Study On Construction And Randomness Analysis Of Pseudorandom Sequences

For many years, many families of binary sequences of period 2 n ?1 with optimal correlations have been found, where n is a positive integer, including Gold sequence family, Gold-like sequences which are for an odd integer n and whose correlation distribution is the same as that of Gold sequences, the families of binary sequences with six-valued correlations which are for even n and introduced by Udaya and so on. All these sequences have optimal correlations and are the basic for constructding of many other pseudorandom sequences.For expansing the sequence family with optimal correlations, in this correspondence, combining the construction methods of Gold-like sequences and GKW sequences, we constructed a new family G of binary sequences of period 2 n ?1 for a positive integer e such that n/e is an odd integer. The new family G has four-valued correlations, which are the same as those of GKW sequences. The Gold-like sequence family is a special ensample of the family G when e =1. For an integer e such that n/e is an even integer, using the same method of construction as was used for the family G, we also construct a new family L of binary sequences of period 2 n ?1. It has been shown that the new family L has six-valued correlations. The family of binary sequences by Udaya is a special ensample of the family L when e =1. Applying the lifting idea which is be shown in the sixth chapter to the families G and L, two new families GE and LE of binary sequences with the same correlation distributions and large linear span are also constructed. And we also proved these.Since the primitive element and primitive polynomial are the key for the generating of the pseudorandom sequence, and take the very important status in the other applications in the cryptology, in the last part of the thesis, we give out arithmetic for searching the primitive polynomial, to offer effective tools for doing more research for the future.