Pseudo-Randomness of Certain Sequences of k Symbols with Length pq  

作　　者：陈智雄 杜小妮 吴晨煌 

机构地区：[1]Department of Mathematics,Putian University [2]State Key Lab.of ISN,Xidian University [3]College of Mathematics and Information Science,Northwest Normal University

出　　处：《Journal of Computer Science & Technology》2011年第2期276-282,共7页计算机科学技术学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No. 61063041;the Program for New Century Excellent Talents of Universities in Fujian Province under Grant No. JK2010047;the Funds of the Education Department of Gansu Province under Grant No. 1001-09

摘　　要：The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.The theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sarkozy and later extended to sequences of k symbols （or k-ary sequences）. Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.

关 键 词：stream ciphers pseudo-random sequences well-distribution measure correlation measure discrete logarithm modulo pq residue class rings character sums 

分 类 号：TN918.1[电子电信—通信与信息系统]