New chosen-ciphertext secure identity-based encryption with tight security reduction to the bilinear Diffie–Hellman problem

Abstract

We propose a new identity-based encryption (IBE) system that achieves a tight security reduction to the bilinear Diffie–Hellman (BDH) problem in the random oracle model. Tightness indicates that some level of IBE system security can be straightforwardly based on the hardness of the BDH problem at the same security level. Achieving such tightness requires two strategies: (1) a key generation technique for all identities, and (2) a searching method for the solution to the BDH problem. To implement the first strategy, our system relies on a key generation paradigm recently introduced with the Park–Lee IBE system. To implement the second strategy, we base our system on the strong twin BDH problem that includes access to a decision oracle. We compare the efficiency of our system with that of the previous Nishioka IBE system (based on the Katz–Wang key generation paradigm) combined with another tight variant of the Fujisaki–Okamoto transform.