We present an Identity Based Encryption (IBE) system that is fully secure in the standard model and has several advantages over previous such systems - namely, computational efficiency, shorter public parameters, and a "tight" security reduction, albeit to a stronger assumption that depends on the number of private key generation queries made by the adversary. Our assumption is a variant of Boneh et al.'s decisional Bilinear Diffie-Hellman Exponent assumption, which has been used to construct efficient hierarchical IBE and broadcast encryption systems. The construction is remarkably simple. It also provides recipient anonymity automatically, providing a second (and more efficient) solution to the problem of achieving anonymous IBE without random oracles. Finally, our proof of CCA2 security, which has more in common with the security proof for the Cramer-Shoup encryption scheme than with security proofs for other IBE systems, may be of independent interest.
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