密码函数的安全性指标研究

项目名称： 密码函数的安全性指标研究

项目编号： No.61272484

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 屈龙江

作者单位： 中国人民解放军国防科学技术大学

项目金额： 80万元

中文摘要： 密码函数包括布尔函数与向量函数两大类，是序列密码、分组密码和Hash 函数的重要组件，其密码学性质的好坏直接关系到密码算法的安全性。密码函数的差分均匀度、非线性度和代数免疫度是衡量以其为组件的密码算法抵抗差分攻击、线性攻击和代数攻击的能力的安全性指标。本项目将以代数学、纠错编码和组合设计等多学科的理论与方法为工具，研究密码函数的安全性指标，着重差分均匀度、非线性度和代数免疫度研究。具体研究内容包括：PN函数、APN函数等低差分函数的性质、构造与CCZ等价性研究，低差分置换的性质与构造；bent函数、向量bent函数和AB函数等高度非线性函数的性质、构造与分布研究；构造具有高代数免疫度的布尔函数与向量函数，尤其是同时具有高非线性度、高代数次数等多种安全性指标的密码函数。本项目的创新研究成果将构造出多种安全性指标折衷最优的密码函数，从而为密码算法中安全组件的选取提供新的理论依据和实现方法

中文关键词： 布尔函数；S-盒；非线性度；差分均匀度；代数免疫度

英文摘要： Composing by the two large classes of Boolean functions and vectorial functions,cryptographic functions are the most important components of stream cipher, block cipher and Hash function. Their cryptographic properties are crucial to the security of the ciphers. Differential uniformity, nonlinearity and algebraic immunity are three important security criteria of cryptographic functions, which can be used to measure the immunity of the ciphers who use these functions as their components to differential attack, linear attack and algebraic attack respectively. By using the theory and the methods of severial subjects such as algebra, error-correcting code and combinatorial design theory, this project will focus on the research of the security criteria of cryptographic functions, especially on the differential uniformity, nonlinearity and algebraic immunity. The main research contents of this project are as follows. (1) Properties, constructions and CCZ equivalence of the functions with low uniformity such as perfect nonlinear functions, almost perfect nonlinear functions, 4-uniform functions, etc. Properties and constructions of permutations with low differential uniformity. (2) Properties, constructions and the distribution of the functions with high nonlinearity such as bent functions, vectorial bent functions, a

英文关键词： Boolean function；S-box；nonlinearity；differential uniformity；algebraic immunity