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Outsourced decryption ABE system largely reduces the computation cost for users who intend to access the encrypted files stored in cloud. However, the correctness of the transformation ciphertext cannot be guaranteed because the user does not have the original ciphertext. Lai et al. provided an ABE scheme with verifiable outsourced decryption which helps the user to check whether the transformation done by the cloud is correct. In order to improve the computation performance and reduce communication overhead, we propose a new verifiable outsourcing scheme with constant ciphertext length. To be specific, our scheme achieves the following goals. (1) Our scheme is verifiable which ensures that the user efficiently checks whether the transformation is done correctly by the CSP. (2) The size of ciphertext and the number of expensive pairing operations are constant, which do not grow with the complexity of the access structure. (3) The access structure in our scheme is AND gates on multivalued attributes and we prove our scheme is verifiable and it is secure against selectively chosen-plaintext attack in the standard model. (4) We give some performance analysis which indicates that our scheme is adaptable for various limited bandwidth and computation-constrained devices, such as mobile phone

Verifiable Outsourced Decryption of Attribute-Based Encryption with Constant Ciphertext Length