Abstract
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.
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Toli, I., Zanoni, A. (2005). An Algebraic Interpretation of \(\mathcal{AES}\) 128 . In: Dobbertin, H., Rijmen, V., Sowa, A. (eds) Advanced Encryption Standard – AES. AES 2004. Lecture Notes in Computer Science, vol 3373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11506447_8
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DOI: https://doi.org/10.1007/11506447_8
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