Extended Diffie-Hellmann Protocol Based on Lucas Actions


Keywords:
Lucas group actions, Lucas Semigroup actions, Generalized discrete log problems, Extended Diffie-Hellmann protocolAbstract
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.
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Copyright (c) 2023 International Journal of Mathematics And its Applications

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