  Here we present a new protocol for controlled quantum key agreement and
another protocol for key agreement with a specific focus on the security
analysis. Specifically, detailed security proof is provided against
impersonated fraudulent attack and collective attacks and it is established
that the proposed protocols are not only secure, but they also satisfy other
desired properties of such schemes (i.e., fairness and correctness). Further,
the proposed schemes are critically compared with a set of schemes for quantum
key agreement and an existing scheme for controlled quantum key agreement (Tang
et al.'s protocol) in terms of efficiency and the required quantum resources.
Especially, it is observed that in contrast to the existing schemes, the
present scheme does not require quantum memory. In addition, the protocol for
controlled quantum key agreement proposed here is found to require quantum
resources (Bell state and single photon state) that are easier to produce and
maintain compared to the quantum resources (GHZ states) required by the only
known existing protocol for the same purpose, i.e., Tang et al.'s protocol.
