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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)
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
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Short URL
https://ia.cr/2013/532
License
Creative Commons Attribution
CC BY
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