Paper 2013/532
On a Relation between the Ate Pairing and the Weil Pairing for Supersingular Elliptic Curves
Takakazu Satoh
Abstract
The hyperelliptic curve Ate pairing provides an efficient way to compute a bilinear pairing on the Jacobian variety of a hyperelliptic curve. We prove that, for supersingular elliptic curves with embedding degree two, square of the Ate pairing is nothing but the Weil pairing. Using the formula, we develop an X-coordinate only pairing inversion method. However, the algorithm is still infeasible for cryptographic size problems.
Note: Errors in Lemma 3.2, Lemma 4.1 and Theorem 4.3 are corrected. Statements of main results are not affected.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Ate pairingWeil pairing
- Contact author(s)
- satoh df603 @ gmail com
- History
- 2019-04-07: last of 2 revisions
- 2013-08-30: received
- See all versions
- Short URL
- https://ia.cr/2013/532
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2013/532,
author = {Takakazu Satoh},
title = {On a Relation between the Ate Pairing and the Weil Pairing for Supersingular Elliptic Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/532},
year = {2013},
url = {https://eprint.iacr.org/2013/532}
}
