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劉華寧: Correlation measures of binary sequences derived from Euler quotients

時間:2021-09-13來源:數學學院

報告時間:2021年9月14日(星期二)15:00

報告平臺:騰訊會議 ID: 321 959 917

:劉華寧 教授

工作單位:西北大學

舉辦單位:數學學院

報告簡介

Fermat-Euler quotients arose from the study of the first case of Fermat's Last Theorem, and have numerous applications in number theory. Recently they were studied from the cryptographic aspects by constructing many pseudorandom binary sequences, whose linear complexities and trace representations were calculated. In this work, we further study their correlation measures by using the approach based on Dirichlet characters, Ramanujan sums and Gauss sums. Our results show that the $4$-order correlation measures of these sequences are very large. Therefore they may not be suggested for cryptography.

報告人簡介

劉華寧,西北大學數學學院教授、博士生導師,劍橋大學與山東大學博士后。目前擔任《純粹數學與應用數學》執行編委。研究方向為解析數論及其應用,發表論文90余篇。先后主持多項國家自然科學基金,曾獲得鐘家慶數學獎、全國優秀博士學位論文提名、霍英東教育基金會青年教師獎以及兩項省部級科學技術獎。

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