An instantiation of the Cramer-Shoup encryption paradigm using bilinear map groups

A new instantiation of the Cramer-Shoup paradigm for secure encryption is presented, which is built using bilinear map groups. The security is based on the Bilinear Decisional Diffie-Hellman assumption. The recent efficiency improvements introduced in [KD04,GS04] are also applied to our constructions. One of the schemes thereby obtained presents efficiency similar to the most efficient encryption schemes with chosen-ciphertext security in the standard model proposed in the literature. Our new scheme presents advantages compared to a trivial Cramer-Shoup instantiation using bilinear map groups, which we also describe here for the first time. Only three practical instantiations of the Cramer-Shoup framework were previously known.