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Erschienen in:
2008 | OriginalPaper | Buchkapitel
A Tree-Based Approach for Computing Double-Base Chains
verfasst von : Christophe Doche, Laurent Habsieger
Erschienen in: Information Security and Privacy
Verlag: Springer Berlin Heidelberg
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We introduce a tree-based method to find short Double-Base chains. As compared to the classical greedy approach, this new method is not only simpler to implement and faster, experimentally it also returns shorter chains on average. The complexity analysis shows that the average length of a chain returned by this tree-based approach is
$\frac{\log_2 n }{4.6419}\cdotp$
This tends to suggest that the average length of DB-chains generated by the greedy approach is not
O
(log
n
/loglog
n
). We also discuss generalizations of this method, namely to compute Step Multi-Base Representation chains involving more than 2 bases and extended DB-chains having nontrivial coefficients.