Between Hashed DH and Computational DH: Compact Encryption from Weaker Assumption

In this paper, we introduce the intermediate hashed Diffie-Hellman (IHDH) assumption which is weaker than the hashed DH (HDH) assumption (and thus the decisional DH assumption), and is stronger than the computational DH assumption. We then present two public key encryption schemes with short ciphertexts which are both chosen-ciphertext secure under this assumption. The short-message scheme has smaller size of ciphertexts than Kurosawa-Desmedt (KD) scheme, and the long-message scheme is a KD-size scheme (with arbitrary plaintext length) which is based on a weaker assumption than the HDH assumption.