多变量混沌Hash函数的构造与安全性分析

发布时间：2018-06-27 18:55

本文选题：Hash函数 + 混沌理论　；参考：《长沙理工大学》2014年硕士论文

【摘要】：单向Hash函数,也可被称做单向散列函数、单向凑杂函数,它是一种用于将任意长度的消息明文压缩为固定长度的消息摘要的函数,它被广泛应用于数据完整性认证、身份认证、数字签名等。经典的Hash函数采用Merkle-Damgard结构,如MD族和SHA族算法,而这类Hash函数的安全性能被证实不可靠,现已有多种针对广为使用的MD5算法和SHA-1算法的攻击。而且基于Merkle-Damgard结构的算法所采用的串行结构,对消息明文是按分组顺序依次压缩,导致数据处理效率很低,如何构造更为安全、更为快速的Hash函数引起了学者们广泛的研究。与此同时,由于混沌的各项特征与密码学上扩散与混乱的要求一致,利用混沌理论构造Hash函数成为信息安全领域中的热门。本论文立足于前人对混沌Hash算法的大量研究的基础,尝试着结合混沌理论的复杂性和MQ问题的难解性来构造单向Hash函数。本文的主要工作如下：(1)论文对单向Hash函数的发展过程和研究现状略作介绍,重点对现有的混沌Hash算法进行了归纳总结。(2)经典的混沌并行Hash函数效率很高,但存在着被伪造攻击的风险,因此本文提出一种交叉处理的混沌多变量Hash函数。算法的安全性基于多变量多项式方程组求解困难性和混沌理论复杂性的Hash算法。该算法的并行模块交叉处理上一轮迭代值,并且在并行模块后添加一个二次多变量多项式结构,以解决并行Hash函数算法中明文分块之间联系不够紧密的问题。本文还对该算法做了详细的理论分析和仿真验证,结果表明该算法的并行交叉处理结构大大弥补了传统多变量多项式密码的运行效率不足,且输出函数的合理选用使的算法可以抵御伪造攻击、差分攻击等常见攻击,满足Hash函数的多项性能要求。(3)借鉴HAIFA结构本文构造了一种不带密钥的混沌多变量Hash算法,可以抵御对传统Merkle-Damgard结构的多种攻击。算法的压缩函数中采用了混沌映射进行并行处理,以提高HAIFA结构的处理速度,算法的输出函数使用一个多变量多项式方程组结构来调整输出Hash值的长度。算法的仿真与分析表明算法可以抵抗各类常见的攻击,是一种安全的单向Hash函数。
[Abstract]:One-way Hash function, also known as one-way hash function, is a function used to compress arbitrary length message plaintext into fixed length message digest. It is widely used in data integrity authentication, identity authentication, and data integrity authentication. Digital signature, etc. The classical Hash function uses Merkle-Damgard structure, such as MD family and SHA family algorithm. However, the security performance of these Hash functions has been proved to be unreliable. There are many attacks against the widely used MD5 algorithm and SHA-1 algorithm. Moreover, the serial structure based on Merkle-Damgard structure, which compresses the message plaintext in the order of grouping, leads to the low efficiency of data processing, how to construct more secure Hash function, and the more rapid Hash function has been widely studied by scholars. At the same time, because the characteristics of chaos are consistent with the requirements of cryptography diffusion and chaos, the construction of Hash function using chaos theory has become a hot topic in the field of information security. Based on the previous researches on chaotic Hash algorithm, this paper attempts to construct unidirectional Hash function by combining the complexity of chaos theory and the difficulty of MQ problem. The main work of this paper is as follows: (1) the development process and research status of unidirectional Hash function are introduced in this paper, and the existing chaotic Hash algorithm is summarized. (2) the classical chaotic parallel Hash function is highly efficient. However, there is the risk of forgery attack, so this paper presents a chaotic multivariable Hash function with cross-processing. The security of the algorithm is based on the Hash algorithm, which is based on the difficulty of solving multivariable polynomial equations and the complexity of chaos theory. The parallel module of the algorithm cross-processes the last iteration value and adds a quadratic multivariable polynomial structure after the parallel module to solve the problem that the block of plaintext in the parallel Hash function algorithm is not close enough. This paper also makes a detailed theoretical analysis and simulation of the algorithm, the results show that the parallel cross-processing structure of the algorithm greatly makes up for the traditional multi-variable polynomial cipher running efficiency is insufficient. The reasonable selection of output function enables the algorithm to resist common attacks such as forgery attack, differential attack and so on. (3) A chaotic multivariable Hash algorithm without key is constructed by using HAIFA structure for reference. It can resist multiple attacks on traditional Merkle-Damgard structure. Chaotic mapping is used in the compression function of the algorithm to improve the processing speed of HAIFA structure. The output function of the algorithm uses a multivariable polynomial equations structure to adjust the length of the output hash value. The simulation and analysis of the algorithm show that the algorithm can resist all kinds of common attacks and is a safe one-way Hash function.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.1

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