  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.
