A New Public-Key Encryption Scheme Secure against Adaptive Chosen Ciphertext Attack

A new public key encryption scheme is proposed and analyzed, which is based on a vector space over some finite field with respect to a class of matrix semigroup action. The scheme is proved secure against adaptive chosen ciphertext attack under EDDH assumption. Since EDDH assumption is weaker than DDH assumption for generic bilinear groups, the new encryption scheme is a good replacement for Cramer-Shoup encryption scheme when bilinear group is adopted as construction platform.