Calculation for the linear complexity of primitive σ-LFSR sequences

σ-LFSR is a kind of word-oriented LFSR with high efficiency and good cryptographic properties, especially its software implementation is efficient for modern processors. In practice, primitive σ-LFSR sequences are of the most valuable, and linear complexity is an important parameter of sequences' security. In this paper, linear complexity of primitive σ-LFSR sequences is studied firstly. Then, with the tool of circulant matrix, a method to determine the linear complexity of primitive σ-LFSR sequence is obtained, which could help us calculate linear complexity of σ-LFSR easily.