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

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.