Information-theoretical Secret-key agreement and Bound information

Abstract

One big problem of the communication between two parties is the secrecy. That means how much information a third party can obtain by intercepting the messages transmitted from one honest party to the other one. Therefore cryptography offers a wide range of protocols to ensure security with assumptions on the eavesdropper. So one was looking for an information-theoretical description of the scenario to get unconditional secure communication. In this scenario we are considering two honest parties that want to communicate over an authenticated channel that the eavesdropper is wiretapping. This scenario introduced the definition of the intrinsic information and the secret-key rate which are a measure of the secrecy in this setting. Later because of strong analogies to quantum mechanics it turned out that this description was lacking a phenomena called bound information which is the disability of a probability distribution to create a secret-key even though it has predicted secrecy. Nearly ten years of research have shown the existence of bound information for the multipartite case where several parties are communicating but not yet for the bipartite case. Hence the approach of non-distillability seems a very promising one to find this conjecture. Motivated by this the approach we implemented this tool and simulated some distributions that have conjectured bound information. Thereby we improved the tool to reduce its calculationtime and to get closer to the aim.