Gesellschaft fr Informatik e.V.

Lecture Notes in Informatics

WEWoRC 2005 -Western European Workshop on Research in Cryptology P-74, 13-21 (2005).

Gesellschaft für Informatik, Bonn


Christopher Wolf, Stefan Lucks, Po-Wah Yau (eds.)

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Algebraic attacks and annihilators

Frederik Armknecht


Algebraic attacks on block ciphers and stream ciphers have gained more and more attention in cryptography. Their idea is to express a cipher by a system of equations whose solution reveals the secret key. The complexity of an algebraic attack generally increases with the degree of the equations. Hence, low-degree equations are crucial for the efficiency of algebraic attacks. In the case of simple combiners over $GF(2)$, it was proved in [9] that the existence of low-degree equations is equivalent to the existence of low-degree annihilators, and the term ”algebraic immunity” was introduced. This result was extended to general finite fields GF (q) in [4]. In this paper, which improves parts of the unpublished eprint paper [2], we present a generalized framework which additionally covers combiners with memory and S- Boxes over GF (q). In all three cases, the existence of low-degree equations can be reduced to the existence of certain annihilators. This might serve as a starting point for further research.

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Gesellschaft für Informatik, Bonn
ISBN 3-88579-403-9

Last changed 24.01.2012 21:52:36