中文摘要：

证明了本原σ-线性反馈移位寄存器（σ-LFSR）序列距离向量的计算与有限域上离散对数的计算等价,同时给出一个本原σ-LFSR序列距离向量的计算方法。还给出一类特殊本原σ-LFSR序列距离向量的计算方法,该方法将有限域上离散对数的计算转化到其子域上离散对数的计算,复杂度显著降低。

英文摘要：

The equivalence between calculation of interval vectors of primitive s-linear feedback shift register（σ-LFSR） sequences and calculation of discrete logarithms over finite field was proved,at the same time a calculation method for interval vectors of primitive σ-LFSR sequences was given.Then another calculation method for interval vectors of a class of primitive σ-LFSR sequences was obtained,which converted the calculation of discrete logarithms over finite field to its subfield and the complexity was much lower.