Cloud computing offers resource-constrained users big-volume data storage and energy-consuming complicated computation. However, owing to the lack of full trust in the cloud, the cloud users prefer privacy-preserving outsourced data computation with correctness verification. However, cryptography-based schemes introduce high computational costs to both the cloud and its users for verifiable computation with privacy preservation, which makes it difficult to support complicated computations in practice. Intel Software Guard Extensions (SGX) as a trusted execution environment is widely researched in various fields (such as secure data analytics and computation), and is regarded as a promising way to achieve efficient outsourced data computation with privacy preservation over the cloud. But we find two types of threats towards the computation with SGX: Disarranging Data-Related Code threat and Output Tampering and Misrouting threat. In this paper, we depict these threats using formal methods and successfully conduct the two threats on the enclave program constructed by Rust SGX SDK to demonstrate their impacts on the correctness of computations over SGX enclaves. In order to provide countermeasures, we propose an efficient and secure scheme to resist the threats and realize verifiable computation for Intel SGX. We prove the security and show the efficiency and correctness of our proposed scheme through theoretic analysis and extensive experiments. Furthermore, we compare the performance of our scheme with that of some cryptography-based schemes to show its high efficiency.
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