This paper addresses the problem of generating the initial key K and makes two contributions. First, we prove that without such a key, secret key agreement in the BSM is impossible unless Alice and Bob have themselves very high storage capacity, thus proving the optimality of a scheme proposed by Cachin and Maurer. Second, we investigate the hybrid model where K is generated by a computationally secure key agreement protocol. The motivation for the hybrid model is to achieve provable security under the sole assumption that Eve cannot break the key agreement scheme during the storage phase, even if afterwards she may gain infinite computing power (or at least be able to break the key agreement scheme). In earlier work on the BSM, it was suggested that such a hybrid scheme is secure because if Eve has no information about K during the storage phase, then she has missed any opportunity to know anything about X, even when later learning K. We show that this very intuitive and apparently correct reasoning is false by giving an example of a secure (according to the standard definition) computational key-agreement scheme for which the BSM-scheme is nevertheless completely insecure. One of the surprising consequences of this example is that existing definitions for the computational security of key-agreement and encryption are still too weak and therefore new, stronger definitions are needed.