Stateful public key encryption: How to remove gap assumptions and maintaining tight reductions

Stateful public key encryption schemes are introduced recently with improved efficiency over traditional stateless schemes. However, previous proposals are either based on strong assumptions; or admitting very loose security reductions. In this paper, we improve these aspects by presenting a stateful public key encryption scheme with tight security reduction to the computational Diffie-Hellman assumption (cf. gap Diffie-Hellman in [5]), as well as a stateful identity based encryption scheme with tighter security reduction (than [12]) to the computational bilinear Diffie-Hellman problem. It is worth reminding that it is always desirable to have the proofs with tight reductions such that the actual schemes can be practically-meaningful.