基于准并矢纠错码的公钥密码方案研究

发布时间：2018-03-18 01:07

本文选题：准并矢纠错码　切入点：零知识身份认证　出处：《江苏大学》2017年硕士论文　论文类型：学位论文

【摘要】：量子计算机技术的不断发展,使得基于数论难题的公钥密码体制面临严重挑战,因此具有抗量子计算机攻击特性的公钥密码体制受到了密码学界的广泛关注。区别于大整数因式分解和离散对数等数论中的NP困难问题,纠错码理论中的一般线性译码问题为NPC困难问题,可以抵抗量子计算机攻击。因此,将纠错码理论和密码学相结合,对可以抵抗量子计算机攻击的基于纠错码公钥密码体制进行理论研究具有重要意义。基于纠错码的公钥密码方案的实现过程仅需异或运算,与RSA和ECC等公钥密码体制相比,效率较高,因此具有在嵌入式系统等资源有限环境中使用的基本特征,即符合轻量级密码的高效要求。然而原始的基于纠错码的公钥加密体制,身份认证方案及数字签名方案,因其密钥体积过大,很难在实用于现实应用场景中,因此设计安全高效的基于纠错码的公钥密码方案是现代密码学研究领域的热点和难题。本文围绕基于QD-MDPC码的公钥密码体制进行如下研究。首先,构造密钥体积小的基于QD-MDPC码公钥密码算法。设计准并矢中密度奇偶校验码(Quasi-dyadic Moderate Density Parity Check Code,QD-MDPC)以减小密钥体积,并计算QD-MDPC码的生成矩阵,同时选取随机非奇异矩阵和置换矩阵,生成该密码算法加解密的公私钥。在加密过程中引入随机错误矢量,增强算法安全性能。并且针对密码算法进行结构攻击和译码攻击分析,证明了该算法的安全性。通过构造这种QD-MDPC码,密码算法的密钥体积大大减小,满足在存储资源有限的嵌入式设备中应用要求。然后,结合上述提出的基于QD-MDPC码的公钥密码算法,构造两种零知识身份认证方案。这两种认证方案基于编码理论中的不同困难问题,并且具有不同的认证效率。前一种认证协议通过计算每轮认证中一个委托的哈希值,减少所需发送的委托数量,从而减小了认证通信的开销。接着对所提方案的完整性、可靠性和零知识性等安全性质进行了分析。然后基于一般译码问题,构造了第二种性能更加优化的认证协议,该协议计算每轮中的两个委托的哈希值,进一步地减少了认证通信开销。而且性能分析表明,相比于其它的零知识身份认证方案,所提出的方案优化了密钥存储空间和交互认证通信开销,尤其是第二种认证协议,在存储资源和计算能力有限的设备中具有更大的应用优势。最后,本文设计了一种基于准并矢纠错码的不可否认签名方案。该签名方案由初始化、签名和验证三个算法组成,初始化算法生成签名者的公私钥和公开参数,签名算法生成一个签名三元组,验证算法是一个五次交互的零知识协议,验证者通过与签名者进行交互对签名三元组进行验证。本文对不可否认签名方案的完备性、可靠性、零知识性、不可伪造性、不可见性以及不可传递性等安全性质进行了分析。性能分析表明,该方案的签名长度和通信开销都优于对比方案。
[Abstract]:The development of quantum computer technology, the public key cryptosystem based on number theoretic problems facing serious challenges, so the public key cryptosystem with anti attack properties of quantum computers have attracted much attention in cryptography field. NP difficult problem is different from the large integer factorization and discrete logarithm in number theory, general linear decoding problem in the theory of error correcting codes is a NPC hard problem, can resist quantum computer attacks. Therefore, the theory of error correcting codes and cryptography combined, can resist the attack of the quantum computer has important significance for theoretical research in public key cryptosystem based on error correcting codes. The implementation process of public key cryptography scheme, error correcting codes only based on XOR operation, compared with RSA and ECC public key cryptosystem has high efficiency, so it has the basic features used in embedded systems with limited resources in the environment, which is in line with the light Efficient password required. However the original error correcting codes based on public key encryption, identity authentication and digital signature scheme, because of its key size is too large, difficult in practical application in the real scene, so the design of safe and efficient public key encryption scheme based on ECC is a hot and difficult problem in the research field of modern cryptography. The research of public key cryptosystem based on QD-MDPC code in this dissertation. First, the small size structure key cryptography algorithm based on QD-MDPC code. The design of quasi dyadic medium density parity check code (Quasi-dyadic Moderate Density Parity Check Code, QD-MDPC) to reduce the key size, and calculate the generation matrix of the QD-MDPC code, and select the random non singular matrix and the permutation matrix, the password generated private key encryption and decryption algorithms. The introduction of random error vector in the encryption process, enhance the safety performance of the algorithm and the needle. The structure of attack and attack analysis of decoding algorithm, proves the security of the algorithm. By constructing the QD-MDPC code, the volume key cryptographic algorithm is greatly reduced, meet the application requirements in embedded devices with limited storage resources. Then, according to the above proposed public key cryptosystem based on QD-MDPC codes, constructed two kinds of zero knowledge of identity authentication scheme. The two authentication schemes of different problems based on the encoding theory, and has different authentication efficiency. Before an authentication protocol by computing a hash value in each round of entrusted authentication, reduce the number required to send the client less, thus reducing the communication overhead and authentication integrity. In the proposed scheme, the reliability and the zero knowledge security properties are analyzed. Then the general decoding problem based on the structural properties of second kinds of authentication protocol more optimized, the agreement. The hash is two delegates each round in value, further reduces the communication overhead and authentication. The performance analysis shows that compared to the zero knowledge authentication scheme, the proposed scheme optimizes the key storage space and interactive authentication communication overhead, especially the second kinds of authentication protocol, has the advantage of greater in the storage resources and limited computing capability of equipment. Finally, this paper designs a kind of quasi dyadic codes based undeniable signature scheme. The scheme is composed of initialization, signature and verification of three algorithms, initialization algorithm into the private key of the signer and the public parameter signature algorithm to generate a signature three tuple verification algorithm is a five interactive zero knowledge protocol, through interaction with the signature verifier verifies the signature of three tuple. In this paper, the non repudiation signature completeness, reliability, The security properties of zero knowledge, non forgery, invisibility and non transitivity are analyzed. The performance analysis shows that the signature length and communication cost of the scheme are better than those of the comparison scheme.

【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN918

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