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Algebraic attacks over GF(q)
Recent algebraic attacks on LFSR-based stream ciphers and S-boxes have generated much interest as they appear to be extremely powerful. Theoretical work has been developed focusing around the Boo- lean function case. In this paper, we generalize this theory to arbitrary finite fields and extend the theory of annihilators and ideals introduced at Eurocrypt 2004 by Meier, Pasalic and Carlet. In particular, we prove that for any function f in the multivariate polynomial ring over GF(q), f has a low degree multiple precisely when two low degree functions appear in the same coset of the annihilator of f q – 1 – 1. In this case, many such low degree multiples exist.
History
Journal
Lecture notes in computer scienceVolume
3348Pagination
84 - 91Publisher
Springer-VerlagLocation
Berlin, GermanyPublisher DOI
ISSN
0302-9743eISSN
1611-3349Language
engPublication classification
C1 Refereed article in a scholarly journalCopyright notice
2004, Springer-VerlagUsage metrics
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