Problems On Joint Linear Complexity Of Multisequences

The linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, in the study of vectorized stream cipher systems, the joint linear complexity of multisequences has been investigated. In this paper, at the first, we give the degrees for canonical factors of the monic polynomial h₁(x)…h_k(x) that is the canonical factorization of xⁿ-1. Then we study the joint linear complexity of multisequences consisting of linear recurring sequences. For fixed joint linear complexity, we give a general formula for the counting functions. At last, The expection and variance of the joint linear complexity of random multisequence consisting of linear recurring sequences are determined.In this paper, we obtain above results using a new method. By establishing the relations between the sequences and the polynomials, the polynomials and the sets, we obtain the relations between the sequences and the sets. Then, we study the counting funtions of the sets. With these results we obtain a set of counting formulas for multisequences.