Complete group law for genus 2 Jacobians on Jacobian coordinates

Elif Ozbay Gurler; Huseyin Hisil

Paper 2024/623

Complete group law for genus 2 Jacobians on Jacobian coordinates

Elif Ozbay Gurler

, TU Darmstadt

Huseyin Hisil

, University of Wollongong

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 $c h a r (K) \neq 2$ . 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: Published elsewhere. Journal of Cryptographic Engineering
DOI: 10.1007/s13389-024-00351-7
Keywords: group law genus 2 hyperelliptic curves explicit formulas Jacobian coordinates
Contact author(s): elif oezbay @ tu-darmstadt de
hhisil @ uow edu au
History: 2024-04-26: approved; 2024-04-22: received; See all versions
Short URL: https://ia.cr/2024/623
License: CC BY

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},
      doi = {10.1007/s13389-024-00351-7},
      url = {https://eprint.iacr.org/2024/623}
}