Autocorrelation of two Legendre-Sidelnikov sequences  

作　　者：XIE Jia GAO Jun-tao YUE Zhao LI Xue-lian 

机构地区：[1]The State Key Laboratory of Integrated Services Network,Xidian University [2]Department of Mathematics, Xidian University [3]State Key Laboratory of Information Security Chinese Academy of Sciences

出　　处：《The Journal of China Universities of Posts and Telecommunications》2014年第5期83-88,93,共7页中国邮电高校学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (60833008);the Science and Technology on Communication Security Laboratory (9140C110201110C1102);the Fundamental Research Funds for the Central Universities (K5051270003, K50511010007)

摘　　要：Sequences with nice pseudo-randomness play an important role in not only communication system but also cryptography system. Based on the Legendre-Sidelnikov sequence, a modified Legendre-Sidelnikov sequence was introduced. The exact value of the autocorrelation function was derived by strict computation. According to the values of the autocorrelation functions of the two Legendre-Sidelnikov sequences, it is proven that both of them have perfect pseudo-randomness. Furthermore, a detailed comparison between autocorrelation functions of the two Legendre-Sidelnikov sequences was deduced. It indicates that no matter which parameters are chosen, the modified sequence has pseudo-randomness as good as the primitive sequence, which is of great significance for applications.Sequences with nice pseudo-randomness play an important role in not only communication system but also cryptography system. Based on the Legendre-Sidelnikov sequence, a modified Legendre-Sidelnikov sequence was introduced. The exact value of the autocorrelation function was derived by strict computation. According to the values of the autocorrelation functions of the two Legendre-Sidelnikov sequences, it is proven that both of them have perfect pseudo-randomness. Furthermore, a detailed comparison between autocorrelation functions of the two Legendre-Sidelnikov sequences was deduced. It indicates that no matter which parameters are chosen, the modified sequence has pseudo-randomness as good as the primitive sequence, which is of great significance for applications.

关 键 词：AUTOCORRELATION PSEUDO-RANDOMNESS binary sequence quadratic character Legendre-Sidelnikov sequence two-prime generator 

分 类 号：TN918.1[电子电信—通信与信息系统]