A zero-dimensional gröbner basis for AES-128

Authors:
Johannes Buchmann;Andrei Pyshkin;Ralf-Philipp Weinmann
Affiliations:
Fachbereich Informatik, Technische Universität Darmstadt, Darmstadt, Germany;Fachbereich Informatik, Technische Universität Darmstadt, Darmstadt, Germany;Fachbereich Informatik, Technische Universität Darmstadt, Darmstadt, Germany
Venue:
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
Year:
2006

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Abstract

We demonstrate an efficient method for computing a Gröbner basis of a zero-dimensional ideal describing the key-recovery problem from a single plaintext/ciphertext pair for the full AES-128. This Gröbner basis is relative to a degree-lexicographical order. We investigate whether the existence of this Gröbner basis has any security implications for the AES.