Received: 2025-01-08 Accepted: 2025-03-11 | Kamil Klucznik and Giacomo Santato
This paper addresses the issue of circuit privacy and ciphertext sanitization for homomorphic encryption over approximate arithmetic. The authors introduce formal models to reason about circuit privacy and show that approximate homomorphic encryption can be made circuit private using differential privacy techniques. Specifically, they demonstrate that applying exponential Gaussian noise to the evaluated ciphertexts removes useful information about the circuit. The noise parameter is shown to be tight, and smaller parameters can lead to efficient adversaries. The paper also extends these results to multikey and threshold homomorphic encryption, providing formal definitions and security analyses. It concludes by discussing the impact of noise on the precision of CKKS-type schemes and presenting parameters for machine learning inference. The key contributions include formal definitions of circuit privacy, a proof that exponential noise is necessary for security, and an analysis of the precision loss in modified CKKS schemes.This paper addresses the issue of circuit privacy and ciphertext sanitization for homomorphic encryption over approximate arithmetic. The authors introduce formal models to reason about circuit privacy and show that approximate homomorphic encryption can be made circuit private using differential privacy techniques. Specifically, they demonstrate that applying exponential Gaussian noise to the evaluated ciphertexts removes useful information about the circuit. The noise parameter is shown to be tight, and smaller parameters can lead to efficient adversaries. The paper also extends these results to multikey and threshold homomorphic encryption, providing formal definitions and security analyses. It concludes by discussing the impact of noise on the precision of CKKS-type schemes and presenting parameters for machine learning inference. The key contributions include formal definitions of circuit privacy, a proof that exponential noise is necessary for security, and an analysis of the precision loss in modified CKKS schemes.