Perfect Secrecy under Deep Random Assumption

Modern cryptography mostly relies on mathematical problems commonly trusted as very difficult to solve such as large integer factorization or discrete logarithm belonging to complexity theory. No certainty exist on the actual difficulty of those problems not even the truth of the famous P≠NP conjecture. Furthermore most of them are not resistant to quantum computing which should make them useless in the next decades. In this work a new idea is presented to design secure communication protocols capable to resist to unlimited opponents. Those protocols use a new form of randomness called « Deep Random » capable to hide its probability distribution to the observers and thus to prevent them performing Bayesian inference over public information to estimate the private information. The theoretical foundations are established and an example is presented with its proof of security.