Big data offers significant benefits; however, security and privacy problems must be considered,especially with regard to outsourced big data. Auditing outsourced big data is an important factor in security and privacy. However, most of the existing auditing techniques are not suitable for outsourced big data due to their high computational and communication costs at the auditor and the data owner （DO） side. In this paper, we propose an efficient auditing scheme for outsourced big data based on algebraic signatures and an XOR-homomorphic function, that can achieve numerous advantages, such as fewer challenges and proofs,non-block verification, data privacy preservation, and lower computational and communication costs. The proposed scheme enables a trusted third-party auditor, on behalf of DOs, to audit the outsourced data in a cloud. Thus, reducing the computational burden on the DOs. Subsequently, we construct a new data structure called a Record Table（RTable） and extend the basic auditing scheme to support the data dynamic operations. As our extended scheme does not use public key encryption, the entire process of updating the data incurs only a small computational and communication overhead with regard to the auditor, the DOs,and the cloud server. Finally, the proposed basic scheme is proved secure under the security model against various attacks. Analysis of the performance shows that both our basic scheme and extended scheme are highly efficient.
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