High-precision Functional Bootstrapping for CKKS from Fourier Extension

Abstract. We propose a high-precision functional bootstrapping method for the CKKS fully homomorphic encryption scheme based on Fourier extension techniques. The CKKS scheme is widely used for privacy-preserving machine learning due to its support for approximate arithmetic over real numbers. However, CKKS bootstrapping can introduce non-negligible errors that accumulate over multiple operations. Our approach leverages Fourier extension to approximate the modular reduction function with significantly higher accuracy than prior methods, achieving bootstrapping with substantially reduced error rates. We provide a rigorous error analysis and demonstrate through experiments that our method attains improved precision across various parameter regimes, enabling more reliable computation in applications requiring high numerical accuracy.