A group key agreement (GKA) protocol allows a set of users to establish a common secret via open networks. Observing that a major goal of GKAs for most applications is to establish a confidential channel among group members, we revisit the group key agreement definition and distinguish the conventional (symmetric) group key agreement from asymmetric group key agreement (ASGKA) protocols. Instead of a common secret key, only a shared encryption key is negotiated in an ASGKA protocol. This encryption key is accessible to attackers and corresponds to different decryption keys, each of which is only computable by one group member. We propose a generic construction of one-round ASGKAs based on a new primitive referred to as aggregatable signaturebased broadcast (ASBB), in which the public key can be simultaneously used to verify signatures and encrypt messages while any signature can be used to decrypt ciphertexts under this public key. Using bilinear pairings, we realize an efficient ASBB scheme equipped with useful properties. Following the generic construction, we instantiate a one-round ASGKA protocol tightly reduced to the decision Bilinear Diffie-Hellman Exponentiation (BDHE) assumption in the standard model.