A cryptographic communications system enables two entities related by an insecure communication channel and having initially no privately shared knowledge, to agree on a shared unconditionally secure information. Each one of the entities has the capability to generate a new form of randomness called Deep Random, such that any other entity than itself cannot know anything about the probability distribution except a given public characteristic. The internal system of each entity is made up with: (1) a Deep Random Generator (DRG) capable of generating Deep Random signals and of making calculations using the generated signals, and (2) an Interactive Communication Module (ICM) capable of publishing to and reading from the insecure channel. The two entities execute a communication protocol such that they can each compute their respective estimations of the shared information that are probabilistically as close as desired from perfect equality.