On the Security of Homomorphic Encryption Schemes with Restricted Decryption Oracles

Fully homomorphic encryption (FHE) can be used for privacy-preserving aggregation of medical data. In this typical application, the security against passive attacks has been well studied by Li and Micciancio (2021). In this paper, the authors further consider a “nearly passive” kind of attack, where the attacker may behave like a passive attacker in the view of the third-party server. To capture the security against this hard-to-detect attack, the authors propose a new notion of IND-CPA^rD security. The authors show that the standard LWE encryption and its related FHE schemes can not defend against IND-CPA^rD attack, even under a stricter rule limiting the content and number of queries made by the attacker. To make the application of FHE schemes more secure, the authors discuss some possible modifications that may serve as countermeasures to IND-CPA^rD attack.