On the k-error linear complexity of binary sequences derived from polynomial quotients  

作　　者：CHEN ZhiXiong NIU ZhiHua WU ChenHuang 

机构地区：[1]School of Mathematics, Putian University [2]School of Computer Engineering and Science, Shanghai University

出　　处：《Science China(Information Sciences)》2015年第9期79-93,共15页中国科学（信息科学）（英文版）

基　　金：Chen Z X and Wu C H were supported by National Natural Science Foundation of China(Grant No.61373140);the Special Scientific Research Program in Fujian Province Universities of China(Grant No.JK2013044);Niu Z H was supported by National Natural Science Foundation of China(Grant Nos.61272096,61202395);Shanghai Municipal Natural Science Foundation(Grant Nos.13ZR1416100,12ZR1443700);Chen Z X and Niu Z H were also supported by the State Scholarship Fund of China Scholarship Council

摘　　要：The k-error linear complexity is an important cryptographic measure of pseudorandom sequences in stream ciphers. In this paper, we investigate the k-error linear complexity of p2-periodic binary sequences defined from the polynomial quotients modulo p, which are the generalizations of the well-studied Fermat quotients. Indeed, first we determine exact values of the k-error linear complexity over the finite field F2 for these binary sequences under the assumption of 2 being a primitive root modulo p2, and then we determine their k-error linear complexity over the finite field Fp. Theoretical results obtained indicate that such sequences possess ＇good＇ error linear complexity.The k-error linear complexity is an important cryptographic measure of pseudorandom sequences in stream ciphers. In this paper, we investigate the k-error linear complexity of p2-periodic binary sequences defined from the polynomial quotients modulo p, which are the generalizations of the well-studied Fermat quotients. Indeed, first we determine exact values of the k-error linear complexity over the finite field F2 for these binary sequences under the assumption of 2 being a primitive root modulo p2, and then we determine their k-error linear complexity over the finite field Fp. Theoretical results obtained indicate that such sequences possess ＇good＇ error linear complexity.

关 键 词：CRYPTOGRAPHY Fermat quotients polynomial quotients binary sequences linear complexity k-error linear complexity 

分 类 号：TN918.1[电子电信—通信与信息系统] TN911.1[电子电信—信息与通信工程]