows us to yield minimal codes from certain subcodes of Reed-Muller codes and vectorial Boolean functions with high algebraic immunity.
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报告人简介：唐春明，男，博士，西华师范大学数学与信息学院研究员, 2021年度布尔奖（George Boole Prize）的杰出青年学者奖获得者。博士毕业于北京大学，先后在巴黎第八大学和香港科技大学从事研究工作。主要研究包括密码、编码及其相关的数学理论。主持国家级和省部级项目多项，在国内外重要学术期刊如《IEEE Transactions on Information Theory》、《Finite Fields and Their Applications 》、《Designs, Codes and Cryptography 》、《Science China》等发表六十多篇论文。目前担任编码与通信领域国际学术期刊《Cryptography and Communications》、《International Journal of Information and Coding Theory》等的编委。