ScholarLens Back to search
2002•Hindustan Book AgencyRequires access

The Addition Law on Hyperelliptic Jacobians

V. Kumar Murty

Open publisher page 1 citations

Abstract

It is a classical result that the addition law on the Jacobian of a hyperelliptic curve can be described in terms of explicit equations. Over the complex numbers, this can be done using theta function identities. Abstractly, the group law was written down by Cantor [1]. As observed by Koblitz [2], this makes it possible to use the set of points on the Jacobian of a hyperelliptic curve (or more succintly, a hyperelliptic Jacobian) over a finite field as the basis of a public-key cryptosystem.

About this research paper

What this paper is about

It is a classical result that the addition law on the Jacobian of a hyperelliptic curve can be described in terms of explicit equations. Over the complex numbers, this can be done using theta function identities. Abstractly, the group law was written down by Cantor [1]. As observed by Koblitz [2], this makes it possible to use the set of points on the Jacobian of a hyperelliptic curve (or more succintly, a hyperelliptic Jacobian) over a finite field as the basis of a public-key cryptosystem.

Why it matters

OpenAlex reports 1 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

It is a classical result that the addition law on the Jacobian of a hyperelliptic curve can be described in terms of explicit equations. Over the complex numbers, this can be done using theta function identities. Abstractly, the group law was written down by Cantor [1]. As observed by Koblitz [2], this makes it possible to use the set of points on the Jacobian of a hyperelliptic curve (or more succintly, a hyperelliptic Jacobian) over a finite field as the basis of a public-key cryptosystem.

Key concepts: Hyperelliptic curve, Jacobian matrix and determinant, Hyperelliptic curve cryptography, Mathematics, Group (periodic table), Pure mathematics, Algebra over a field, Law

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
The Addition Law on Hyperelliptic Jacobians — Research Paper | ScholarLens