Pollard RHO algorithm implemented to Discrete Log with Lucas sequences

Abstract

The Diffie - Hellman problem may be used securely over the multiplicative group F*p, (Z/nZ)* and the group of rational points on an elliptic curve over a finite field. These groups involve large key sizes or expensive arithmetic operations. In the paper [17] paper we considered the group of Lucas sequences and described the generalization of discrete log problem with the group of Lucas sequences and adapted the baby-step giant-step algorithm to the generalization and for the computations we gave an algorithm to fast computing methods for lucas sequences based on the idea proposed by P.J.Smith. In this paper we consider the group of Lucas sequences and implement the pollard rho algorithm to the generalization of discrete log problem to the group of Lucas sequences. For the computations we implement with fast computing algorithm.