二元W-广义割圆序列的线性复杂度

Linear complexity of binary whiteman generalized cyclotomic sequences

周期为pq上的2阶W-广义割圆序列的线性复杂度和极小多项式是丁存生于1998年给出的.采用有限域上的多项式理论,考虑了任意的W-广义割圆序列的线性复杂度和极小多项式,并完全解决了这一问题.结果表明这类序列的线性复杂度的上界和下界分别是pq-1和(p-1)(q-1)/2.从密码学的角度看,多数的二元W-广义割圆序列具有很好的线性复杂度性质,以它们做密钥流序列的密码系统具有很强的抵抗B-M算法攻击的能力.

Based on the polynomial theory on a Galois field, the author presents linear complexity and minimal polynomials of all binary Whiternan generalized cyclotornic sequences with the period pq. The results obtained show that the upper bound and the lower bound of their linear complexity are pq-1 and （p-1）（q-1）/2 respectively. From the viewpoint of stream cipher cryptosysterns, almost all these sequences have good linear complexity. They can resist the attacks from the application of the BerlekampMassey algorithm.