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

Authors:
Sanjit Chatterjee
Darrel Hankerson
Alfred Menezes
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URL: http://eprint.iacr.org/2010/388
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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 the Type 4 setting was introduced in the literature, is trivially insecure, and we describe a small modification that appears to restore its security.
BibTeX
@misc{eprint-2010-23289,
  title={On the Efficiency and Security of Pairing-Based Protocols in the Type 1 and Type 4 Settings},
  booktitle={IACR Eprint archive},
  keywords={cryptographic protocols / pairing-based cryptography, Type 1 and type 4 pairings},
  url={http://eprint.iacr.org/2010/388},
  note={Abbreviated version appears in the proceedings of WAIFI 2010. s2chatte@uwaterloo.ca 14799 received 8 Jul 2010},
  author={Sanjit Chatterjee and Darrel Hankerson and Alfred Menezes},
  year=2010
}