An Application of Nodal Curves

TL;DR

This paper introduces an efficient computational method for generalized Jacobians of nodal curves and demonstrates its application in a probabilistic public key cryptographic algorithm.

Contribution

It presents a novel polynomial-based representation for elements in the Jacobian of nodal curves and applies this to develop a new cryptographic scheme.

Findings

Efficient computation method for generalized Jacobians of nodal curves.

A new probabilistic public key algorithm utilizing nodal curves.

Improved performance over existing methods for similar cryptographic operations.

Abstract

In this work, we present an efficient method for computing in the generalized Jacobian of special singular curves, nodal curves. The efficiency of the operation is due to the representation of an element in the Jacobian group by a single polynomial. In addition, we propose a probabilistic public key algorithm as an application of nodal curves.