Extended Diffie-Hellmann Protocol Based on Lucas Actions

Abstract

Discrete log problem (DLP) is a special case of semigroup action problem (SAP) that leads to generalized DLP. The cryptographic protocols like Diffie-Helman/ Elgamal based on DLP may be extended using semigroup action problem (SAP). The effect of square root attacks like Pollard Rho, Shanks baby step - giant step on these extensions with group actions, led to the study of a square root attacks on the generalized DLP, in the cases when, the semigroup has a large sub group and with Matrix action on abelian groups. We propose to extend the study of square root attack, Shank's Baby-step Giant-step on the generalized DLP considering the special case of LUCAS actions on abelian groups.