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Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti

CiteScore 2018: 1.41

SCImago Journal Rank (SJR) 2018: 0.342
Source Normalized Impact per Paper (SNIP) 2018: 1.076

Mathematical Citation Quotient (MCQ) 2018: 0.75

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Volume 7, Issue 1


Self-pairings on hyperelliptic curves

Steven D. Galbraith / Chang-An Zhao
Published Online: 2013-05-14 | DOI: https://doi.org/10.1515/jmc-2012-0009


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.

Keywords: Tate pairing; Weil pairing; self-pairing; pairing based cryptography

About the article

Received: 2012-05-09

Revised: 2012-11-15

Accepted: 2013-04-18

Published Online: 2013-05-14

Published in Print: 2013-07-01

Citation Information: Journal of Mathematical Cryptology, Volume 7, Issue 1, Pages 31–42, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc-2012-0009.

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