A cryptanalytic attack on the LUC cryptosystem using continued fractions

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 $mgeq -1$ and nonnegative integers $r$ and $s$, using continued fractions. We derive bounds for $r$ and $s$ using results on Diophantine approximations