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An Algebraic Interpretation of \(\mathcal{AES}\)128

  • Ilia Toli
  • Alberto Zanoni
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3373)

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.

Keywords

Block Cipher Advance Encryption Standard Hilbert Series Block Diagonal Matrix Linear Cryptanalysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ilia Toli
    • 1
  • Alberto Zanoni
    • 1
  1. 1.Dipartimento di Matematica Leonida TonelliUniversità di PisaPisaItaly

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