The hyperelliptic curve Ate pairing provides an efficient way to compute a bilinear pairing on the Jacobian variety of a hyperelliptic curve. We prove that, for supersingular elliptic curves with embedding degree two, square of the Ate pairing is nothing but the Weil pairing. Using the formula, we develop an X -coordinate only pairing inversion method. However, the algorithm is still infeasible...

Frey and Rück have described a non-degenerate bilinear pairing on the Jacobians of curves; this includes elliptic curves. We present a new mathematical foundation for this pairing and use it to give a different proof of its non-degeneracy. We then present yet another method of looking at this pairing using isogenies.

Pairing-based cryptosystems rely on bilinear non-degenerate maps called pairings, such as the Tate and Weil pairings defined over certain elliptic curve groups. In this paper we show how to compress pairing values, how to couple this technique with that of point compression, and how to benefit from the compressed representation to speed up exponentiations involving pairing values, as required i...

Authenticated multiple key exchange (AMKE) protocols not only allow participants to warrant multiple session keys within one run of the protocol but also ensure the authenticity of the other party. Many AMKE protocols using bilinear pairings have been proposed. However, the relative computation cost of the pairing is approximately twenty times higher than that of the scalar multiplication over ...

Certificateless public key cryptography with bilinear pairing needs costly operations, which is not appropriate for a practical application. In this paper, we present a certificateless public key encryption scheme without bilinear pairing. This encryption scheme achieves Girault’s trust Level 3 as in traditional public key infrastructure based cryptography, and which is proved to be secure in t...

In many pairing-based cryptosystems, the secret keys are elements of bilinear groups. For safeguarding such secret keys or decrypting or signing in a threshold manner, Verifiable Secret Sharing (VSS) in bilinear groups is required. In this paper, we show a method of verifiably sharing a random secret in a bilinear group. Our method is simple and practical. It can be regarded as a generalisation...

Authenticated multiple key exchange (AMKE) protocols not only allow participants to warrant multiple session keys within one run of the protocol but also ensure the authenticity of the other party. Many AMKE protocols using bilinear pairings have been proposed. However, the relative computation cost of the pairing is approximately twenty times higher than that of the scalar multiplication over ...

A new ID-based group signature scheme, in which group managers and group members are all ID-based, is presented in this paper. Our scheme is obtained by using a new way to the construction of group signature schemes and based on an ID-based signature scheme from bilinear pairing. Due to the nice and simple constructive method and the sound properties of bilinear pairing, it is shown that the pr...

We present the first identity-based traitor tracing scheme. The scheme is shown to be secure in the standard model, assuming the bilinear decision Diffie-Hellman (DBDH) is hard in the asymmetric bilinear pairing setting, and that the DDH assumption holds in the group defining the first coordinate of the asymmetric pairing. Our traitor tracing system allows adaptive pirates to be traced. The sch...

Certificateless cryptography introduced by Al-Riyami and Paterson eliminates the key escrow problem inherent in identity based cryptosystems. Even though building practical identity based signcryption schemes without bilinear pairing are considered to be almost impossible, it will be interesting to explore possibilities of constructing such systems in other settings like certificateless cryptog...