周期为pq的四元广义分圆序列的线性复杂度

Linear Complexity of Quaternary Generalized Cyclotomic Sequences with Period pq

基于Gray映射和Ding-广义分圆理论,在Z_4上构造了一类周期为pq的四元广义分圆序列。在有限域F_r(r≥5为奇素数)上研究了新序列对应的傅里叶谱序列,并依据傅里叶谱序列的重量确定了新序列的线性复杂度。结果表明,新序列具有良好的线性复杂度性质,能够抗击B-M算法的攻击,是密码学意义上性质良好的伪随机序列。

Based on the theory of Gray mapping and Ding-generalized cyclotomic,a new class of quaternary sequence over Z_4 with period pq was constructed firstly.Then we determined the corresponding Fourier spectral sequence of the new sequence over the finite field F_r（r≥5,prime）.Finally,we obtained the linear complexity of the new sequence from the weights of its Fourier spectral sequence.Results show that the sequence has large linear complexity and can resist the attack by B-M algorithm.It＇s a good pseudorandom sequence from the viewpoint of cryptography.