本文選題：周期序列　切入點：k錯線性復雜度　出處：《安徽工業(yè)大學》2015年碩士論文　論文類型：學位論文

【摘要】：密碼編碼學作為一門綜合性的尖端學科,主要內容是研究密碼編碼學和密碼破譯學的一門科學。其中密碼編碼學是指對明文序列編碼進行加密,用這種方法來確保通信安全。而密碼破譯學則正好相反,是指對已經加密的信息進行破譯以獲取明碼。序列密碼(即流密碼)又是密碼編碼學中的一個極其重要組成部分,而序列密碼的安全性,主要看密鑰序列。所以在研究密碼編碼學中對密鑰序列的深入研究的重要性十分重要。在序列密碼的研究中線性復雜度以及k錯線性復雜度具有十分重要研究價值,因為在衡量密鑰序列強度的過程中,它們是重要的指標。所以為了研究線性復雜度以及k錯線性復雜度的相關性質,本文利用構造方法以及方體理論來進行討論具有特定線性復雜度和k錯線性復雜度的密鑰序列。眾所周知,在序列密碼中,密鑰流的線性復雜度非常大的時候,不一定就是最穩(wěn)定的。k錯線性復雜度相關概念的提出正好保證了一個密鑰流序列的線性復雜度的穩(wěn)定性,所以k錯線性復雜度在流密碼中的地位更加重要。再者,方體理論在研究序列密碼性質的時候具有非常重要的作用,利用方體理論可以是序列密碼的研究更加清晰易懂,也更便捷。所以本文。利用方體理論對k錯線性復雜度的相關性質進行深入地研究。最終得到了以下幾項主要成果：1、以GameS-Chan算法為基礎,利用方體理論,分析了具有第一次下降點為2錯線性復雜度,且第二次下降點為6錯線性復雜度的2n周期的二進制序列的相關性質,并且推導出了滿足L6(s(n))L5(s(n))=…=L2(s(n))L1(s(n))=L(s(n))的序列的具體的計數公式。2、利用方體理論,對給定線性復雜度和k錯線性復雜度的序列,去構造所有滿足條件L9(s(n))L8(s(n))=L7(s(n))L6(s(n))=…=L2(s(n))L1(s(n))=L(s(n))且漢明重量為9的2n周期序列,即利用方體理論去構造具有1,7和9下降點的k錯線性復雜度簡況。3、基于方體理論并且利用構造方法去討論2n周期序列的3錯線性復雜度分布情況,并且給出計算公式和方法。
[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，

本文編號：1585601