New construction of group secret handshakes based on pairings

In a secret handshake protocol, an honest member in the group will never reveal his group affiliation unless the other party is a valid member of the same group. However, most prior work of secret handshake are for 2-party secret handshakes. Tsudik and Xu extended the notion of secret handshake to a multi-party setting in 2005. Unfortunately, this seminal work is rather inefficient, since they consider a generic construction of such a scheme. Following this work, Jarecki et al. proposed an efficient solution to multi-party secret handshake. The aim of this paper is twofold. Firstly, we show that Jarecki et al.'s scheme has some drawbacks and therefore the scheme does not fulfill the security requirements of secret handshake. Secondly, we present a new construction of the group secret handshake scheme. In a group secret handshake protocol, a valid member in the group should never reveals his group affiliation unless all the other parties are valid members of the same group. In other words, if a handshake among this group of parties fails, the identities of every involved parties will not be disclosed. We then show that our scheme is secure under the bilinear Diffie-Hellman assumption and decisional bilinear Diffie-Hellman assumption in the random oracle model.