  A fundamental question that has been studied in cryptography and in
information theory is whether two parties can communicate confidentially using
exclusively an open channel. We consider the model in which the two parties
hold inputs that are correlated in a certain sense. This model has been studied
extensively in information theory, and communication protocols have been
designed which exploit the correlation to extract from the inputs a shared
secret key. However, all the existing protocols are not universal in the sense
that they require that the two parties also know some attributes of the
correlation. In other words, they require that each party knows something about
the other party's input. We present a protocol that does not require any prior
additional information. It uses space-bounded Kolmogorov complexity to measure
correlation and it allows the two legal parties to obtain a common key that
looks random to an eavesdropper that observes the communication and is
restricted to use a bounded amount of space for the attack. Thus the protocol
achieves complexity-theoretical security, but it does not use any unproven
result from computational complexity. On the negative side, the protocol is not
efficient in the sense that the computation of the two legal parties uses more
space than the space allowed to the adversary.
