一类新的周期为p^3的GF(l)上广义割圆序列的线性复杂度

On the linear complexity of a new generalized cyclotomic sequence with length p^3 over GF(l)

线性复杂度是度量序列随机性的一个重要指标。基于Ding-广义割圆序列,构造了GF(l)上一类新的周期为p^3的广义割圆序列(其中l为一奇素数h的幂),且该序列为平衡序列,并通过有限域上的多项式理论确定了该序列的线性复杂度。结果表明,该类序列具有良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抵抗B-M算法攻击的能力。

Linear complexity is the most important index for measuring the randomness properties of sequences. Based on the Ding-generalized cyclotomy, a new class of generalized cyclotomic sequences with length p3 over the finite field of power of odd prime order is constructed, and the sequence is balanced. The linear complexity of the sequences is de- termined using the theory of polynomial over finite field. It is shown that the sequence has good linear complexity, and it can resist attacks from the application of the Berlekamp-Massey algorithm.