Study Of Key Stream Generators Based On Whiteman Generalized Cyclotomy

Key stream generator is the most important and central part of a stream cipher system. The key stream generated by the generators must possess good pseudo-random properties. So the design and analysis of key stream generators with good pseudo-random properties is the central work of the stream cipher study. Meanwhile, many sequences with pseudo-random properties can be used in the public key systems, measuring distance, spread spectrum communications, multiple access communications, radar, navigation, software testing and other engineering.To meet the need for information security, communications engineering requires a lot of types of key stream generator. Whiteman generalized cyclotomic generators constructed in 1998 by Ding C. are good prospect key stream generators. Such generators are always even order. Of all the Whiteman generalized cyclotomic generators, the case of order 2 is the most studied, which has been proved to possess cryptographic linear complexity (larger than the half of its period), autocorrelation, cross-correlation and other random-pseudo measure. This paper formerly studies the stability of its linear complexity, namely the variability of the linear complexity when the sequence is changed by minority bits. A formal way to show the linear complexity decreases is to construct an error sequence which is close to the origin sequence and possesses low complexity, but it is very difficult to form it for the case of order 2 of each of the different period studied in this paper. Then this paper adopts a new way instead, which is required to form two related error sequences closed to the origin sequence and confirm at least one of it possess low complexity for each of the different period. The results show that the stability of its linear complexity is very bad, that is, when (?)bits of this sequence are changed, its linear complexity will decrease rapidly and become much smaller than the cryptographic low bound. Then the generator of order 2 cannot resist the attack of BM algorithm. Since the autocorrelation of the generator of order 4 is 4-valued and not uniform, this cannot meet the requirement of cryptography. Then this paper focuses on the case of order 6. Its generative polynomial is constructed firstly, and then, with the minimal polynomial method, the lower bound of its linear complexity is obtained, which can meet the requirement of cryptography.