Attribute-based signature (ABS) enables users to sign messages over attributes without revealing any information other than the fact that they have attested to the messages. However, heavy computational cost is required during signing in existing work of ABS, which grows linearly with the size of the predicate formula. As a result, this presents a significant challenge for resource-constrained devices (such as mobile devices or RFID tags) to perform such heavy computations independently. Aiming at tackling the challenge above, we first propose and formalize a new paradigm called Outsourced ABS, i.e., OABS, in which the computational overhead at user side is greatly reduced through outsourcing intensive computations to an untrusted signing-cloud service provider (S-CSP). Furthermore, we apply this novel paradigm to existing ABS schemes to reduce the complexity. As a result, we present two concrete OABS schemes: i) in the first OABS scheme, the number of exponentiations involving in signing is reduced from O(d) to O(1) (nearly three), where d is the upper bound of threshold value defined in the predicate; ii) our second scheme is built on Herranz et al.\u27s construction with constant-size signatures. The number of exponentiations in signing is reduced from O(d2) to O(d) and the communication overhead is O(1). Security analysis demonstrates that both OABS schemes are secure in terms of the unforgeability and attribute-signer privacy definitions specified in the proposed security model. Finally, to allow for high efficiency and flexibility, we discuss extensions of OABS and show how to achieve accountability as well.
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