Advertisement
Published in:
2006 | OriginalPaper | Chapter
Efficient Computation of Algebraic Immunity for Algebraic and Fast Algebraic Attacks
Authors : Frederik Armknecht, Claude Carlet, Philippe Gaborit, Simon Künzli, Willi Meier, Olivier Ruatta
Published in: Advances in Cryptology - EUROCRYPT 2006
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
In this paper we propose several efficient algorithms for assessing the resistance of Boolean functions against algebraic and fast algebraic attacks when implemented in LFSR-based stream ciphers. An algorithm is described which permits to compute the algebraic immunity
d
of a Boolean function with
n
variables in
$\mathcal{O}(D^2)$
operations, for
$D \approx \binom{n}{d}$
, rather than in
$\mathcal{O}(D^3)$
operations necessary in all previous algorithms. Our algorithm is based on multivariate polynomial interpolation. For assessing the vulnerability of arbitrary Boolean functions with respect to fast algebraic attacks, an efficient generic algorithm is presented that is not based on interpolation. This algorithm is demonstrated to be particularly efficient for symmetric Boolean functions. As an application it is shown that large classes of symmetric functions are very vulnerable to fast algebraic attacks despite their proven resistance against conventional algebraic attacks.