密码向量函数的关键问题研究

密码向量函数在许多密码算法的设计中起核心作用， 是应用密码领域的重要研究课题之一。本项目研究密码向量函数理论中的关键问题。这些问题包括APN函数的构造方法和相关的理论问题；在二元域的偶数维空间上，具有最佳非线性度，高的代数次数和 代数免疫度的4差分置换的构造方法和相关的理论问题；具有轻量实现的最佳扩散层的构造方法和相关的理论问题；几乎Bent函数的CCZ等价类的几个相关公开问题的研究。对这些问题的研究一方面可以产生一些构造这些关键密码向量函数的方法，更加清楚地理解这些函数所遵循的规律；另一方面可以解决该领域一些公开问题，建立这些重要函数之间的内在联系。该项目将产生一批有实质意义的成果，并将提升我们在密码向量函数方面的研究能力。

Vectorial Boolean functions for Cryptography have been played an essentail role in design of cryptographic algorithms, is one of the important research topics for applied cryptography. The project investigates the key problems of vectorial Boolean functions for cryptography. These problems include construction methods and related theory for APN functions, differentially 4-uniform permutations in even numbers of variables (hopefully equal to powers of two) with optimal nonlinearity ,hight algebraic degrees and algebraic immunities, diffusive primitives with lightweight implementations. It also investigates several open problems related to CCZ-equivalence of Almost Bent functions. The project will produces some construction methods of these vectirial functions for cryptography and understand the roles followed by these functions on one hand, and will solve some open problems and establish some links among these key functions on the other hand. The project will generate some significant results, and enhance our research ability in vectorial Boolean functions for crytography.