Using the Power-Of-Two Vector Padding to Enhance Efficiency and Speed in CKKS Homomorphic Encryption

Abstract The Cheon-Kim-Kim-Song (CKKS) encryption scheme has enabled secure data processing in sensitive domains and hence has transformed privacy-preserving computations due to its unique ability to support approximate arithmetic on real numbers. However, the computational challenges associated with non-power-of-two input vector lengths largely limit the broader adoption of the CKKS. This paper, proposes the Power-of-Two CKKS (P2PCKKS), an enhanced CKKS scheme that adopts a dynamic padding technique to align input vector lengths with the nearest power-of-two. The proposed scheme addresses key drawbacks such as computational errors and overflow, hence optimizing the Fast Fourier Transform (FFT) for polynomial operations. While maintaining accuracy, the proposed scheme demonstrated an enhanced efficiency and speed, compared to the conventional CKKS scheme, even for vector inputs with lengths already as powers-of-two. The experiments’ results confirmed a 100% success rate across all computations, making the P2P-CKKS a robust solution for real-world applications requiring scalable and efficient homomorphic encryption. This paper prepares the groundwork for exploring how adaptive padding techniques can potentially be used to revolutionize encryption models.