In this thesis, through the use of some basic cryptography tools ( digital signature, Hash function, secret sharing and zero-knowledge proof, and so on), the systemic research and design of secure electronic auction is carried out.

Based on the ideas of undeniable digital signature and confirmer digital signature, a new zero-knowledge proof scheme of possessing a DSA digital signature is proposed which can be used to prevent the arbitrary distribution of digital signature.

基于不可否认签名和可证实签名的思想，提出了一种拥有DSA数字签名的零知识证明新方案。

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In the scheme the prover has not to give directly the DSA signature of a message, but to give a zero-knowledge proof of possessing a DSA digital signature of the message.

该方案给出了防止DSA数字签名任意传播的一种新方法&签名者不直接提供对信息M的签名，而是提供拥有该信息的数字签名的一个零知识证明。

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At the same time, same security level as RSA has can be achieved by ellipse curve-based zero knowledge proof with the key much shorter in length than that of RSA.

同时基于椭圆曲线上的零知识证明可以用比RSA短得多的密钥，达到与RSA同等级别的安全性。

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Now there have been some cryptography protocol designed in UC framework and proved its security: such as encryption, digital signatures, zero-knowledge proof.

现在已有一些密码学协议基于UC框架进行设计，并证明其安全性：如加密、数字签名、零知识证明等。

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The dissertation constructs zero-knowledge proof and Brands' restrictive blind signature based on elliptic curve cryptosystem, and then applies these schems to electronic payment system based on elliptic curve cryptosystem.

本文构造了基于椭圆曲线加密体制的零知识证明和Brands限制性盲签名方案，应用于本文构造的基于椭圆曲线加密体制的电子支付系统。

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Improvement of A Zero Knowledge Password Authentication Based on Ellipse Curve on Kerberos System

基于椭圆曲线的零知识证明方法对Kerberos系统的改进

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Improving Solution to Zero-knowledge Proving of Decoding RSA Capability

破译RSA能力的零知识证明的改进方案

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XML Digital Signature Scheme Based on Zero Knowledge Proof

基于零知识证明的XML数字签名方案

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Zero-knowledge proof schemes of possessing a RSA digital signature are proposed.

提出了一种拥有RSA数字签名的零知识证明方案。

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A Zero-Knowledge Proof Scheme of Possessing a DSA Digital Signature

DSA数字签名的零知识证明

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It is proposed to apply the theory of private homomorphism to encrypt the database important or sensitive information, thus realizing direct operation of encrypted message.

提出了把秘密同态理论应用于加密数据库中重要或敏感的信息，从而可以实现直接对数据库密文进行操作的方法。

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Based on the combination of a public-key cryptosystem of the homomorphic encryption and on the theoretic construction relying on the F-hiding assumption, a protocol for comparing information of equality is proposed. The protocol needs only a single round of interaction and ensures fairness, efficiency and security.

基于F-隐藏假设以及同态公钥加密体制的语义安全性假设，给出了一个特殊的安全双方计算协议枣无信息泄漏的比较相等协议。

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This paper presents a new type of anonymous fingerprinting scheme, which is based on homomorphic public key cryptosystems.

分析了现有的基于同态公钥加密体制的数字指纹方案所存在的问题，提出了一种基于同态公钥加密体制的匿名数字指纹方案。

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An Anonymous Fingerprinting Scheme Based on Homomorphic Public Key Cryptosystems

一种基于同态公钥加密体制的匿名数字指纹方案

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Compared with the general encryption algorithm, homomorphic encryption can implement not only the basic cryptographic operations, but also specific types of computations on ciphertexts, which means the results of calculating before decrypting is same as decrypting before calculating.

与一般加密算法相比，同态加密除了能实现基本的加密操作之外，还能实现密文间的多种计算功能，即先计算后解密可等价于先解密后计算。

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The second system ( i.e., the strengthened version of the first one) achieved more efficient security reduction by incorporating the straight-line extraction paradigm and removed random oracles by using the non-interactive zero-knowledge argument from homomorphic encryption.

第二个系统（即前一个系统的增强版本）利用直线提取技术实现了更为高效的安全性归约过程，并借助基于同态加密的非交互零知识论证避免了对随机预言机的使用。

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In this paper, the main work of the homomorphic encryption as follows: First of all, introduce several typical homomorphic encryption schemes, including partially homomorphic encryption schemes and fully homomorphic encryption schemes.

本文在同态加密领域的主要工作如下：首先，介绍分析了几种典型的同态加密方案，包括半同态和全同态方案。

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With the strict analysis of the characteristics of homomorphic encryption, we realize that the reasonable using of this technology can reduce the computational complexity and communication complexity of multi-party computation.

通过对同态加密技术特点的深入分析，得知合理利用此技术可降低多方计算协议的计算复杂度与通信复杂度。

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But the defects of homomorphic encryption system still limit the scope of its application. Therefore, research on the theory and applications of homomorphic encryption is of great significance.

但目前同态加密体制的自身缺陷也限制了其应用的范围，所以从理论和应用两个方面研究同态加密具有重要的价值。

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Based on these work, we summarize the existing problems of homomorphic encryption cryptosystems, and propose further ideas. Next, introduce the "many-to-one" homomorphic encryption scheme.

在此基础上，总结同态加密体制存在的问题，并提出进一步研究设想。其次，提出并设计了多对一的同态加密方案。

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