Differential privacy mechanisms can offer a trade-off between privacy and utility by using privacy metrics and utility metrics. The trade-off of differential privacy shows that one thing increases and another decreases in terms of privacy metrics and utility metrics. However, there is no unified trade-off measurement of differential privacy mechanisms. To this end, we proposed the definition of privacy-preserving monotonicity of differential privacy, which measured the trade-off between privacy and utility. First, to formulate the trade-off, we presented the definition of privacy-preserving monotonicity based on computational indistinguishability. Second, building on privacy metrics of the expected estimation error and entropy, we theoretically and numerically showed privacy-preserving monotonicity of Laplace mechanism, Gaussian mechanism, exponential mechanism, and randomized response mechanism. In addition, we also theoretically and numerically analyzed the utility monotonicity of these several differential privacy mechanisms based on utility metrics of modulus of characteristic function and variant of normalized entropy. Third, according to the privacy-preserving monotonicity of differential privacy, we presented a method to seek trade-off under a semi-honest model and analyzed a unilateral trade-off under a rational model. Therefore, privacy-preserving monotonicity can be used as a criterion to evaluate the trade-off between privacy and utility in differential privacy mechanisms under the semi-honest model. However, privacy-preserving monotonicity results in a unilateral trade-off of the rational model, which can lead to severe consequences.

Homomorphic encryption can protect user’s privacy when operating on user’s data in cloud computing. But it is not practical for wide using as the data and services types in cloud computing are diverse. Among these data types, digital image is an important personal data for users. There are also many image processing services in cloud computing. To protect user’s privacy in these services, this paper proposed a scheme using homomorphic encryption in image processing. Firstly, a secret key homomorphic encryption (IGHE) was constructed for encrypting image. IGHE can operate on encrypted floating numbers efficiently to adapt to the image processing service. Then, by translating the traditional image processing methods into the operations on encrypted pixels, the encrypted image can be processed homomorphically. That is, service can process the encrypted image directly, and the result after decryption is the same as processing the plain image. To illustrate our scheme, three common image processing instances were given in this paper. The experiments show that our scheme is secure, correct, and efficient enough to be used in practical image processing applications.

The existing work has conducted in-depth research and analysis on global differential privacy (GDP) and local differential privacy (LDP) based on information theory. However, the data privacy preserving community does not systematically review and analyze GDP and LDP based on the information-theoretic channel model. To this end, we systematically reviewed GDP and LDP from the perspective of the information-theoretic channel in this survey. First, we presented the privacy threat model under information-theoretic channel. Second, we described and compared the information-theoretic channel models of GDP and LDP. Third, we summarized and analyzed definitions, privacy-utility metrics, properties, and mechanisms of GDP and LDP under their channel models. Finally, we discussed the open problems of GDP and LDP based on different types of information-theoretic channel models according to the above systematic review. Our main contribution provides a systematic survey of channel models, definitions, privacy-utility metrics, properties, and mechanisms for GDP and LDP from the perspective of information-theoretic channel and surveys the differential privacy synthetic data generation application using generative adversarial network and federated learning, respectively. Our work is helpful for systematically understanding the privacy threat model, definitions, privacy-utility metrics, properties, and mechanisms of GDP and LDP from the perspective of information-theoretic channel and promotes in-depth research and analysis of GDP and LDP based on different types of information-theoretic channel models.

In this paper, a fine-grained query authorization scheme with integrity verification is proposed over encrypted spatial data for location-based services (LBS). The fine-grained query authorization is enabled based on a distribution of spatial data by employing a non-uniform partition in the spatial domain to generate a density-based space filling curve (DSC), which can be used to generate index values for querying and transformation keys. The transformation keys can be used to generate query tokens for a secure spatial query as well as construct a transformation key tree whose subtree can be distributed by the LBS provider to an authorized user as transformation key for query tokens generation. Furthermore, the proposed scheme constructs a Merkle quad tree (MQ-tree) to support integrity verification by aggregating a digest of spatial data based on DSC and employing MQ-tree as a verification structure. The LBS provider can share a subtree of MQ-tree to authorized user as his verification structure, which corresponds to the transformation key of the authorized user. In this way, the authorized user can only generate the valid query tokens and verify query results in his authorized region. Extensive experimental results demonstrate the high efficiency of verification structure generation and verification operations

As cloud computing services and location-aware devices are fully developed, a large amount of spatial data needs to be outsourced to the cloud storage provider, so the research on privacy protection for outsourced spatial data gets increasing attention from academia and industry. As a kind of spatial transformation method, Hilbert curve is widely used to protect the location privacy for spatial data. But sufficient security analysis for standard Hilbert curve (SHC) is seldom proceeded. In this paper, we propose an index modification method for SHC (SHC^∗) and a density-based space filling curve (DSC) to improve the security of SHC; they can partially violate the distance-preserving property of SHC, so as to achieve better security. We formally define theindistinguishabilityand attack model for measuring the privacy disclosure risk of spatial transformation methods. The evaluation results indicate that SHC^∗and DSC are more secure than SHC, and DSC achieves the best index generation performance.