Traceable CP-ABE on Prime Order Groups: Fully Secure and Fully Collusion-resistant Blackbox Traceable

In Ciphertext-Policy Attribute-Based Encryption (CP-ABE), access policies associated with the ciphertexts are generally role-based and the attributes satisfying the policies are generally \emph{shared} by multiple users. If a malicious user, with his attributes shared with multiple other users, created a decryption blackbox for sale, this malicious user could be difficult to identify from the blackbox. Hence in practice, a useful CP-ABE scheme should have some tracing mechanism to identify this `traitor\u27 from the blackbox. In this paper, we propose the first CP-ABE scheme which simultaneously achieves (1) fully collusion-resistant blackbox traceability in the standard model, (2) full security in the standard model, and (3) on prime order groups. When compared with the latest fully collusion-resistant blackbox traceable CP-ABE schemes, this new scheme achieves the same efficiency level, enjoying the sub-linear overhead of $O(\sqrt{N})$, where $N$ is the number of users in the system. This new scheme is highly expressive and can take any monotonic access structures as ciphertext policies