On the Security of Homomorphic Encryption on Approximate Numbers.
Baiyu Li, Daniele Micciancio · IACR Cryptology ePrint Archive · 2020
We present passive attacks against CKKS, the homomorphic encryption scheme for arithmetic on approximate numbers presented at Asiacrypt 2017. The attack is both theoretically efficient (running in expected polynomial time) and very practical, leading to complete key recovery with high probability and very modest running times. We implemented and tested the attack against major open source homomorphic encryption libraries, including HEAAN, SEAL, HElib and PALISADE, and when computing several functions that often arise in applications of the CKKS scheme to machine learning on encrypted data, like mean and variance computations, and approximation of logistic and exponential functions using their Maclaurin series.