Attribute-based key exchange (ABKE) is a useful cryptographic primitive that allows authorized users to establish a session key for data transport based on whether their attributes satisfy a policy. In this paper, we reconstruct ABKE from fast attribute-based encryptions (ABE) and efficient authenticated key exchanges (AKE). Fast ABE supports adaptive security and fast decryption. Efficient AKE allows authorized users to establish session keys with minimal communication overhead and perfect forward secrecy (PFS). Our main contribution is a generic construction of ABKE with enhanced security and optimal efficiency. For enhanced security, our construction offers adaptive security, PFS and impersonation-resistance. For optimal efficiency, our construction ensures that the session key establishment runs fast and the communication between users incurs minimal overhead. We present concrete ABKE instantiation and confirm that its performance outperforms the existing ABKE schemes through implementation and evaluation. Briefly, our ABKE scheme requires a constant number of pairings for session key establishment, which is not offered by existing ones. More concretely, a user requires 0.15 s to establish a session key for a policy with 100 attributes.