The Research On Theory Of Sequences Over Galois Rings

While the computer and communication networks are widely used, information security is more and more attention. Since cryptography is to ensure the security of critical information technology, along with the further development, cryptography will be more widely used.Stream cipher is an important research direction, and has been used as a diplomatic and military situation in one of the major cryptography technology. Stream cipher algorithm is completely determined by the security strength of the pseudo-random sequence whether it generates good or bad. Generating the best possible sequence of pseudo-random sequences will become a very important issue. Linear complexity is important property of pseudo-random sequences.From the middle of the last century, the most studied is the pseudo-random key sequence in the field. To the last two decades, sequences over Galois ring became the hotspot. As the structure of Galois rings structure is more complex than the field, the sequence over Galois ring is not only more but better pseudo-randomness, more difficult to attack. Studying the sequence of Galois rings is still very short time, many problems in this regard is not clear. The study of Galois ring is relatively small. This article continues research in this area.This paper creates a new class of sequences in Galois rings Z2---No sequence S x|v, and received a series of results, As follows:Definition of No sequence: Let u = 2, T = 2 r+ 1, v∈R'*and x∈R.Letξbe an element of order 2 ru ? 1in R ' and it's order is 2 ru ? 1. Associated with the permutation? ,we can define the No sequence S x|vover Galois rings Z2Theorem 1 The minimal positive period of sequence S x|vis 2 ru ? 1.Theorem 2 The linear complexities of sequences of NNo satisfy LC ( S x|v )≥r 2r?1,...