Algebraic attacks over GF(q)

Batten, Lynn 2004, Algebraic attacks over GF(q), Lecture notes in computer science, vol. 3348, pp. 84-91, doi: 10.1007/b104579.

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Title Algebraic attacks over GF(q)
Formatted title Algebraic attacks over GF(q)
Author(s) Batten, LynnORCID iD for Batten, Lynn
Journal name Lecture notes in computer science
Volume number 3348
Start page 84
End page 91
Publisher Springer-Verlag
Place of publication Berlin, Germany
Publication date 2004
ISSN 0302-9743
Keyword(s) algebraic attacks
stream ciphers
finite fields
Summary 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.
Language eng
DOI 10.1007/b104579
Field of Research 080499 Data Format not elsewhere classified
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
HERDC collection year 2004
Copyright notice ©2004, Springer-Verlag
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