基于钟控方法的伪随机序列生成器的设计和分析
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摘要
伪随机序列在模拟仿真、通信系统、软件测试以及密码学领域都有着广泛的应用。流密码体制在资源极端受限的领域及需要极高加解密速度的地方依然具有不可比拟的优势。以往的流密码通常采用硬件实现，而软件实现效率较低。如何弥补流密码在软件方面的弱点，发挥其优势，设计具有稳定性高、速度快和占用资源少的流密码算法一直是众多密码学家追求的目标。
流密码的优势是简单快速，特别是硬件实现模块体积小，运行速度远高于其他密码体制。流密码的劣势是仅适用于持续的保密通信，不适用于灵活的文件加解密。流密码，特别是其使用的伪随机序列在各个系统中的广泛应用，使得流密码仍然是密码学研究的热点。密钥流生成器的设计与分析永远是流密码学研究的中心课题，在这个领域的研究工作一直都是生机勃发，成果倍出。
本文在总结已有研究结果的基础上，也做了一些有益的尝试和探索，主要取得以下成果：
1．通过分析一般布尔函数的Walsh谱，得到了布尔函数相关免疫性的一个判定条件，给出了n元布尔函数f(x)是m阶相关免疫的充分条件，并给出了一些相关免疫布尔函数的性质；通过讨论相关免疫的和函数的相关免疫性，得出了有限个相关免疫和函数为相关免疫的等价条件。
2．通过对两个级数互素的LFSR诱导出的乘积序列的分析，得到周期序列的自相关函数与乘积序列的重量之间的关系，由此得到两个周期互素的m序列的乘积序列的自相关函数的值及其在一个周期内的Hamming重量。
3.通过对任意有限个级数互素的m序列的乘积序列的相关分析，得出对于任意l个m序列的乘积序列，其自相关函数永远是l+1值函数，且其主峰值R Y(0)很高。
4.基于抵抗BAA攻击和基于稳定性理论的其它攻击，利用钟控方法产生的控制序列，并对钟控序列生成器的内部结构作一定的改进，使其各个移位寄存器产生相互控制的关系，构造了“互控”钟控移位寄存器模型（该模型及所谓“互控”的概念由本论文作者提出，参见本论文“攻读博士学位期间的研究成果”部分），分析了其输出序列的伪随机性质，证明了由其产生的序列具有大的周期及相当高的线性复杂度。通过分析指出，“互控”钟控移位寄存器序列综合了安全性和稳定性指标，理论上是可行的，并且软件实现效率较高，具有一定的实用价值。
Pseudorandom sequences witness wide applications in simulation， softwaretesting，global positioning systems，ranging systems，code division multiple-accesssystems，radar navigation systems，spread-spectrum communication systems，andstream ciphers.Stream cipher still has incomparable advantages in extremely limitedresources and high decryption speed place. Stream cipher previous usually withhardware,and software implementation low efficiency. How to make up the streamcipher software weakness, give play to its advantage, the design has high stability, fastspeed and less resource stream cipher algorithm has been many cryptographers goal.
In this paper, based on summarizing existing research results, the author madesome beneficial attempt and exploration, following the major achievements:
1. The analysis of general Boolean function of the Walsh spectrum, a criterion ofcorrelation immunity Boolean function is achieved, the n element Boolean function f (x)is a sufficient condition of m order correlation immune, and gives some properties ofBoolean functions with correlation immunity; Based on the discussion of the relatedimmune function of the sum function,the equivalent conditions for a finite correlationimmunity sum function is still immune function were obtained.
2On the analysis of the product sequence of two series of Coprime LFSR induced,the relationship between periodic sequence autocorrelation function and productsequence of weight is achieved, the value of two coprime period m-sequences productautocorrelation and Hamming weight in a period is also obtained.
3. Through the correlation analysis of product sequences on any finite ordercoprime m sequence, the autocorrelation function is always the l+1value function forthe product of the sequence of arbitrary l m sequences,, and the peak value of RY(0)high.
4. Based on the resistance of BAA attack and other attacks based on stability theory,the control sequence generated by the clock control method, a modified internalstructure and control sequence generator on the clock, make its each shift registergenerates relationship of mutual control, constructed the clock "mutual-controlled"shift register model, analyzes the pseudorandom properties its output sequences, provedthat the sequence generated by the large period and linear complexity is very high.Through the analysis pointed out that, clock "mutual controlled" shift register sequenceof comprehensive security and stability index, the theory is feasible, and the software to achieve higher efficiency, has a certain practical value.
流密码的优势是简单快速，特别是硬件实现模块体积小，运行速度远高于其他密码体制。流密码的劣势是仅适用于持续的保密通信，不适用于灵活的文件加解密。流密码，特别是其使用的伪随机序列在各个系统中的广泛应用，使得流密码仍然是密码学研究的热点。密钥流生成器的设计与分析永远是流密码学研究的中心课题，在这个领域的研究工作一直都是生机勃发，成果倍出。
本文在总结已有研究结果的基础上，也做了一些有益的尝试和探索，主要取得以下成果：
1．通过分析一般布尔函数的Walsh谱，得到了布尔函数相关免疫性的一个判定条件，给出了n元布尔函数f(x)是m阶相关免疫的充分条件，并给出了一些相关免疫布尔函数的性质；通过讨论相关免疫的和函数的相关免疫性，得出了有限个相关免疫和函数为相关免疫的等价条件。
2．通过对两个级数互素的LFSR诱导出的乘积序列的分析，得到周期序列的自相关函数与乘积序列的重量之间的关系，由此得到两个周期互素的m序列的乘积序列的自相关函数的值及其在一个周期内的Hamming重量。
3.通过对任意有限个级数互素的m序列的乘积序列的相关分析，得出对于任意l个m序列的乘积序列，其自相关函数永远是l+1值函数，且其主峰值R Y(0)很高。
4.基于抵抗BAA攻击和基于稳定性理论的其它攻击，利用钟控方法产生的控制序列，并对钟控序列生成器的内部结构作一定的改进，使其各个移位寄存器产生相互控制的关系，构造了“互控”钟控移位寄存器模型（该模型及所谓“互控”的概念由本论文作者提出，参见本论文“攻读博士学位期间的研究成果”部分），分析了其输出序列的伪随机性质，证明了由其产生的序列具有大的周期及相当高的线性复杂度。通过分析指出，“互控”钟控移位寄存器序列综合了安全性和稳定性指标，理论上是可行的，并且软件实现效率较高，具有一定的实用价值。
Pseudorandom sequences witness wide applications in simulation， softwaretesting，global positioning systems，ranging systems，code division multiple-accesssystems，radar navigation systems，spread-spectrum communication systems，andstream ciphers.Stream cipher still has incomparable advantages in extremely limitedresources and high decryption speed place. Stream cipher previous usually withhardware,and software implementation low efficiency. How to make up the streamcipher software weakness, give play to its advantage, the design has high stability, fastspeed and less resource stream cipher algorithm has been many cryptographers goal.
In this paper, based on summarizing existing research results, the author madesome beneficial attempt and exploration, following the major achievements:
1. The analysis of general Boolean function of the Walsh spectrum, a criterion ofcorrelation immunity Boolean function is achieved, the n element Boolean function f (x)is a sufficient condition of m order correlation immune, and gives some properties ofBoolean functions with correlation immunity; Based on the discussion of the relatedimmune function of the sum function,the equivalent conditions for a finite correlationimmunity sum function is still immune function were obtained.
2On the analysis of the product sequence of two series of Coprime LFSR induced,the relationship between periodic sequence autocorrelation function and productsequence of weight is achieved, the value of two coprime period m-sequences productautocorrelation and Hamming weight in a period is also obtained.
3. Through the correlation analysis of product sequences on any finite ordercoprime m sequence, the autocorrelation function is always the l+1value function forthe product of the sequence of arbitrary l m sequences,, and the peak value of RY(0)high.
4. Based on the resistance of BAA attack and other attacks based on stability theory,the control sequence generated by the clock control method, a modified internalstructure and control sequence generator on the clock, make its each shift registergenerates relationship of mutual control, constructed the clock "mutual-controlled"shift register model, analyzes the pseudorandom properties its output sequences, provedthat the sequence generated by the large period and linear complexity is very high.Through the analysis pointed out that, clock "mutual controlled" shift register sequenceof comprehensive security and stability index, the theory is feasible, and the software to achieve higher efficiency, has a certain practical value.
引文
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