8阶二元广义割圆序列的线性复杂度

Linear complexity of binary generalized cyclotomic sequences of order eight

为了从剩余类环上的二元广义割圆序列中寻求满足需要的密钥流序列,考虑了双素数积剩余类环Zpq上的一类二元广义8阶割圆序列,利用有限域理论,给出了该序列在不同情形下的极小多项式,进而得到了它的线性复杂度。结果表明,该序列有很好的复杂度性质,可以通过选取适当的奇素数p和q,使得其线性复杂度足够大。

In order to get suitable binary sequences for key streams, binary generalized cyclotomic sequences of order eight on the two-prime residue class ring were considered. By means of the polynomial theory over finite fields, minimal polynomials and linear complexity of these sequences were obtained. The results show that sequences with high linear complexity can be produced if the values of p and q are small enough, where p and q are distinct odd primes.