Welcome to the resource topic for 2004/367
Title:
On the Affine Transformations of HFE-Cryptosystems and Systems with Branches
Authors: Patrick Felke
Abstract:We show how to recover the affine parts of the secret key for a
certain class of HFE-Cryptosystems. Further we will show that any
system build on branches can be decomposed in its single branches
in polynomial time on average. The first part generalizes the
result from \cite{geisel} to a bigger class of systems and is
achieved by a different approach. Dispite the fact that systems
with branches are not used anymore (see
\cite{patarin1, goubin}), our second result is a still of
interest as it applies to a very general class of
HFE-cryptosystems and thus is a contribution to the list of
algebraic properties, which cannot be hidden by composition with
the secret affine transformations. We derived both algorithms by
considering the cryptosystem as objects from the theory of
nonassociative algebras and applying classical techniques from
this theory. This general framework might be useful for future
investigations of HFE-Cryptosysstems or to generalize other
attacks known so far.
ePrint: https://eprint.iacr.org/2004/367
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