全同态密码理论研究
发布时间：2018-07-26 17:50
【摘要】：公钥密码学已经走过了36个年头,历史上诞生的公钥密码体制大都具有同态特性,但是构造“完美”的全同态密码体制也一直是密码学上的难题。云计算关键技术,密文检索技术,安全多方计算以及远程数据完整性校验对密码学发展提出了新的要求,设计安全高效的全同态密码体制变得很必要。因此,研究全同态密码相关理论,设计实用的全同态密码体制成了学者们关注的热点。本文的工作正是基于此展开,主要包括以下几个方面:首先,为了对全同态密码有一个全面而深入的分析,本文对具有代表性的同态密码体制进行了研究。历史上的经典体制如RSA密码体制,Paillier密码体制和ElGamal密码体制的同态性产生都有各自不同的特点,本文重点剖析了这些公钥密码体制同态特性的产生方法,对同态密码体制进行分类,归纳了多种同态特性。在此基础上,设计了一种语义安全的靶向全同态密码体制,并利用上述密码体制,设计了一种安全两方点积计算协议。其次,为了把握全同态密码体制的设计方法,本文对基于Gentry思想设计的、两个经典的全同态密码体制—基于整数的(又名DGHV密码体制)和基于理想格的全同态密码体制进行了研究和分析。在分析理想格的密码学特性及其局限性和DGHV全同态密码体制的基础上,对经典的DGHV全同态密码体制进行了改进,设计了一种公钥尺寸小、效率更高的Somewhat同态密码体制。再次,为了构造格上全同态密码体制,本文设计了一种基于后量子安全假设LWE的全同态密码体制。在文中,首先以LWE为载体,研究并给出了全同态密码体制设计的关键技术,结合矩阵运算的特点,设计了一种基于密文展缩的全同态密码体制,该体制避开了经典全同态设计中引入额外的安全假设的环节,安全性更加明确。其公私钥尺寸为O(n2l),而明密文扩展为O(n2l),这两点和之前的全同态密码体制相比,都有很大改善。最后,全同态密码体制的研究和设计给同态数字签名和同态消息认证带来了新的思路,本文在研究全同态密码体制的基础上,对消息认证过程进行分析,设计了一种改进的全同态消息认证算法。该同态消息认证码的安全性是基于伪随机函数的设计,本文的改进算法保证了明文的不泄露性和两类不可伪造性,给部分数据的完整性认证提供了新的思路和方法。在本文的结尾,对全文的工作进行总结,并给出了下一步的工作计划。
[Abstract]:Public key cryptography has gone through 36 years. Most of the public key cryptosystems in history have homomorphic characteristics, but the construction of "perfect" homomorphic cryptosystem has always been a difficult problem in cryptography. With new requirements, it is necessary to design a safe and efficient all homomorphic cryptosystem. Therefore, it is a hot topic for scholars to study the whole homomorphic cipher theory and design a practical homomorphic cryptosystem. The work of this paper is based on the following aspects: first, there is a comprehensive analysis of all homomorphic ciphers. In depth analysis, a representative homomorphic cryptosystem has been studied in this paper. The classical system in history, such as the RSA cryptosystem, the Paillier cryptosystem and the homomorphism of the ElGamal cryptosystem, has its own characteristics. This paper focuses on the analysis of the homomorphic characteristics of the public key cryptosystems, and the homomorphic ciphers. The system is classified and generalizes a variety of homomorphism characteristics. On this basis, a semantic security target full homomorphic cryptosystem is designed, and a secure two party point product calculation protocol is designed by using the above cryptosystem. Secondly, in order to grasp the design method of the whole homomorphic cryptosystem, this paper designs two classics based on Gentry thought. The whole homomorphism cryptosystem, an integer based (also called DGHV cryptosystem) and an all homomorphic cryptosystem based on ideal lattice, is studied and analyzed. On the basis of the analysis of the cryptology characteristics and limitations of the ideal lattice and the DGHV homomorphism cryptosystem, the classical DGHV homomorphism cryptosystem is improved and a kind of public cryptosystem is designed. Somewhat homomorphic Cryptosystem with small key size and higher efficiency. Again, in order to construct the whole homomorphic cryptosystem on the lattice, this paper designs a all homomorphic cryptosystem based on the post quantum security hypothesis LWE. In this paper, the key technology of the whole homomorphic cryptosystem is studied and given the key technology of the whole homomorphic cryptosystem, and the characteristic of the matrix operation is combined with the LWE as the carrier. An all homomorphism cryptosystem based on ciphertext expansion is designed, which avoids the additional security hypothesis in the classical homomorphism design. The security is more explicit. The public key size is O (n2l), and the plaintext is extended to O (n2l). The research and design of cryptosystem bring new ideas to homomorphic digital signature and homomorphic message authentication. On the basis of studying the whole homomorphism cryptosystem, this paper analyzes the message authentication process and designs an improved whole homomorphic message authentication algorithm. The security of the homomorphic message identification code is based on the design of pseudo random function. The improved algorithm in this paper ensures the non leaking and two kinds of non forgery of the plaintext, and provides new ideas and methods for the integrity authentication of some data. At the end of this paper, the work of the full text is summarized, and the next work plan is given.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.4
[Abstract]:Public key cryptography has gone through 36 years. Most of the public key cryptosystems in history have homomorphic characteristics, but the construction of "perfect" homomorphic cryptosystem has always been a difficult problem in cryptography. With new requirements, it is necessary to design a safe and efficient all homomorphic cryptosystem. Therefore, it is a hot topic for scholars to study the whole homomorphic cipher theory and design a practical homomorphic cryptosystem. The work of this paper is based on the following aspects: first, there is a comprehensive analysis of all homomorphic ciphers. In depth analysis, a representative homomorphic cryptosystem has been studied in this paper. The classical system in history, such as the RSA cryptosystem, the Paillier cryptosystem and the homomorphism of the ElGamal cryptosystem, has its own characteristics. This paper focuses on the analysis of the homomorphic characteristics of the public key cryptosystems, and the homomorphic ciphers. The system is classified and generalizes a variety of homomorphism characteristics. On this basis, a semantic security target full homomorphic cryptosystem is designed, and a secure two party point product calculation protocol is designed by using the above cryptosystem. Secondly, in order to grasp the design method of the whole homomorphic cryptosystem, this paper designs two classics based on Gentry thought. The whole homomorphism cryptosystem, an integer based (also called DGHV cryptosystem) and an all homomorphic cryptosystem based on ideal lattice, is studied and analyzed. On the basis of the analysis of the cryptology characteristics and limitations of the ideal lattice and the DGHV homomorphism cryptosystem, the classical DGHV homomorphism cryptosystem is improved and a kind of public cryptosystem is designed. Somewhat homomorphic Cryptosystem with small key size and higher efficiency. Again, in order to construct the whole homomorphic cryptosystem on the lattice, this paper designs a all homomorphic cryptosystem based on the post quantum security hypothesis LWE. In this paper, the key technology of the whole homomorphic cryptosystem is studied and given the key technology of the whole homomorphic cryptosystem, and the characteristic of the matrix operation is combined with the LWE as the carrier. An all homomorphism cryptosystem based on ciphertext expansion is designed, which avoids the additional security hypothesis in the classical homomorphism design. The security is more explicit. The public key size is O (n2l), and the plaintext is extended to O (n2l). The research and design of cryptosystem bring new ideas to homomorphic digital signature and homomorphic message authentication. On the basis of studying the whole homomorphism cryptosystem, this paper analyzes the message authentication process and designs an improved whole homomorphic message authentication algorithm. The security of the homomorphic message identification code is based on the design of pseudo random function. The improved algorithm in this paper ensures the non leaking and two kinds of non forgery of the plaintext, and provides new ideas and methods for the integrity authentication of some data. At the end of this paper, the work of the full text is summarized, and the next work plan is given.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.4
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