Mobile edge computing (MEC) is proposed as an extension of cloud computing in the scenarios where the end devices desire better services in terms of response time. Because the edges are usually owned by individuals or small organizations with limited operation capabilities, the data on the edges are easily corrupted (due to external attacks or internal hardware failures). Therefore, it is essential to verify data integrity in the MEC. We propose two Integrity Checking protocols for the mobile Edge storage, called ICE-basic and ICE-batch. Our protocols allow a third-party verifier to check the data integrity on the edges without violating users data privacy and query pattern privacy. We rigorously prove the security and privacy guarantees of the protocols. In addition, we have investigated how to let the end devices cache some verification tags such that the communication cost between end devices and the cloud can be further reduced when a user connects to multiple edges in sequence. We have implemented a proof-of-concept system that runs ICE, and extensive experiments are conducted to evaluate the performance of the proposed protocols. The theoretical analysis and experimental results demonstrate the proposed protocols are efficient both in computation and communication.

Multikey fully homomorphic encryption proposed by Lopez-Alt et al. (STOC12) is a significant primitive that allows one to perform computation on the ciphertexts encrypted by multiple different keys independently. Then, several schemes were constructed based on decisional small polynomial ratio or learning with errors. These schemes all require an expansion algorithm to transform a ciphertext under a single key into an encryption of the same message under a set of keys. To achieve the expansion algorithm without interaction with these key-keepers, their encryption algorithm not only outputs a ciphertext of a plaintext but also exports auxiliary information generated from the randomness used in the former encryption process. Beyond that, the size of the ciphertext encrypted by multiple keys increases linearly or quadratically in the number of participants. In this paper, we studied the problem whether someone can directly perform arbitrary computation on ciphertexts encrypted by different keys without any auxiliary information in the output of the encryption algorithm and an increase in the size of the ciphertext in the expansion algorithm. To this end, we proposed a novel and simple scheme of secure computation on ciphertexts under two different keys directly without any auxiliary information. In other words, each party just provides its own ciphertexts encrypted by the GSW scheme (CRYPTO13). In the procedure of executing evaluation on these ciphertexts, the size of the new ciphertext remains the same as that of the GSW ciphertext.

Mobile edge computing (MEC) is proposed as an extension of cloud computing in the scenarios where the end devices desire better services in terms of response time. Edge nodes are deployed at the proximity of the end devices, and it can pre-download parts of data stored in the cloud so that the end devices can access these data with low latency. However, because the edges are usually owned by individuals and small organizations, which have limited operation capacities for maintaining the machines, the data on the edges are easily corrupted (due to external attacks or internal hardware failures). Therefore, it is essential to verify data integrity in the MEC. We propose two Integrity Checking protocols for mobile Edge computing, called ICE-basic and ICE-batch, which are designed for the cases where the user wants to check data integrity on a single edge or multiple edges, respectively. Based on the concept of provable data possession and the technique of private information retrieval, our protocols allow a third-party verifier to check the data integrity on the edges without violating users' data privacy and query pattern privacy. We rigorously prove the security and privacy guarantees of the protocols. Furthermore, we have implemented a proof-of-concept system that runs ICE, and extensive experiments are conducted. The theoretical analysis and experimental results demonstrate the proposed protocols are efficient both in computation and communication.

We design a secure protocol that a server can compute the minimum number of all participants' data while kept unknown additional information about the users' data in its execution. Ours protocol is based on fully homomorphic encryption and we utilize it to fix the problem of securely computing the minimum value. Besides, the used FHE scheme is a lattice-based cryptosystem that can resist some quantum adversaries who can carry out quantum computations on classical queries. We also expand the secure min computing protocol to the privacy-preserving the k-th min computing protocol, and present the security analysis of the two protocols on the assumption of the semi-honest model. In the previous literature, their solutions are based on secure arithmetic sum computations as well as secure bitwise XOR computations. Our protocols are more secure with the comparison to them.