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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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
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