An algebraic interpretation of AES-128

Abstract

We analyze an algebraic representation of AεS-128 as an embedding in BES, due to Murphy and Robshaw. We present two systems of equations S* and K* concerning encryption and key generation processes. After some simple but rather cumbersome substitutions, we should obtain two new systems C1 and C2. C1 has 16 very dense equations of degree up to 255 in each of its 16 variables. With a single pair (p, c), with p a cleartext and c its encryption, its roots give all possible keys that should encrypt p to c. C2 may be defined using 11 or more pairs (p, c), and has 16 times as many equations in 176 variables. K* and most of S* is invariant for all key choices. © Springer-Verlag Berlin Heidelberg 2005.