基于Ding-Helleseth广义割圆类构造的伪随机k元序列

Pseudorandom Sequences of k Symbols Constructed by Using DingHelleseth Generalized Cyclotomic Classes

伪随机序列在信息安全系统中扮演着十分重要的角色,虽然有较多的伪随机序列被给出和应用,但仍然满足不了人们日益增长的需求。构造方法及随机性分析是伪随机序列理论中的主要问题,一致分布测度、自相关性以及碰撞与雪崩效应是判断伪随机序列好坏的重要标准。MAUDUIT等人在一系列论文中利用数论方法提出并且研究了一些k元序列的伪随机性,但是仍有很多问题值得研究。文章基于Ding-Helleseth广义割圆类,构造了一大族长度为pq的伪随机k元序列。综合应用数论中的三角恒等式、指数和、特征和的估计,研究了序列的一致分布测度、相关性以及碰撞与雪崩效应。

Pseudorandom sequences play an important role in information security system. Although there are many sequences have been given and studied, the search for new approaches and new constructions should be continued. The construction methods and pseudorandom analysis is the main research content of pseudorandom theory. The well-distribution measure, correlation measure, collision and avalanche effect become the important indexes of pseudorandom sequences to determine good or bad. In a series of papers Mauduit and others introduced and studied the measures of finite sequences of k symbols. In this paper we construct a large family of pseudorandom sequences of k symbols with length pq by using Ding-Helleseth generalized cyclotomic classes, and study the well-distribution measure, correlation measure, collision and avalanche effect by using the properties of trigonometric identity, exponential sum and character sum.