Essential Algebraic Structure within the AES

摘要

One difficulty in the cryptanalysis of the Advanced Encryption Standard AES is the tension between operations in the two fields GF(2~8) and GF(2). This paper outlines a new approach that avoids this conflict. We define a new block cipher, the BES, that uses only simple algebraic operations in GF(2~8). Yet the AES can be regarded as being identical to the BES with a restricted message space and key space, thus enabling the AES to be realised solely using simple algebraic operations in one field GF(2~8). This permits the exploration of the AES within a broad and rich setting. One consequence is that AES encryption can be described by an extremely sparse overdetermined multivariate quadratic system over GF(2~8), whose solution would recover an AES key.