基于钟控方法的伪随机序列生成器的设计和分析

发布时间：2018-05-15 19:30

本文选题：伪随机序列 + 相关免疫　；参考：《西安电子科技大学》2014年博士论文

【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。
[Abstract]:Pseudorandom sequences are widely used in simulation, communication systems, software testing and cryptography. Stream cryptosystems still have incomparable advantages in areas where resources are extremely limited and where very high encryption and decryption speed is required. In the past, stream ciphers were usually implemented by hardware, but the efficiency of software implementation was low. How to make up for the weakness of stream cipher in software, give full play to its advantages, design a stream cipher algorithm with high stability, high speed and less resources has been the goal pursued by many cryptographers. The advantage of stream cipher is that it is simple and fast, especially the hardware implementation module is small in size and runs much faster than other cryptosystems. The disadvantage of stream cipher is that it is only suitable for continuous secure communication, not for flexible file encryption and decryption. Stream cipher, especially its pseudorandom sequences, is widely used in various systems, which makes stream cipher still a hotspot in cryptography. The design and analysis of key stream generator is always the central subject of stream cryptography. On the basis of summarizing the existing research results, this paper has also made some useful attempts and explorations, and has mainly achieved the following results: 1. By analyzing the Walsh spectrum of general Boolean functions, a criterion for the correlation immunity of Boolean functions is obtained. The sufficient conditions for n-variable Boolean functions to be m-order correlated immunity are given, and some properties of correlated immune Boolean functions are given. By discussing the correlation immunity of the sum function of the correlation immunity, we obtain the equivalent conditions for the finite number of correlation immunity and function to be the correlation immunity. 2. By analyzing the product sequence induced by LFSR of two series, the relation between the autocorrelation function of periodic sequence and the weight of product sequence is obtained. The value of autocorrelation function of the product sequence of m sequence of two periodic coprimes and its Hamming weight in one period are obtained. 3. Through the correlation analysis of the product sequences of the m sequences of any finite series, it is concluded that for the product sequences of any l m sequences, the autocorrelation function is always a l 1 valued function, and its principal peak value R Y 0) is very high. 4. Based on resisting the BAA attack and other attacks based on the stability theory, the control sequence generated by the clock control method is used, and the internal structure of the clock-controlled sequence generator is improved to make each shift register control each other. A clock-controlled shift register model of "mutual control" is constructed (this model and the concept of "intercontrol" are put forward by the author of this paper. See part of this paper "the research results during the study of doctoral degree"), the pseudorandom nature of the output sequence is analyzed. It is proved that the sequence produced by it has large period and high linear complexity. Through analysis, it is pointed out that the "mutual control" clock-controlled shift register sequence integrates the security and stability indexes, is feasible in theory, and has high efficiency in software implementation, and has certain practical value.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN918

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