The Boneh-Katz Transformation, Revisited: Pseudorandom/Obliviously-Samplable PKE from Lattices and Codes and Its Application

The Boneh-Katz transformation (CT-RSA 2005) converts a selectively-secure identity/tag-based encryption scheme into a public-key encryption scheme secure against chosen-ciphertext attacks. We show that if the underlying primitives are pseudorandom, then the public-key encryption scheme obtained by the Boneh-Katz transformation is also pseudorandom. A similar result holds for oblivious sampleability (Canetti and Fischlin (CRYPTO 2001)). As applications, we can construct - pseudorandom and obliviously-samplable public-key encryption schemes from lattices and codes, - universally-composable non-interactive bit-commitment from lattices, - public-key steganography which is steganographically secure against adaptive chosen-covertext attacks and steganographic key-exchange from lattices and codes, - anonymous authenticated key exchange from lattices and codes, - public-key encryption secure against simulation-based, selectiveopening chosen-ciphertext attacks from lattices and codes.