Computational and Algebraic Aspects of the Advanced Encryption Standard

The new Advanced Encryption Standard (AES) has been recently selected by the US government to replace the old Data Encryption Standard (DES) for protecting sensitive official information. Due to its simplicity and elegant algebraic structure, the choice of the AES algorithm has motivated the study of a new approach to the analysis of block ciphers. While conventional methods of cryptanalysis (e.g. differential and linear cryptanalysis) are usually based on a “statistical” approach, where an attacker attempts to construct statistical patterns through many interactions of the cipher, the so-called algebraic attacks exploit the intrinsic algebraic structure of a cipher. More specifically, the attacker expresses the encryption transformation as a set of multivariate polynomial equations and attempts to recover the encryption key by solving the system. In this paper we consider a number of algebraic aspects of the AES, and examine a few computational and algebraic techniques that could be used in the cryptanalysis of cipher. We show how one can express the cipher as a very large, though surprisingly simple, system of multivariate quadratic equations over the finite field F28 , and consider some approaches that can be used to solve this system.