Outsourced attribute-based signatures with perfect privacy for circuits in cloud computing

Attribute-based signature (ABS) is a widely used cryptographic primitive, that provides both data integrity and fine-grained privacy protection. However, the signing overhead of ABS is usually too large, making it unsuitable for resource-constrained devices. Using cloud computing technology, the notion of outsourced attribute-based signatures (OABS) was introduced to overcome this drawback. In OABS, the user can outsource him/her signing tasks to the signing-cloud service provider (S-CSP). The previous notion of privacy of OABS does not take the S-CSP's attack into account, so it is not strong enough. To conform to the reality of cloud computing, we present a more accurate notion of privacy, called perfect privacy, which ensures that any adversary, even the S-CSP, cannot identify which policy is used to generate the signature. Then, we propose a key-policy OABS scheme for circuits based on multilinear mapping with perfect privacy. By using the outsourcing technique, in our scheme, the computation cost of the signer is only three or four pairing operations, which is independent of the complexity of the policy and the size of the attribute set. Our scheme achieves three advantages: perfect privacy, expressive policy, and constant signing cost, simultaneously.