题目：Arithmetic Correlation of Pseudorandom Sequences （伪随机序列的算术相关性）

主讲人：陈智雄 教授

时间：2022年4月2日（周六）上午9：00

地点：腾讯会议（会议号904350694）

主办单位：理学院

主讲人简介：陈智雄，福建莆田人，教授、博士、硕士生导师。2006年毕业于西安电子科技大学密码学专业。主要从事应用数学、密码学理论研究工作。主持完成国家自然科学基金3项，其中面上项目2项、国际（地区）合作交流项目1项。获得国家公派留学基金，在奥地利科学院、美国肯塔基大学从事访问学者。在《IEEE Transactions on Information Theory》、《Designs, Codes and Cryptography》、《Science China: Information Sciences》及其它专业学术期刊发表学术论文100多篇。任中国工业与应用数学学会编码密码及相关组合理论专业委员会委员；福建省数学学会副理事长；中国密码学会高级会员；EI学术期刊《Journal of Network Intelligence》编委。

摘要：Feedback with carry shift registers (FCSRs), which were invented by M. Goresky and A. Klapper in 1990's, play an important role in spread-spectrum multiple-access communication and cryptography for the design of pseudo-random sequences. FCSRs can be implemented in hardware for high speed calculation and they have an algebraic theory parallel to that of linear feedback shift registers(LFSRs). In this talk, We consider the arithmetic autocorrelation of FCSR sequences and introduce some recent results: (1) the arithmetic crosscorrelation is constant for two binary sequences of coprime periods, which complements the analogous result for the classical crosscorrelation. (2) a nontrivial upper bound on the arithmetic autocorrelation of m-sequences, it is close to half of the period and hence rather large, which gives an undesirable feature.