基于多变量公钥密码体制的盲签名、环签名研究

发布时间：2018-04-09 12:02

本文选题：多变量公钥密码体制　切入点：MQ问题　出处：《复旦大学》2014年硕士论文

【摘要】：传统数字签名的安全性主要是基于大素数分解和离散对数问题,在1994年Shor提出了在量子计算机下能够破解这两大问题的量子算法后,抗量子计算的密码安全引起了密码学界的广泛关注与研究,需要提出其他复杂性假设来设计新方案,而多变量公钥密码体制(MPKC)则是抗量子计算的候选密码体制之一。MPKC是基于MQ难解问题构建的公钥密码体系,具有占用资源较少的特点,适用于低消耗的设备,如RFID芯片,智能卡等移动设备上,在现实生活中应用的意义非常大,目前已有很多基于MPKC的数字签名协议相继被提出,其中包括安全性较高的Rainbow和UOV签名协议。与此同时,在MPKC签名协议的基础上引入传统数字签名中适用于不同场景的签名思想也是对MPKC方案进行拓展和应用的主要研究方向,如基于MQ的环签名、盲签名、代理签名等。此外,MPKC签名协议仍存有一些不足,一方面,大多数签名方案的构造引入了IP难解问题,使得方案基于两种难解问题的结合而增大了不安全性的风险,另一方面,签名协议构建中公私钥过大,对其应用场景有一定的限制。本文通过分析国内外基于多变量公钥密码体制的签名协议的最新研究进展,主要关注于将传统数字签名协议中的环签名和盲签名的思想引入MPKC签名协议的构造中,以构建基于新困难性问题MQ问题的签名方案来拓展MPKC签名协议在量子计算机下的应用。首先,提出一个局部基于MPKC的可证明安全的环签名协议,该协议的主要思想在于去除部分对IP问题的依赖性,以提高签名协议的安全性,同时证明了该协议的安全性；其次,针对基于MPKC的签名协议的公私钥普遍过大的问题,采用矩阵变换的方式对之前提出的局部MPKC签名协议进行优化设计,降低了协议中私钥的大小,并提高了签名生成的效率；最后,从MPKC方案中中心映射的另一个构造角度出发,提出了一个基于MPKC的盲签名协议,并证明了该协议的盲性和不可伪造性。
[Abstract]:The security of traditional digital signature is mainly based on the decomposition of large prime numbers and discrete logarithm. After Shor proposed a quantum algorithm to solve these two problems in 1994,The cryptographic security of anti-quantum computing has attracted wide attention and research in cryptography, and other complexity assumptions need to be proposed to design a new scheme.The multivariable public key cryptosystem (MPKC) is one of the candidate cryptosystems to resist quantum computing. MPKC is a public-key cryptosystem based on MQ intractable problem.The application of smart card and other mobile devices is of great significance in real life. At present, many digital signature protocols based on MPKC have been proposed, including Rainbow and UOV signature protocols with high security.At the same time, based on the MPKC signature protocol, it is also the main research direction to extend and apply the traditional digital signature to different scenarios, such as MQ based ring signature, blind signature, proxy signature and so on.In addition, MPKC signature protocol still has some shortcomings. On the one hand, the construction of most signature schemes introduces IP intractable problem, which makes the scheme increase the risk of insecurity based on the combination of two difficult problems, on the other hand,The public and private key is too large in the construction of signature protocol, which has some limitations on its application scenario.By analyzing the latest research progress of signature protocols based on multivariable public key cryptosystem at home and abroad, this paper mainly focuses on introducing the idea of ring signature and blind signature in traditional digital signature protocols into the construction of MPKC signature protocols.In order to extend the application of MPKC signature protocol in quantum computer, we construct a signature scheme based on MQ problem.Firstly, a provable secure ring signature protocol based on MPKC is proposed. The main idea of this protocol is to remove the dependence of some IP problems to improve the security of the signature protocol and to prove the security of the protocol.Aiming at the problem that the public and private keys of the signature protocol based on MPKC are too large, this paper optimizes the design of the local MPKC signature protocol based on matrix transformation, which reduces the size of the private key in the protocol and improves the efficiency of signature generation.Finally, from another point of view of center mapping in MPKC scheme, a blind signature protocol based on MPKC is proposed, and its blindness and unforgeability are proved.
【学位授予单位】：复旦大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.91

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