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We show that monogamy of Bell's inequality violations, which is strictlyweaker condition than no-signaling is enough to prove security of quantum keydistribution. We derive our results for a whole class of monogamy constraintsand generalize our results to any theory that communicating parties may haveaccess to. Some of these theories do not respect no-signaling principle yetstill allow for secure communication. This proves that no-signaling is only asufficient condition for the possibility of secure communication, but not thenecessary one. We also present some new qualitative results concerning thesecurity of existing quantum key distribution protocols.

Security proof for cryptographic protocols based only on the monogamy of Bell's inequality violations