本文選題：布爾函數 + 代數免疫度��； 參考：《西安郵電大學》2017年碩士論文

【摘要】：在當今的信息社會里,信息化已經普及到了人們生活的方方面面。但是,近些年來,個人信息泄漏導致的詐騙案件和各種泄密事件的發(fā)生,使得信息安全成為社會關注的焦點問題,這也推動了現代密碼學理論的研究和技術的應用�，F代密碼體制分為私鑰密碼體制和公鑰密碼體制。私鑰密碼體制需要使用布爾函數作為非線性部件,以增強密碼體制的安全性。為了保證密碼體制的安全性,布爾函數必須具備優(yōu)良的密碼學性質以抵抗不同的密碼學攻擊。由于近些年代數攻擊的興起,構造具有最優(yōu)代數免疫度的函數成了布爾函數的熱點研究內容之一。本文首先研究分析現有的基于Reed-Muller碼的構造函數,在其基礎上,提出了兩種新的具有最優(yōu)代數免疫度的布爾函數的構造方法,并證明了新的構造函數具有很高的非線性度。主要工作如下:1)令n是奇數,通過修改擇多函數的支撐集合,我們構造了一類基于Reed-Muller碼的具有最優(yōu)代數免疫度的n元布爾函數。當n = ｛11,13,15,19,21｝時,這類函數可以接近其他同類的非線性度。當n = 17時,這類函數具有比其他同類高的非線性度。借助Simon Fischer的程序驗證,當n比較小時,構造函數f具有較高的抵抗快速代數攻擊的能力,FAI(f)= n—3。2)令n是偶數,通過修改擇多函數的支撐集合,我們構造了一類基于Reed-Muller碼的具有最優(yōu)代數免疫度的n元布爾函數。當n比較小時,這類函數的非線性度可以接近同類的函數。借助Simon Fischer的程序驗證,當n比較小時,構造函數f具有接近次優(yōu)的抵抗快速代數攻擊的能力,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.
【學位授予單位】：西安郵電大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN918.1

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本文編號：2092252