Semi-generic construction of public key encryption and identity-based encryption with equality test

Public key encryption with equality test (PKEET), which was first introduced by Yang et al. (CT-RSA, 2010), has various applications including facilitating keyword search on encrypted data and partitioning encrypted data on the cloud. It can be also applied to manage personal health records on the internet. For these reasons, there have been improvements on earlier PKEET schemes in terms of performance and functionality. We present a semi-generic method for PKEET constructions, assuming only the existence of IND-CCA2 secure traditional public key encryption (PKE) schemes, the hardness of Computational Diffie-Hellman (CDH) problems, and random oracles. Our approach has several advantages; it enables us to understand requirements for the equality test functionality more clearly. Furthermore, our approach is quite general, in that if we change the underlying PKE scheme with the identity-based encryption (IBE) scheme (and we assume the hardness of Bilinear Diffie-Hellman problems instead of CDH), then we obtain the first IBE scheme with equality test (IBEET) satisfying analogous security arguments to those of PKEET. Although an IBEET construction was recently proposed, but we note that it satisfies only weak security requirements.