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Erschienen in:
2010 | OriginalPaper | Buchkapitel
On the Efficiency and Security of Pairing-Based Protocols in the Type 1 and Type 4 Settings
verfasst von : Sanjit Chatterjee, Darrel Hankerson, Alfred Menezes
Erschienen in: Arithmetic of Finite Fields
Verlag: Springer Berlin Heidelberg
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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.