Coded Cooperative Data Exchange for a Secret Key

We consider a coded cooperative data exchange problem with the goal of generating a secret key. Specifically, 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 fewest number of linear transmissions is NP-hard, while it is known that the analogous problem in traditional cooperative data exchange 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.Comment: Full version of a paper that appeared at ISIT 2014. 19 pages, 2 figure

Neutrino Physics Without Oscillations

There is a tremendous potential for neutrinos to yield valuable new information about strongly interacting systems. Here we provide a taste of this potential, beginning with the existence of a rigorous sum rule for the proton and neutron spin structure functions based on the measurement of the flavor singlet axial charge of the nucleon. We also comment on the NuTeV report of a 3$\sigma$ deviation of the value of $\sin^2 \theta_W$ measured in neutrino (and anti-neutrino) scattering from that expected within the Standard Model.Comment: Presentation at the Fourth Tropical Workshop on Particle Physics and Cosmology, Cairns Qld., June 200