Secure outsourced computation is critical for cloud computing to safeguard data confidentiality and ensure data usability. Recently, secure outsourced computation schemes following a twin-server architecture based on partially homomorphic cryptosystems have received increasing attention. The Secure Outsourced Computation on Integers (SOCI) [1] toolkit is the state-of-the-art among these schemes which can perform secure computation on integers without requiring the costly bootstrapping operation as in fully homomorphic encryption; however, SOCI suffers from relatively large computation and communication overhead. In this paper, we propose SOCI+ which significantly improves the performance of SOCI. Specifically, SOCI+ employs a novel (2, 2)-threshold Paillier cryptosystem with fast encryption and decryption as its cryptographic primitive, and supports a suite of efficient secure arithmetic computation on integers protocols, including a secure multiplication protocol (SMUL), a secure comparison protocol (SCMP), a secure sign bit-acquisition protocol (SSBA), and a secure division protocol (SDIV), all based on the (2, 2)-threshold Paillier cryptosystem with fast encryption and decryption. In addition, SOCI+ incorporates an offline and online computation mechanism to further optimize its performance. We perform rigorous theoretical analysis to prove the correctness and security of SOCI+. Compared with SOCI, our experimental evaluation shows that SOCI+ is up to 5.4 times more efficient in computation and 40% less in communication overhead.

翻译：安全外包计算对于云计算保障数据机密性和可用性至关重要。近年来，基于部分同态密码系统的双服务器架构安全外包计算方案受到越来越多关注。其中，整数安全外包计算（SOCI）[1]工具包是该领域的先进方案，可在无需完全同态加密中昂贵的自举操作下实现整数安全计算。然而，SOCI存在计算和通信开销较大的问题。本文提出SOCI^+，显著提升了SOCI的性能。具体而言，SOCI^+采用新型（2,2）-门限Paillier密码系统（支持快速加密和解密）作为其密码学原语，并支持一系列高效的整数安全算术计算协议，包括安全乘法协议（SMUL）、安全比较协议（SCMP）、安全符号位获取协议（SSBA）和安全除法协议（SDIV），所有协议均基于该快速加密解密的（2,2）-门限Paillier密码系统。此外，SOCI^+引入离线与在线计算机制以进一步优化性能。我们通过严格的理论分析证明了SOCI^+的正确性和安全性。与SOCI相比，实验评估表明SOCI^+的计算效率最高提升至5.4倍，通信开销降低40%。