Block ciphers sensitive to gröbner basis attacks

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:
CT-RSA'06 Proceedings of the 2006 The Cryptographers' Track at the RSA conference on Topics in Cryptology
Year:
2006

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Abstract

We construct and analyze Feistel and SPN ciphers that have a sound design strategy against linear and differential attacks but for which the encryption process can be described by very simple polynomial equations. For a block and key size of 128 bits, we present ciphers for which practical Gröbner basis attacks can recover the full cipher key requiring only a minimal number of plaintext/ciphertext pairs. We show how Gröbner bases for a subset of these ciphers can be constructed with neglegible computational effort. This reduces the key–recovery problem to a Gröbner basis conversion problem. By bounding the running time of a Gröbner basis conversion algorithm, FGLM, we demonstrate the existence of block ciphers resistant against differential and linear cryptanalysis but vulnerable against Gröbner basis attacks.