Paper 2010/388

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

Sanjit Chatterjee, Darrel Hankerson, and Alfred Menezes


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.

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. Abbreviated version appears in the proceedings of WAIFI 2010.
pairing-based cryptographyType 1 and type 4 pairings
Contact author(s)
s2chatte @ uwaterloo ca
2010-07-09: received
Short URL
Creative Commons Attribution


      author = {Sanjit Chatterjee and Darrel Hankerson and Alfred Menezes},
      title = {On the Efficiency and Security of Pairing-Based Protocols in the Type 1 and Type 4 Settings},
      howpublished = {Cryptology ePrint Archive, Paper 2010/388},
      year = {2010},
      note = {\url{}},
      url = {}
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