tl;dr: Prove that the incorrectness property of encryption scheme implies differential privacy. Plus, an example on how this can be exploited in a real scheme.
Paper: ISC 2017 or personal pdf.
Carlo Brunetta, Christos Dimitrakakis, Bei Liang, Aikaterini Mitrokotsa
Encrypting data with a semantically secure cryptosystem guarantees that nothing is learned about the plaintext from the ciphertext. However, querying a database about individuals or requesting for summary statistics can leak information. Differential privacy (DP) offers a formal framework to bound the amount of information that an adversary can discover from a database with private data, when statistical findings of the stored data are communicated to an untrusted party. Although both encryption schemes and differential private mechanisms can provide important privacy guarantees, when employed in isolation they do not guarantee full privacy-preservation.
This paper investigates how to efficiently combine DP and an encryption scheme to prevent leakage of information. More precisely, we introduce and instantiate differentially private encryption schemes that provide both DP and confidentiality.