A Pairing-based Homomorphic Encryption Scheme for Multi-User Settings

A new method is presented to privately outsource computation of different users. As a significant cryptographic primitive in cloud computing, homomorphic encryption (HE) can evaluate on ciphertext directly without decryption, thus avoid information leakage. However, most of the available HE schemes are single-user, which means that they could only evaluate on ciphertexts encrypted by the same public key. Adopting the idea of proxy re-encryption, and focusing on the compatibility of computation, the authors provide a pairing-based multi-user homomorphic encryption scheme. The scheme is a somewhat homomorphic one, which can do infinite additions and one multiplication operation. Security of the scheme is based on subgroup decision problem. The authors give a concrete security model and detailed security analysis.