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.
In 2016, Courtade et al. characterized the minimum number of public transmissions for key agreement REF with an arbitrary key distribution.
Coded Cooperative Data Exchange for a Secret Key
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Mathematics Computer Science