Original scientific paper
A cryptanalytic attack on the LUC cryptosystem using continued fractions
Bernadin Ibrahimpašić
orcid.org/0009-0003-5902-7208
; Pedagogical Faculty, University of Bihać, Bihać, Bosnia and Herzegovina
Abstract
The LUC cryptosystem is a modification of the RSA cryptosystem based on Lucas sequences.
In this paper we extend the Verheul - van Tilborg and Dujella variants
of the Wiener attack on RSA to the LUC cryptosystem. We describe an
algorithm for finding a secret key $d$ of the form $d = r q_{m+1} \pm s q_m$, for some $m\geq -1$ and nonnegative integers $r$ and $s$, using continued fractions.
We derive bounds for $r$ and $s$ using results on Diophantine approximations.
Keywords
cryptanalysis; LUC cryptosystem; diophantine approximations
Hrčak ID:
37366
URI
Publication date:
3.6.2009.
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