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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: Introduction: some changes for clarification. Theorem 2.1(ii): vanishing of linear terms is added Lemma 4.4(ii): the statement is corrected. Conjecture on (5.3): an obvious necessary condition is added.
Metadata
- Available format(s)
- 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