Secure Storage Capacity Under Rate Constraints-Continuity and Super Activation

• Published in: IEEE transactions on information forensics and security Vol. 15; pp. 959 - 970
• Main Authors: Baur, Sebastian, Boche, Holger, Schaefer, Rafael F., Poor, H. Vincent
• Format: Journal Article
• Language: English
• Published: New York IEEE 2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Activation; Constraints; Continuity (mathematics); continuity of capacity; Data models; Information theory; Memory; Public Key Infrastructure; rate constraint; Secret key (SK) generation; Secure storage; Security; Storage capacity; super activation; Terminals
• ISSN: 1556-6013; 1556-6021
• DOI: 10.1109/TIFS.2019.2929945

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.