Privacy-Preserving State Estimation: An Encrypted Extended Kalman Filter Using CKKS Homomorphic Encryption

Abstract

Fully Homomorphic Encryption (FHE) enables mathematical operations directly on encrypted data without decryption. Any operation that a polynomial can approximate can, in principle, be executed under an FHE scheme. To protect cyber-physical systems from eavesdropping on sensitive measurements, we integrate CKKS, an FHE scheme for encrypted real and complex arithmetic, into a state estimator. The estimator is an Extended Kalman Filter (EKF) that fuses GPS and Inertial Measurement Unit (IMU) data to estimate vehicle position, velocity, linear acceleration, yaw angle, and turn rate. We implement CKKS using the Microsoft SEAL library, which supports only a limited number of homomorphic arithmetic operations, creating major challenges for EKF steps such as matrix inversion. We address these constraints with operation-efficient approximations and structured compromises. Frobenius norm analysis shows that the encrypted EKF preserves the precision of the plaintext EKF while reducing data exposure, at the cost of increased latency.