Paper 2024/623 Original: eprint.iacr.org/2024/623 ↗
Complete group law for genus 2 Jacobians on Jacobian coordinates
Abstract
This manuscript provides complete, inversion-free, and explicit group law formulas in Jacobian coordinates for the genus 2 hyperelliptic curves of the form $y^2 = x^5 + a_3 x^3 + a_2 x^2 + a_1 x + a_0$ over a field $K$ with $char(K) \ne 2$. The formulas do not require the use of polynomial arithmetic operations such as resultant, mod, or gcd computations but only operations in $K$.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2024-04-22: last updated
- 2024-04-22: published
- Short URL
- https://ia.cr/2024/623
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2024/623,
author = {Elif Ozbay Gurler and Huseyin Hisil},
title = {Complete group law for genus 2 Jacobians on Jacobian coordinates},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/623},
year = {2024},
url = {https://eprint.iacr.org/2024/623}
}