Paper 2010/475
Pairing Computation on Elliptic Curves of Jacobi Quartic Form
Hong Wang, Kunpeng Wang, Lijun Zhang, and Bao Li
Abstract
This paper proposes explicit formulae for the addition step anddoubling step in Miller's algorithm to compute Tate pairing onJacobi quartic curves.We present a geometric interpretation of the group law on Jacobiquartic curves, %and our formulae for Miller's%algorithm come from this interpretation.which leads to formulae for Miller's algorithm. The doubling stepformula is competitive with that for Weierstrass curves and Edwardscurves. Moreover, by carefully choosing the coefficients, thereexist quartic twists of Jacobi quartic curves from which pairingcomputation can benefit a lot. Finally, we provide some examples ofsupersingular and ordinary pairing friendly Jacobi quartic curves.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Published elsewhere. unpublished
- Keywords
- elliptic curvepairinggeometric interpretation
- Contact author(s)
- hwang @is ac cn
- History
- 2010-10-25: revised
- 2010-09-08: received
- See all versions
- Short URL
- https://ia.cr/2010/475
- License
CC BY
BibTeX
@misc{cryptoeprint:2010/475, author = {Hong Wang and Kunpeng Wang and Lijun Zhang and Bao Li}, title = {Pairing Computation on Elliptic Curves of Jacobi Quartic Form}, howpublished = {Cryptology {ePrint} Archive, Paper 2010/475}, year = {2010}, url = {https://eprint.iacr.org/2010/475}}