Compositeness test with nodal curves

ABSTRACT

In this work, we present a use of nodal curves to detect the compositeness of a given odd integer $n\equiv 1\mathrm{mod}4$. The method relies on the extension of Mumford representation and Cantor's algorithm for special singular curves.

KEYWORDS:

• Nodal curves
• generalized Jacobian
• primality test

CLASSIFICATION:

• 11Y11
• 11Y16
• 11G20
• 11G99
• 68W20

Acknowledgments

This study has greatly benefited from the conversations with Larry Washington. I would like to sincerely thank all referees and the associated editor for their constructive comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The research is supported by TUBITAK under Research Grant [BIDEB-2232-114C050].