A Secure Public Key Encryption from Computational Linear Diffe-Hellman Problem

This paper proposes a practical public key encryption scheme which is provable chosen ciphertext(CCA) secure based on the gap computational linear Diffie-Hellman assumption in the standard model. This is the first CCA secure scheme based on the gap computational linear Diffie-Hellman assumption. This scheme is efficient and the proof of the security is tight. We also reduce the size of the public key from n to 2√n based on the twin gap computational linear Diffie-Hellman assumption. And the time for encryption and decryption is significantly reduced. And we point out that a generalization of the scheme can be constructed similarly based on the gap k-computational linear assumption.