ELGamal数字签名

摘要

随着网络的发展，人们之间的各种交流变得越来越来方便，但同时也对信息传递的安全提出了新的要求，数字签名随之广泛的深入到了人们的日常生活中。

ELGamal作为目前应用比较广泛的数字签名算法，其安全性，以及可实现程度，在很大程度上决定了它的应用范围。本文主要对数字签名体制中的签名和认证过程中所需的模块，进行了必要的描述大整数运算算法，素性测试和随机数生成算法，ABSTRACT

With the development of network, the communions between people become more and more convenient, but also it brings forward the new security requirements of information transfer. Digital Signature goes into the people's daily life along with these processes.

As one of the most widely used Digital Signature, the application of the ELGamal Signature is largely depend on his information security and the operation process. In this paper, we will discuss the process of the ELGamal Signature and the attestation. One can check his authorization of the sign which rely on the problem of the discrete logarithm. And then we will analyze the security of the signature. The application the ELGamal signature in the ID-BASE system will also be discussed. The key part of this paper is to introduce the concept the large integer. The arithmetic of the large integer is crucial in most cryptosystems.As to the construction of a large prime integer,we will discuss the method to construct a Random Number and the primality test.Then the high-order-cycle generator method for the formation of the foundation will introduced too.In the last part of the paper,we will go through the process of the ELGamal Signature.

keywords: ELGamal Digital Signature authorization large Integer

large Prime Number generator

目录

第一章 绪论1

1.1 数字签名算法研究的背景1

1.1.1 信息安全的重要性1

1.1.2 数字签名的概念1

1.1.3认证的基本概念2

1.2 ELGamal签名算法概述3

1.3 ELGamal签名算法的主要应用领域4

1.4 本文的研究安排4

第二章 ELGamal数字签名5

2.1 ELGamal公钥密码体制5

2.1.1 Diffie-Helfman体制5

2.1.2 ELGamal密码体制6

2.2 ELGamal数字签名体制6

2.2.1 ELGamal签名体制6

2.2.2 ELGamal签名安全性分析8

2.3 基于身份的ELGamal签名体制9

2.3.1 身份认证概念9

2.3.2 双线性对的概念10

2.3.4 公钥密码体制的概念10

2.3.4 椭圆曲线密码体制的概念11

2.3.5 基于身份的ELGamal签名具体步骤于验证过程12

2.4 本章小结13

第三章 ELGamal签名算法的软件实现15

3.1 大整数的概念15

3.