基于串联寄存器和纯轮换寄存器构造de Bruijn序列的研究
发布时间：2018-08-31 17:09
【摘要】：序列在密码、通信等安全领域有着广泛的应用。随着相关攻击和代数攻击的发展,非线性反馈移位寄存器(NFSR)代替线性反馈移位寄存器(LFSR)成为序列密码设计的焦点,而de Bruijn序列作为一种非常特殊且非常重要的NFSR序列一直是序列研究的热点。本文主要研究了两种构造de Bruijn序列的方法,第一种是基于串联寄存器构造de Brui-jn序列,首先给出了LFSR的串联与并联的相互转化,然后根据这一关系,给出一种特殊的NFSR串LFSR的结构。本文研究了该串联结构的圈结构,给出了求取周期较小的输出序列的方法,并分析了该序列与其他输出序列共轭状态的判断和选取,多次并圈得到de Bruijn序列。第二种是基于纯轮换寄存器构造deBruijn序列,首先研究了纯轮换移位寄存器的圈结构,给出了纯轮换寄存器圈个数与分圆陪集个数间的关系,然后运用插入法构造de Bruijn序列。本文研究的两种构造de Bruijn序列的方法丰富了de Bruijn序列的研究,具有更好的理论价值和应用价值。
[Abstract]:Sequences are widely used in cryptography, communication and other security fields. With the development of correlation attacks and algebraic attacks, nonlinear feedback shift register (NFSR) instead of linear feedback shift register (LFSR) becomes the focus of sequential cryptography design. As a very special and important NFSR sequence, de Bruijn sequence has always been a hot topic in the field of sequence research. In this paper, two methods of constructing de Bruijn sequences are studied. The first is to construct de Brui-jn sequences based on series registers. Firstly, the mutual transformation of LFSR between series and parallel is given, and then according to this relation, A special structure of NFSR string LFSR is given. In this paper, the loop structure of the series structure is studied, the method of finding the output sequence with small period is given, and the judgment and selection of conjugate state between the sequence and other output sequences are analyzed, and the de Bruijn sequence is obtained by multiple cycles. The second is to construct deBruijn sequences based on pure rotation registers. Firstly, the cycle structure of pure rotation shift registers is studied, the relationship between the number of pure rotation registers and the number of cosets is given, and then the de Bruijn sequences are constructed by inserting method. The two methods of constructing de Bruijn sequences in this paper enrich the study of de Bruijn sequences and have better theoretical value and application value.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP332.11;TP309
本文编号：2215627
[Abstract]:Sequences are widely used in cryptography, communication and other security fields. With the development of correlation attacks and algebraic attacks, nonlinear feedback shift register (NFSR) instead of linear feedback shift register (LFSR) becomes the focus of sequential cryptography design. As a very special and important NFSR sequence, de Bruijn sequence has always been a hot topic in the field of sequence research. In this paper, two methods of constructing de Bruijn sequences are studied. The first is to construct de Brui-jn sequences based on series registers. Firstly, the mutual transformation of LFSR between series and parallel is given, and then according to this relation, A special structure of NFSR string LFSR is given. In this paper, the loop structure of the series structure is studied, the method of finding the output sequence with small period is given, and the judgment and selection of conjugate state between the sequence and other output sequences are analyzed, and the de Bruijn sequence is obtained by multiple cycles. The second is to construct deBruijn sequences based on pure rotation registers. Firstly, the cycle structure of pure rotation shift registers is studied, the relationship between the number of pure rotation registers and the number of cosets is given, and then the de Bruijn sequences are constructed by inserting method. The two methods of constructing de Bruijn sequences in this paper enrich the study of de Bruijn sequences and have better theoretical value and application value.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP332.11;TP309
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