基于k错线性复杂度的2~n周期序列构造研究

发布时间：2018-03-08 21:18

  本文选题：周期序列　切入点：k错线性复杂度　出处：《安徽工业大学》2015年硕士论文　论文类型：学位论文

【摘要】：密码编码学作为一门综合性的尖端学科,主要内容是研究密码编码学和密码破译学的一门科学。其中密码编码学是指对明文序列编码进行加密,用这种方法来确保通信安全。而密码破译学则正好相反,是指对已经加密的信息进行破译以获取明码。序列密码(即流密码)又是密码编码学中的一个极其重要组成部分,而序列密码的安全性,主要看密钥序列。所以在研究密码编码学中对密钥序列的深入研究的重要性十分重要。在序列密码的研究中线性复杂度以及k错线性复杂度具有十分重要研究价值,因为在衡量密钥序列强度的过程中,它们是重要的指标。所以为了研究线性复杂度以及k错线性复杂度的相关性质,本文利用构造方法以及方体理论来进行讨论具有特定线性复杂度和k错线性复杂度的密钥序列。众所周知,在序列密码中,密钥流的线性复杂度非常大的时候,不一定就是最稳定的。k错线性复杂度相关概念的提出正好保证了一个密钥流序列的线性复杂度的稳定性,所以k错线性复杂度在流密码中的地位更加重要。再者,方体理论在研究序列密码性质的时候具有非常重要的作用,利用方体理论可以是序列密码的研究更加清晰易懂,也更便捷。所以本文。利用方体理论对k错线性复杂度的相关性质进行深入地研究。最终得到了以下几项主要成果：1、以GameS-Chan算法为基础,利用方体理论,分析了具有第一次下降点为2错线性复杂度,且第二次下降点为6错线性复杂度的2n周期的二进制序列的相关性质,并且推导出了满足L6(s(n))L5(s(n))=…=L2(s(n))L1(s(n))=L(s(n))的序列的具体的计数公式。2、利用方体理论,对给定线性复杂度和k错线性复杂度的序列,去构造所有满足条件L9(s(n))L8(s(n))=L7(s(n))L6(s(n))=…=L2(s(n))L1(s(n))=L(s(n))且汉明重量为9的2n周期序列,即利用方体理论去构造具有1,7和9下降点的k错线性复杂度简况。3、基于方体理论并且利用构造方法去讨论2n周期序列的3错线性复杂度分布情况,并且给出计算公式和方法。
[Abstract]:As a comprehensive and cutting-edge subject, cryptography is mainly concerned with the study of cryptography and cryptography. This method is used to ensure the security of communications. Cryptography, on the contrary, refers to the decoding of encrypted information to obtain clear codes. Sequence ciphers (that is, stream ciphers) are also an extremely important part of cryptography. And the security of sequence ciphers, So it is very important to study the key sequence in the research of cryptography. The linear complexity and k-error linear complexity are very important in the research of sequence cryptography. Because they are important indicators in measuring the strength of key sequences, in order to study the properties of linear complexity and k-error linear complexity, In this paper, we discuss key sequences with specific linear complexity and k-error linear complexity by means of construction method and cube theory. It is well known that in sequence ciphers, the linear complexity of the key stream is very high. The concept of linear complexity of k error is not necessarily the most stable, which ensures the stability of the linear complexity of a key stream sequence, so the linear complexity of k error is more important in stream cryptography. Cube theory plays a very important role in studying the properties of sequence cipher, and the use of cube theory can be used to study sequence cipher more clearly and easily. In this paper, we use square theory to study the related properties of k error linear complexity. Finally, we get the following main results: 1, based on GameS-Chan algorithm, using square theory, The correlation properties of binary sequences with 2n cycles with the first descent point being 2 error linear complexity and the second drop point with 6 error linear complexity are analyzed. Furthermore, a specific counting formula for the sequence that satisfies L6 / sSN / L5 / L5 / NU = 鈥，

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