I. Introduction
In the sixties of the 20th century, Massey proposed the Berlekamp-Massey algorithm. According to the algorithm[1], if the linear complexity of a sequence is , we can compute the entire sequence with continuous 2 bits. So a cryptographically secure sequence must have a high linear complexity. Later, more and more papers devoted to the study of the linear complexity[2]–[5]. However, a high linear complexity is not enough to ensure a sequence being cryptographically secure. For example, let be a period of an -periodic sequence . It is obviously that has the maximum possible linear complexity . But it is cryptographically weak. After changing every bit from 1 to 0, the linear complexity will decrease to zero. So such sequences are not secure for being used in cryptography. And we can conclude that a cryptographically secure sequence should have a stable linear complexity.