Coded Cooperative Data Exchange for a Secret Key

• Published in: IEEE transactions on information theory Vol. 62; no. 7; pp. 3785 - 3795
• Main Authors: Courtade, Thomas A., Halford, Thomas R.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Clients; Coded cooperative data exchange; Codes; Coding; Data exchange; Data integrity; Electrical engineering; Electronic mail; Encoding; Indexes; Information theory; Integers; Network coding; Polynomials; Probability; Protocols; Random variables; secrecy; universal recovery; Coded cooperative data exchange; network coding; secrecy; universal recovery
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2016.2539347

We consider a coded cooperative data exchange problem with the goal of generating a secret key. In particular, we investigate the number of public transmissions required for a set of clients to agree on a secret key with probability one, subject to the constraint that it remains private from an eavesdropper. Although the problems are closely related, we prove that secret key generation with the fewest number of linear transmissions is NP-hard, while it is known that the analogous problem in the traditional cooperative data exchange setting can be solved in polynomial time. In doing this, we completely characterize the best possible performance of linear coding schemes, and also prove that linear codes can be strictly suboptimal. Finally, we extend the single-key results to characterize the minimum number of public transmissions required to generate a desired integer number of statistically independent secret keys.