Rijndael算法的代数描述

摘要

This paper gives algebraic descriptions of Rijndael Advanced Encryption Standard (AES). It provides first the algebraic descriptions of the two important steps, which are S-boxes and key Schedule, for only one round in the most popular AES-128, then work out the equations for one-round with the results. Logically induct multiple round from single ones, promote it to AES-192 and AES-256 with discussing the possibility, and at last, states simply the realization of these algebraic descriptions with computers.%给出Rijndael高级密码标准方法的代数描述.首先针对最常用的AES-128给出单次循环中两个主要步骤S-boxes和key Schedule的代数描述,然后利用结果推导单次循环的表达式,并将其合理组合归纳得多次循环.之后推广至AES-192和AES-256,并探讨可行性.最后简单讨论该代数描述方法的计算机实现.