Duffing oscillator and elliptic curve cryptography

TL;DR

This paper introduces a novel discretization method for the Duffing oscillator using elliptic curve cryptography, resulting in integrable maps that do not rely on small parameter assumptions.

Contribution

It presents a new approach combining elliptic curve cryptography with the discretization of the Duffing equation, creating integrable maps without small parameter constraints.

Findings

Derived integrable discrete maps for the Duffing oscillator

Utilized elliptic curve cryptography operations in discretization

Achieved discretization independent of small parameter assumptions

Abstract

A new approach to discretization of the Duffing equation is presented. Integrable discrete maps are obtained by using well-studied encrypting operations in elliptic curve cryptography and, therefore, they do not depend upon standard small parameter assumption.