Extending Fuzzy Identity-Based Encryption with delegating capabilities

We propose an efficient and provably secure Fuzzy Identity-Based Encryption scheme with delegating capabilities, where the delegation algorithm allows an identity to generate private keys for some other identities. Compared to the Sahai-Waters Large Universe construction, our scheme supports arbitrary strings as attributes and identities can consist of variable numbers of attributes. Besides, our scheme is more efficient by using a hash function modeled as a random oracle. And we give the security proof of our scheme in the Fuzzy Selective ID model under the Decisional Bilinear Diffie-Hellman assumption in the random oracle.