Abstract: Linear complexity and kerror linear complexity of the stream cipher are two important standards to scale the randomicity of key sequences. In this paper, for the period length 2pn(p>3), where p is an odd prime and 2 is a primitive root modulo p2, the upper bound on the minimum value k for which the kerror linear complexity is strictly less than the linear complexity is further analyzed and this upper bound can be reached mostly for the period length 2p is proved.

Key words: Stream cipher, Linear complexity, k, error linear complexity

摘要： 序列的线性复杂度与k错线性复杂度是度量密钥序列伪随机性的两个重要指标。在p(p>3)为奇素数且2是模p2本原根的情况下， 对于周期为2pn的二元序列，文章进一步分析了满足k错线性复杂度严格小于序列复杂度的k的最小值的上界，并指出当周期为2p(p>3)时，在大多数情况下可以达到该上界。

关键词: 序列密码, 线性复杂度, k, 错线性复杂度