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 G2 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.
S. Chatterjee, D. Hankerson, and A. Menezes REF reported preliminary timings for Type 1 (symmetric) pairings on supersingular genus-2 curves of characteristic 2 at the 128-bit security level.
A.: On the efficiency and security of pairing-based protocols in the type 1 and type 4 settings
IACR Cryptology ePrint Archive
IACR Cryptology ePrint Archive
Mathematics Computer Science