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BY-NC-ND 3.0 license Open Access Published by De Gruyter May 14, 2013

Self-pairings on hyperelliptic curves

  • Steven D. Galbraith EMAIL logo and Chang-An Zhao


A self-pairing is a pairing computation where both inputs are the same group element. Self-pairings are used in some cryptographic schemes and protocols. In this paper, we show how to compute the Tate–Lichtenbaum pairing on a curve more efficiently than the general case. The speedup is obtained by using a simpler final exponentiation. We also discuss how to use this pairing in cryptographic applications.

Received: 2012-05-09
Revised: 2012-11-15
Accepted: 2013-04-18
Published Online: 2013-05-14
Published in Print: 2013-07-01

© 2013 by Walter de Gruyter Berlin Boston

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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