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On the Efficiency and Security of Pairing-Based Protocols in the Type 1 and Type 4 Settings

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Arithmetic of Finite Fields (WAIFI 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6087))

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Abstract

We focus on the implementation and security aspects of cryptographic protocols that use Type 1 and Type 4 pairings. On the implementation front, we report improved timings for Type 1 pairings derived from supersingular elliptic curves in characteristic 2 and 3 and the first timings for supersingular genus-2 curves in characteristic 2 at the 128-bit security level. In the case of Type 4 pairings, our main contribution is a new method for hashing into \(\mathbb{G}_2\) which makes the Type 4 setting almost as efficient as Type 3. On the security front, for some well-known protocols we discuss to what extent the security arguments are tenable when one moves to genus-2 curves in the Type 1 case. In Type 4, we observe that the Boneh-Shacham group signature scheme, the very first protocol for which Type 4 setting was introduced in the literature, is trivially insecure, and we describe a small modification that appears to restore its security.

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Author information

Authors and Affiliations

  1. Department of Combinatorics & Optimization, University of Waterloo,  

    Sanjit Chatterjee & Alfred Menezes

  2. Department of Mathematics and Statistics, Auburn University,  

    Darrel Hankerson

Authors
  1. Sanjit Chatterjee
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  2. Darrel Hankerson
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  3. Alfred Menezes
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    M. Anwar Hasan

  2. Department of Informatics, HIB, University of Bergen, PB 7803, 5020, Bergen, Norway

    Tor Helleseth

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Chatterjee, S., Hankerson, D., Menezes, A. (2010). On the Efficiency and Security of Pairing-Based Protocols in the Type 1 and Type 4 Settings. In: Hasan, M.A., Helleseth, T. (eds) Arithmetic of Finite Fields. WAIFI 2010. Lecture Notes in Computer Science, vol 6087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13797-6_9

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  • DOI: https://doi.org/10.1007/978-3-642-13797-6_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13796-9

  • Online ISBN: 978-3-642-13797-6

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