Cryptography: Theory and Practice,Second Edition
Cryptography: Theory and Practice,Second Edition
The Design of Rijndael
A Simple Algebraic Representation of Rijndael
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Essential Algebraic Structure within the AES
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
PolyBoRi: A framework for Gröbner-basis computations with Boolean polynomials
Journal of Symbolic Computation
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We analyze an algebraic representation of $\mathcal{AES}$128 as an embedding in $\mathcal{BES}$, 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 ${\mathcal{C}}_{1}$ and ${\mathcal{C}}_{2}$. ${\mathcal{C}}_{1}$ 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. ${\mathcal{C}}_{2}$ 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.