  The discovery of quantum key distribution by Bennett and Brassard (BB84)
bases on the fundamental quantum feature: incompatibility of measurements of
quantum non-commuting observables. In 1991 Ekert showed that cryptographic key
can be generated at a distance with help of entangled (correlated) quantum
particles. Recently Barrett, Hardy and Kent showed that the non-locality used
by Ekert is itself a good resource of cryptographic key even beyond quantum
mechanics. Their result paved the way to new generation of quantum
cryptographic protocols - secure even if the devices are built by the very
eavesdropper. However, there is a question, which is fundamental from both
practical and philosophical point of view: does Nature offer security on
operational level based on the original concept behind quantum cryptography -
that information gain about one bservables must cause disturbance to another,
incompatible one?
  Here we resolve this problem by using in place of non-locality another
striking feature of quantum world - contextuality. It is a strong version of
incompatibility manifested in the famous Kochen-Specker paradox. The crucial
concept is the use of a new class of families of bipartite probability
distributions which locally exhibit the Kochen-Specker paradox conditions and,
in addition, exhibit perfect correlations. We show that if two persons share
systems described by such a family then they can extract secure key.
  This is the first operational protocol that directly implements the
fundamental feature of Nature: the information gain vs. disturbance trade-off.
At the same time it provides natural device-independent cryptographic scheme
within quantum mechanics suitable for current technology.
