Efficient signcryption with key privacy from gap Diffie-Hellman groups

This paper proposes a new public key authenticated encryption (signcryption) scheme based on the Diffie-Hellman problem in Gap Diffie-Hellman groups. This scheme is built on the scheme proposed by Boneh, Lynn and Shacham in 2001 to produce short signatures. The idea is to introduce some randomness into this signature to increase its level of security in the random oracle model and to re-use that randomness to perform encryption. This results in a signcryption protocol that is more efficient than any combination of that signature with an El Gamal like encryption scheme. The new scheme is also shown to satisfy really strong security notions and its strong unforgeability is tightly related to the Diffie-Hellman assumption in Gap Diffie-Hellman groups.