The source model for secret key generation with one way public communication refers to a setting in which a secret key should be agreed upon at two terminals. At both terminals correlated components of a common source are available. In addition, a message can be sent from one terminal to the other via a public channel. In this paper, a related scenario is considered where instead of secret key generation, the goal is to securely store data in a public database. The database allows for error-free storing of the data, but is constrained in its size which imposes a rate constraint on storing. The corresponding capacity for secure storage is known and it has been shown that the capacity-achieving strategy satisfies the strong secrecy criterion. Here, the case when the storage in the public database is subject to errors is considered and the corresponding capacity is characterized. In addition, the continuity properties of the two capacity functions are analyzed. These capacity functions are continuous as opposed to the discontinuous secret key capacity with rate constraint. It is shown that for secure storage the phenomenon of super activation can occur. Finally, it is discussed how the results in this paper differ from previous results on super activation.

Ahlswede and Dueck introduced identification via channels as a new paradigm in information theory. They showed that the number of messages that can reliably be identified over a noisy channel grows doubly exponentially with the block length. In this paper, we also consider identification, but we assume that messages are stored on a database such that they can be identified. In addition, the legitimate users have access to the output of a source. This source allows us to store messages securely. It is also used to increase the number of messages that can be stored securely on the database and identified reliably. We define a protocol for secure storage for identification such that the number of stored messages that can be identified grows doubly exponentially with the number of symbols read from the source and the number of storage cells available, respectively. We also consider the privacy leakage of the protocols used for identification. So, it makes sense to consider two sources. We assume one source is public, whereas the other source is available only to the legitimate users. The public source is used to increase the number of messages that can be identified, while the second source is used to guarantee secrecy. Using the public source does not increase the privacy leakage. So, we can possibly achieve a higher number of messages that can be identified, while the privacy leakage does not increase using two sources. As a by-product, we also get new results on common randomness generation.