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A Ciphertext-Policy Attribute-Based Encryption (CP-ABE) allows users to specify the access policies without having to know the identities of users. In this paper, we contribute by proposing an ABE scheme which enables revoking corrupted users. Given a key-like blackbox, our system can identify at least one of the users whose key must have been used to construct the blackbox and can revoke the key from the system. This paper extends the work of Liu and Wong to achieve traitor revocability. We construct an Augmented Revocable CPABE (AugR-CP-ABE) scheme, and describe its security by message-hiding and index-hiding games. Then we prove that an AugR-CP-ABE scheme with message-hiding and index-hiding properties can be transferred to a secure Revocable CP-ABE with fully collusion-resistant blackbox traceability. In the proof for index-hiding, we divide the adversary’s behaviors in two ways and build direct reductions that use adversary to solve the D3DH problem. Our scheme achieves the sub-linear overhead of O( √ N), whereN is the number of users in the system. This scheme is highly expressive and can take any monotonic access structures as ciphertext policies.

Attribute based Encryption: Traitor Tracing, Revocation and Fully Security on Prime Order Groups