Group Operation on Nodal Curves
Kubra Nari, Enver Ozdemir
TL;DR
This paper introduces an efficient computational method for the Generalized Jacobian of certain singular curves, leveraging polynomial representations to simplify group operations.
Contribution
It presents a novel polynomial-based approach for group operations in the Jacobian of special singular curves, improving computational efficiency.
Findings
Polynomial representation enables faster computations.
Method applies to specific classes of singular curves.
Significantly reduces computational complexity.
Abstract
In this work, we present an efficient method for computing in the Generalized Jacobian of special singular curves. The efficiency of the operation is due to representation of an element in the Jacobian group by a single polynomial.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Cryptography and Residue Arithmetic · Polynomial and algebraic computation