报告题目：Linear Codes from Boolean Functions with High (Fast) Algebraic Immunity

报告人：唐春明教授 （西南交通大学）

报告时间：2024年9月12日（星期四）下午17：00-18：00

报告地点：数学院205

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.

专家简介：唐春明，研究员，西南交通大学信息科学与技术学院。1982年1月出生，2012年7月获得北京大学博士学位，先后在巴黎第八大学与香港科技大学从事博士后研究工作，方向为面向网络空间安全的编码密码理论。以独立/第一/通讯作者身份在领域权威期刊发表论文60余篇，包括编码密码理论最顶级期刊IEEE Transactions on Information Theory 25篇。因在密码函数领域的贡献，荣获密码学国际学术奖：布尔奖（George Boole Prize）；研究成果也曾获教育部自然科学二等奖（排名2/4）；正在主持国家自然科学基金重点项目和面上项目。

【编辑：数学科学学院】