布尔函数在现代密码学中的应用THE APPLICATION OF THE BOOLEAN FUNCTION IN MODERN
CRYPTOGRAPHY
指导教师：
申请学位级别：学士
论文提交日期：2014年6月9日
摘要
在密码学中扮演着重要角色的布尔函数被广泛用于流密码和分组密码的分析和设计中。最主要的原因是布尔函数的密码学性质在某种程度上直接决定系统的安全性。本文是一篇关于布尔函数的密码学性质及其应用的文章。
文中首先介绍了布尔函数的研究背景、重要性及国内外研究现状，并概述了
密码学相关的基础知识，给出了布尔函数的定义，对其各种表示方法和研究方法进行介绍，主要介绍了真值表，小项表示等。
其次讨论了布尔函数的几个密码学性质和定理，重点介绍了作为布尔函数研究的一个重要工具——Walsh谱，并介绍了布尔函数的密码学性质，主要包括非线性、平衡性、相关免疫和严格雪崩等。
最后重点研究了布尔函数在流密码和分组密码中的应用。序列密码体制的安全性取决于密钥流，而密钥流序列由密钥流生成器产生，在密钥流生成器中，布尔函数起着极其关键的作用。分组密码体制的算法中最具有代表性之一的是DES 算法，其设计的关键是S盒，而多输出布尔函数可以很好地用来描述S盒。
关键词：序列密码；分组密码；密钥流生成器；DES算法；S盒；布尔函数；Walsh谱
ABSTRACT
The Boolean function playing an important role in cryptology is widely used in the analyses and designs of stream cipher or block cipher.The main reason is that at some degree the cryptographic properties of Boolean function directly decide the security of system.This dissertation is devoted to the cryptographic properties and applications of the Boolean functions in modern cryptography.
Firstly the research background and significance of Boolean function, and the status-quo of this research both at home and abroad are introduced.And the basic knowledge of cryptography are summarized,and the Boolean function is definited , furthermore the denotation methods and the research methods of the properties of Boolean function,mainly including the truth table and polynomial denotation, etc are summarized .
Secondly several cryptographic properties and theorem about the Boolean function are discussed , Walsh spectrum which is thought as an important tool of studying the Boolean function are introduced, and the cryptographic properties of the Boolean function, mainly including nonlinear, balance, related immune and strict avalanche,etc are introduced.
Finally we focuse on the applications of the Boolean function in stream cipher and block cipher. The security of stream cipher depends on the key stream furthermore the key stream sequences are generated by the key stream generators where the Boolean function plays an important role.One of the most representative block cipher algorithm is DES algorithms, which the key on designing is S-box,which can be described by multiple output Boolean function.
Key word：Stream cipher ; block cipher；key stream generators；S-box；Boolean function; Walsh spectrum
目录
1 前言 (1)
1.1 背景和意义 (1)
1.2 国内外研究现状综述 (1)
1.3 本文研究的主要内容 (2)
2 基本理论知识 (3)
2.1 密码学基本概念 (3)
2.2 布尔函数的基本知识 (5)
2.3 布尔函数的研究方法 (8)
3 布尔函数的密码学性质 (10)
3.1 布尔函数的Walsh变换及其性质 (10)
3.2 布尔函数的线性性 (11)
3.3 布尔函数的非线性性 (12)
3.4 相关免疫性 (13)
3.5 布尔函数的平衡性 (13)
3.6 布尔函数的对称性 (14)
3.7 严格雪崩准则 (14)
3.8 扩散准则 (14)
4 序列密码与布尔函数 (15)
4.1 序列密码概述 (15)
