We investigate a fundamental property of device independent security in
quantum cryptography by characterizing probability distributions which are
necessarily independent of the measurement results of any eavesdropper. We show
that probability distributions that are secure in this sense are exactly the
extremal quantum probability distributions. This allows us to give a
characterization of security in algebraic terms. We apply the method to common
examples for two-party as well as multi-party setups and present a scheme for
verifying security of probability distributions with two parties, two
measurement settings, and two outcomes.Comment: 7 pages, 2 figures, revised version, accepted for publication in
Phys. Rev. Let
