密码意义的置换多项式的存在性及构造问题研究

项目名称： 密码意义的置换多项式的存在性及构造问题研究

项目编号： No.61303255

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 李永强

作者单位： 中国科学院信息工程研究所

项目金额： 24万元

中文摘要： 项目主要目的是研究特征为2的有限域上具有密码学意义的置换多项式的存在性及构造等问题。有限域上的置换多项式可用于密码算法中的S盒。S盒是对称密码算法的重要组件，其安全强度对整个密码算法的安全性有重要影响。在实际应用中，为了算法的快速实现以及更好得抵抗差分攻击和线性攻击，S盒多采用有限域GF(2^{2k})上具有低差分均匀度和高非线性度的置换。但已知的具有良好密码学性质的S盒和构造方法较少，因此如何设计安全的S盒是密码学中一个重要的问题。 本项目建立在申请人已有的研究基础上，进一步系统地研究具有优良密码学性质的S盒的构造方法及相关理论。特别是研究GF(2^{2k})上APN置换的存在性和具有最佳非线性度的4差分均匀置换的构造，以及适用于轻量级密码算法的S盒的构造等兼具理论和实际应用意义的问题。力争在项目周期内，发展出更多的S盒构造方法，在S盒的构造理论以及实际应用方面取得较大进展。

中文关键词： S盒；APN函数；差分均匀度；非线性度；MDS矩阵

英文摘要： The main subject of this research project is to study the existence and construction of cryptographically significant permutation polynomials over finite fields of character 2. These permutations can be used for substitution boxes(S-boxes) in symmetric cryptography algorithms. S-boxes play an important role in symmetric cryptography since they serve as the confusion part and in most cases are the only nonlinear part of round functions. Thus their security is essential for the security of the whole cryptography algorithm. For efficiency of implementations and resistance of differential attack and linear attack, an S-box is often designed as a permutation over GF(2^{2k}) with low differential uniformity and high nonlinearity in practice. On the other hand, only few S-boxes with excellent cryptography properties are known. Thus the problem of constructing excellent S-boxes is a main problem in cryptography. The research project is based on the former work of the applicant and to further study the construction of S-boxes and corresponding theory. Moreover, the project is devoted to study the problems of the existence of APN permutations over GF(2^{2k}), the construction of differentially 4-uniform permutations with the best known nonlinearity over GF(2^{2k}) and the construction of S-boxes suitable for lightweight c

英文关键词： S-box；APN function；differential uniformity；nonlinearity；MDS matrix