Why is Deep Random suitable for cryptology

Abstract

We present a new form of randomness, called Deep Randomness, generated in such a way that probability distribution of the output signal is made unknowledgeable for an observer. By limiting, thanks to Deep Randomness, the capacity of the opponent observer to perform bayesian inference over public information to estimate private information, we can design protocols, beyond Shannon limit, enabling two legitimate partners, sharing originally no common private information, to exchange secret information with accuracy as close as desired from perfection, and knowledge as close as desired from zero by any unlimitedly powered opponent. We discuss the theoretical foundation of Deep Randomness, which lies on Prior Probability theory, introduced and developped by authors like Laplace, Cox, Carnap, Jefferys and Jaynes ; and we introduce computational method to generate such Deep Randomness. V2: we add a commented example of Perfact Secrecy Protocol based on Deep Random assumption V3: we provide a major update of the article. The logic foundation of Deep Random assumption is highly strengthened by avoiding the inconsistency attached to rare events. Such inconsistency could lead to security flaws in previous proposition. At the same time, several variants of the protocol are commented with improved performances. V4: we correct an error due to lack of symmetry in the example of protocol given in annex. We also make some writing improvements in perspective of conference publication. V5: we introduce parallel with former article from Maurer presenting a model of Perfect security based on partially independent channels.Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1507.0825