  We present a new idea to design perfectly secure information exchange
protocol, based on so called Deep Randomness, which means randomness relying on
hidden probability distribution. Such idea drives us to introduce a new axiom
in probability theory, thanks to which we can design a protocol, 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.
