Study On Pseudo-Random Properties Of New Generalized Cyclotomic Sequences

Pseudo-random sequences are widely used in spread spectrum communication system, pseudo-code range measurement, navigation system, software testing, code division multiple access and stream cipher. Especially in sequence cipher, the unpredictability and randomness of key stream plays a very important role in determining security of the cryptosystem. One of the most important measurements of sequence randomness is its linear complexity. According to B-M algorithm, a sequence which has a high linear complexity no less than half a cycle has good secure properties.This paper mainly studies new polyphase generalized cyclotomic sequences of length pq and Whiteman generalized cyclotomic sequences of any order and Ding-Helleseth generalized cyclotomic sequences. Their linear complexity are considered. The results prove that they all have high linear complexity. Main results are as follows:(1) This paper constructs new polyphase generalized cyclotomic sequences and considers its linear complexity. And figures out its lower bound.(2) This paper constructs binary Whiteman generalized cyclotomic sequences of any order and considers its linear complexity.(3) This paper calculates the linear complexity of Ding-Helleseth generalized cyclotomic sequences.The results show that because the lower bound of sequences is more than half period, they can be used to encryption as keystream.