Efficient bidirectional proxy re-encryption with direct chosen-ciphertext security

Proxy re-encryption (PRE) allows a semi-trusted proxy to convert a ciphertext originally intended for a user into another ciphertext of the same message intended for another user, and the proxy, however, cannot learn anything about the message encrypted. In previous papers, in order to achieve the CCA2-security, a common method for constructing PRE schemes was to apply the paradigm of using strongly-unforgeable one-time signature which transforms a selective-identity, CPA-secure identity-based encryption (IBE) scheme into a CCA-secure cryptosystem. In this paper, we propose a direct design of the bidirectional CCA-secure PRE scheme, which makes a direct use of the underlying IBE structure and does not need any auxiliary signature mechanism. Our construction is efficient and suitable for further designing multi-user PRE schemes. Its security is proved on the base of the decisional bilinear Diffie-Hellman assumption in the standard model.