基于数论方法的伪随机二元序列的测度与构造  

Measures and Constructions of Pseudorandom Binary Sequences Arising from Number Theory

作　　者：刘华宁 LIU Huaning(Research Center for Number Theory and Its Applications,School of Mathematics,Northwest University,Xi’an,Shaanxi,710127,P.R.China)

机构地区：[1]西北大学数学学院,数论及其应用研究中心,西安陕西710127

出　　处：《数学进展》2022年第6期961-978,共18页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.12071368);the Science and Technology Program of Shaanxi Province of China(Nos.2019JM-573,2020JM-026)。

摘　　要：密码学中诸多应用领域都需要伪随机二元序列,为此在上世纪产生了很多相关成果.Mauduit与Sárközy等人于1997年从数论角度开展了对伪随机二元序列的研究,目前许多学者基于数论方法发表了很多的论文.本文将介绍源于数论的伪随机二元序列的构造与测度的性质,以及相关的进展与困难.The need for pseudorandom binary sequences arises in many cryptographic applications.Numerous papers have been written on this subject in the last century.In 1997,Mauduit and S´ark¨ozy initiated a comprehensive study of finite pseudorandom binary sequences,and then many pseudorandom binary sequences have been given and studied by using arithmetical methods.In this paper we present a survey of measures and constructions of pseudorandom binary sequences arising from number theory.

关 键 词：二元序列 一致分布 相关性 族复杂度 

分 类 号：O156.4[理学—数学]