Cryptology ePrint Archive, report 2007/074, Feb. 2007.
We describe a CCA-secure public-key encryption scheme, in the Cramer-Shoup paradigm, based on the Linear assumption of Boneh, Boyen, and Shacham. Through a comparison to the Kiltz tag-encryption scheme from TCC 2006, our scheme gives evidence that the Cramer-Shoup paradigm yields CCA encryption with shorter ciphertexts than the Canetti-Halevi-Katz paradigm.
We present a generalization of the Linear assumption into a family of progressively weaker assumptions and show how to instantiate our Linear Cramer-Shoup encryption using the progressively weaker members of this family.