-LFSR序列极小多项式性质研究
doi: 10.3724/SP.J.1146.2009.00061
On the Properties of the Minimal Polynomial of -LFSR Sequence
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摘要: -线性反馈移位寄存器(-LFSR)是基于字设计的，在安全性和效率上达到较好折衷的一种反馈移位寄存器。-LFSR输出序列的特征多项式为有限域上的矩阵多项式。该文利用有限域上矩阵多项式环的代数结构，给出了-LFSR输出序列极小多项式唯一的充分必要条件。Abstract: -Linear Feedback Shift Register (-LFSR) is a word-oriented feedback shift register, which has a better tradeoff between the security and efficiency. The sequence generated by -LFSR is called the -linear recurrence sequence and its characteristic polynomial is the matrix polynomial over finite field. With analysis of the algebra structure of the matrix polynomial ring over finite field, the sufficient and necessary condition for the minimal polynomial of -linear recurrence sequence to be unique is given.
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