Cryptology ePrint Archive: Report 2013/532
On a Relation between the Ate Pairing and the Weil Pairing for Supersingular Elliptic Curves
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.
Category / Keywords: public-key cryptography / Ate pairing, Weil pairing
Date: received 25 Aug 2013, last revised 1 Oct 2013
Contact author: satoh df603 at gmail com
Available format(s): PDF | BibTeX Citation
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.
Version: 20131001:114931 (All versions of this report)
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