Abstract
The Dickson cryptosystem is a modification of the RSA and LUC based on the Dickson polynomial. In this paper, we consider Wiener's attack and Boneh-Durfee's algorithm on RSA to the Dickson cryptosystem. We then efficiently apply them when the secret exponent $d$ is sufficiently small compared to public modulus $n$. We show that if $d<(1/3\sqrt{2})n^{0.5}$, then Wiener's attack works. Furthermore, the bound on Boneh-Durfee's algorithm is extended up to $d<n^{0.585}$.
