BATCH: Secure and Efficient Outsourced Batch Computation for Encrypted Numbers

Secure outsourced computation is a crucial technique for ensuring data security and privacy in cloud computing. While fully homomorphic encryption (FHE) enables computations on encrypted data, its ability to support an unlimited number of arithmetic operations comes at a high computational cost. In recent years, secure computation schemes based on interactions between multiple computation servers and partially ho-momorphic encryption (PHE) have been proposed. These schemes allow efficient execution of unlimited addition and multiplication operations on encrypted data without introducing noise. However, existing solutions often have functional limitations—for example, they may only support computations on natural numbers—or they risk leaking information about the underlying data. To address these challenges, this paper introduces BATCH, a secure outsourced batch computation scheme based on PHE and a dual-server architecture. Compared to existing solutions, BATCH supports batch multiplication and batch squaring on encrypted integers, rather than just natural numbers, while significantly enhancing both security and accuracy. Theoretical analysis and experimental results demonstrate that BATCH outperforms existing approaches in both computational and communication efficiency.