Multi-integer Somewhat Homomorphic Encryption Scheme with China Remainder Theorem

As an effective solution to protect the privacy of the data, homomorphic encryption has become a hot research topic. Existing homomorphic schemes are not truly practical due to their high computational complexity and huge key size. In 2013, Coron et al. proposed a batch homomorphic encryption scheme, i.e. a scheme that supports encrypting and homomorphically evaluating several plaintext bits as a single ciphertext. Based on china remainder theorem, we propose a multi-integer somewhat homomorphic encryption scheme. It can be regarded as a generalization of Coron’s scheme with larger message space. Furthermore, we put forward a new hardness problem, which is called the random approximation greatest common divisor (RAGCD). We prove that RAGCD problem is a stronger version of approximation greatest common divisor (AGCD) problem. Our variant remains semantically secure under RAGCD problem. As a consequence, we obtain a shorter public key without sacrificing the security of the scheme. The estimates are backed up with experiment data. It is expected that, the proposed scheme makes the encrypted data processing practical for suitable applications. Key-Words: Information Security, Cryptography, Somewhat Homomorphic Encryption, Multi-Integer, China Remainder Theorem, Random Approximation Greatest Common Divisor (RAGCD)