On The Impossibility of Basing Identity Based Encryption on Trapdoor PermutationsAuthors: D. Boneh, A. Papakonstantinou, C. Rackoff, Y. Vahlis, and B. Waters
We ask whether an Identity Based Encryption (IBE) system can be built from simpler public-key primitives. We show that there is no black-box construction for IBE from Trapdoor Permutations (TDP) or even from Chosen Ciphertext Secure Public Key Encryption (CCA-PKE). These black-box separation results are based on an essential property of IBE, namely that an IBE system is able to compress exponentially many public-keys into a short public parameters string.
In proceedings of FOCS 2008, pp. 283-292