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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 / Dawson, Ed / 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 2017: 1.43

SCImago Journal Rank (SJR) 2017: 0.293
Source Normalized Impact per Paper (SNIP) 2017: 1.117

Mathematical Citation Quotient (MCQ) 2017: 0.51

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Volume 3, Issue 1


Distortion maps for supersingular genus two curves

Steven D. Galbraith
  • Mathematics Department, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom. Email:
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/ Jordi Pujolàs / Christophe Ritzenthaler
  • Institut de Mathématiques de Luminy, UMR 6206 du CNRS, Luminy, Case 907, 13288 Marseille, France. Email:
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  • De Gruyter OnlineGoogle Scholar
/ Benjamin Smith
  • INRIA Saclay–Île-de-France, Laboratoire d'Informatique (LIX), École polytechnique, 91128 Palaiseau, France. Email:
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  • De Gruyter OnlineGoogle Scholar
Published Online: 2009-06-10 | DOI: https://doi.org/10.1515/JMC.2009.001


Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated, since the full torsion subgroup has rank 2g. In this paper, we prove that distortion maps always exist for supersingular curves of genus g > 1. We also give several examples of curves of genus 2 with explicit distortion maps for embedding degrees 4, 5, 6, and 12.

Keywords.: Hyperelliptic curve cryptography; pairings; supersingular curves; distortion maps

About the article

Received: 2006-11-30

Revised: 2009-01-08

Published Online: 2009-06-10

Published in Print: 2009-05-01

Citation Information: Journal of Mathematical Cryptology, Volume 3, Issue 1, Pages 1–18, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/JMC.2009.001.

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