Practical IBE secure under CBDH - encrypting without pairing

Since the discovery of identity based cryptography, a number of identity based encryption schemes were reported in the literature. Although a few schemes were proposed after its introduction, the first efficient identity based encryption scheme was proposed by Dan Boneh and Matthew K. Franklin in 2001. This encryption scheme uses Weil pairing on elliptic curves during both encryption and decryption process. In this paper, we propose a new identity based encryption scheme and prove its security in the random oracle model. There are two highlighting features in our scheme. First, it does not employ bilinear pairing computation during the encryption process. Second, our scheme does not require full domain hashing, which makes our scheme more practical and efficiently implementable. Moreover, we prove the security of our scheme by reducing it to the well known Computational Bilinear Diffie-Hellman problem. We first prove the security of our scheme in weaker security notion i.e. we prove our scheme to be IND-CPA secure. Then using Fujisaki Okamoto transformation, we convert our scheme to IND-CCA secure version.