Chao Niu
Ant Group, China

Zhicong Huang
Ant Group, China

Zhaomin Yang
Ant Group, China

Yi Chen
Ant Group, China

Liang Kong
Ant Group, China

Cheng Hong
Ant Group, China

Tao Wei

Keywords: homomorphic encryption, bootstrapping, advanced encryption standard, hybrid homomorphic encryption, transciphering

Abstract

The CKKS scheme is traditionally recognized for approximate homomorphic encryption of real numbers, but BLEACH (Drucker et al., JoC 2024) extends its capabilities to handle exact computations on binary or small integer numbers.Despite this advancement, BLEACH’s approach of simulating XOR gates via (a−b)2 incurs one multiplication per gate, which is computationally expensive in homomorphic encryption. To this end, we introduce XBOOT, a new framework built upon BLEACH’s blueprint but allows for almost free evaluation of XOR gates. The core concept of XBOOT involves lazy reduction, where XOR operations are simulated with the less costly addition operation, a+b, leaving the management of potential overflows to later stages. We carefully handle the modulus chain and scale factors to ensure that the overflows are managed during the CKKS bootstrapping phase, preserving the correct XOR result without extra cost. We use AES-CKKS transciphering as a benchmark to test the capability of XBOOT, and achieve a throughput exceeding one kilobyte per second, which represents a 2.5x improvement over the state-of-the-art (Aharoni et al., HES 2023). Moreover, XBOOT enables the practical execution of tasks with extensive XOR operations that were previously challenging for CKKS. For example, we can do Rasta-CKKS transciphering at over two kilobytes per second, more than 10x faster than the baseline without XBOOT.