抗代数攻击的单输出和抗差分攻击的多输出密码函数研究

Single-output and Multi-output Boolean functions are often used as critical blocks in symmetric crypto-systems. In order to resist known attacks such as differential attacks, linear attacks and algebraic attacks et.al, cryptographic Boolean functions are required to meet many cryptographic criteria. In this project, we will focus on some problems as following: firstly, we will study the ability of Single-output Boolean functions to resist both standard and fast algebraic attacks, combining theoretical analysis and clever computer experiment, we will construct cryptographically robust Single-output Boolean functions; secondly, we will study the differential uniformity of Multi-output Boolean functions, we will construct mappings over finite fields, especially non-quadratic mappings with differential uniformity 4 over finite fields with even characteristic and even dimension.

用于对称密码系统的密码函数包括单输出布尔函数和多输出布尔函数，安全的密码函数需要能够抵抗多种已知攻击如差分攻击，线性攻击和代数攻击等，即满足多项安全性指标。本项目研究以下几个方面的问题：单输出布尔函数的抗代数攻击能力研究，包括标准代数攻击和快速代数攻击，通过理论分析结合计算机辅助实验，构造密码学意义上强壮的单输出函数；研究多输出布尔函数的差分均匀性，构造有限域上的低差分置换，特别是偶特征域上的差分均匀度为4的非2次的置换函数。

单输出和多输出密码函数是对称密码算法中的关键性安全性部件。本项目主要研究单输出函数抗代数攻击的性能和多输出置换函数抗差分攻击的性能，进一步分析和理解密码函数的各项安全性指标之间的关系，试图构造可用于实际密码算法的密码函数。置换性方面我们研究了若干特定类型的多项式，包括一类来源于Kloosterman和恒等式的多项式和几类项数稀疏的三项式和四项式，给出了这些多项式为置换的若干充分条件；基于有理函数和分段函数思想，我们构造了偶特征域上几类差分均匀度为6的，综合性质较好的置换。