Paper 2012/551

Faster Pairing Computation on Jacobi quartic Curves with High-Degree Twists

Liangze Li, Hongfeng Wu, and Fan Zhang

Abstract

In this paper, we propose an elaborate geometric approach to explain the group law on Jacobi quartic curves which are seen as the intersection of two quadratic surfaces in space. Using the geometry interpretation we construct the Miller function. Then we present explicit formulae for the addition and doubling steps in Miller's algorithm to compute Tate pairing on Jacobi quartic curves. Both the addition step and doubling step of our formulae for Tate pairing computation on Jacobi curves are faster than previously proposed ones. Finally, we present efficient formulas for Jacobi quartic curves with twists of degree 4 or 6. For twists of degree 4, both the addition steps and doubling steps in our formulas are faster than the fastest result on Weierstrass curves. For twists of degree 6, the addition steps of our formulae are faster than the fastest result on Weierstrass curves.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Elliptic curveJacobi quartic curveTate pairingMiller function
Contact author(s)
whfmath @ gmail com
History
2012-09-24: received
Short URL
https://ia.cr/2012/551
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2012/551,
      author = {Liangze Li and Hongfeng Wu and Fan Zhang},
      title = {Faster Pairing Computation on Jacobi quartic Curves with High-Degree Twists},
      howpublished = {Cryptology ePrint Archive, Paper 2012/551},
      year = {2012},
      note = {\url{https://eprint.iacr.org/2012/551}},
      url = {https://eprint.iacr.org/2012/551}
}
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