具有最优代数免疫度的布尔函数研究

发布时间：2018-07-03 03:46

本文选题：布尔函数 + 代数免疫度　；参考：《西安邮电大学》2017年硕士论文

【摘要】：在当今的信息社会里,信息化已经普及到了人们生活的方方面面。但是,近些年来,个人信息泄漏导致的诈骗案件和各种泄密事件的发生,使得信息安全成为社会关注的焦点问题,这也推动了现代密码学理论的研究和技术的应用。现代密码体制分为私钥密码体制和公钥密码体制。私钥密码体制需要使用布尔函数作为非线性部件,以增强密码体制的安全性。为了保证密码体制的安全性,布尔函数必须具备优良的密码学性质以抵抗不同的密码学攻击。由于近些年代数攻击的兴起,构造具有最优代数免疫度的函数成了布尔函数的热点研究内容之一。本文首先研究分析现有的基于Reed-Muller码的构造函数,在其基础上,提出了两种新的具有最优代数免疫度的布尔函数的构造方法,并证明了新的构造函数具有很高的非线性度。主要工作如下:1)令n是奇数,通过修改择多函数的支撑集合,我们构造了一类基于Reed-Muller码的具有最优代数免疫度的n元布尔函数。当n = ｛11,13,15,19,21｝时,这类函数可以接近其他同类的非线性度。当n = 17时,这类函数具有比其他同类高的非线性度。借助Simon Fischer的程序验证,当n比较小时,构造函数f具有较高的抵抗快速代数攻击的能力,FAI(f)= n—3。2)令n是偶数,通过修改择多函数的支撑集合,我们构造了一类基于Reed-Muller码的具有最优代数免疫度的n元布尔函数。当n比较小时,这类函数的非线性度可以接近同类的函数。借助Simon Fischer的程序验证,当n比较小时,构造函数f具有接近次优的抵抗快速代数攻击的能力,FAI=n-2。
[Abstract]:In today's information society, information has been popularized to all aspects of people's lives. However, in recent years, the fraud cases caused by personal information leakage and the occurrence of various leak incidents make information security become the focus of attention of the society, which also promotes the research of modern cryptography theory and the application of technology. Modern cryptosystem is divided into private key cryptosystem and public key cryptosystem. The private key cryptosystem needs to use Boolean function as a nonlinear component to enhance the security of the cryptosystem. In order to ensure the security of cryptographic systems, Boolean functions must have good cryptographic properties to resist different cryptographic attacks. Due to the rise of algebraic attacks in recent years, the construction of functions with optimal algebraic immunity has become one of the hot topics in the research of Boolean functions. In this paper, we first study and analyze the existing constructors based on Reed-Muller codes. On the basis of them, we propose two new methods of constructing Boolean functions with optimal algebraic immunity, and prove that the new constructors have high nonlinearity. The main work is as follows: 1) Let n be odd. By modifying the support set of multifunction, we construct a class of n-variable Boolean functions with optimal algebraic immunity based on Reed-Muller codes. When n = {1113 / 15 / 19 / 21}, this kind of function can approach the nonlinear degree of other similar class. When n = 17:00, this class of functions has a higher degree of nonlinearity than other similar functions. With the help of Simon Fischer's program, when n is small, the constructor f has a higher ability to resist fast algebraic attack (FAI (f) = n-3.2) so that n is even, and by modifying the support set of multifunction, We construct a class of n-variable Boolean functions with optimal algebraic immunity based on Reed-Muller codes. When n is small, the degree of nonlinearity of this kind of function can be close to that of the same kind of function. With the help of Simon Fischer's program, when n is small, the constructor f has the ability to resist fast algebraic attack.
【学位授予单位】：西安邮电大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN918.1

【参考文献】