Abstract: Lots of new binary sequences of period p and q are presented. These sequences are formed with the Legendre sequences with the periods p and q, where p and q are different odd primes. Based on the constructive relation of these sequences with Legendre sequences, this paper obtains the trace presentations from their defining pairs. Linear complexity is calculated by E.L. Key method. The results show that these sequences possess better properties of symbol balance and linear complexity. Used as key streams, they can resist the attack from the application of the Berlekamp-Massey algorithm.

Key words: stream cipher, Legendre sequences, Jacobi sequences, trace representations, linear complexity

摘要： 利用周期分别为奇素数p 和q的Legendre序列构造大量新的周期为 的二元序列，根据这些序列与Legendre序列在结构上的联系，给出它们的迹表示，依据E.L. Key方法得到其线性复杂度。结果表明该类序列具有良好的符号平衡性和线性复杂度性质，作为密钥流序列可抵抗Berlekamp-Massey算法的攻击。

关键词: 流密码, Legendre序列, Jacobi序列, 迹表示, 线性复杂度

CLC Number: 

• TN918.1