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Any two-party cryptographic primitive can be implemented using quantumcommunication under the assumption that it is difficult to store a large numberof quantum states perfectly. However, achieving reliable quantum communicationover long distances remains a difficult problem. Here, we consider a largenetwork of nodes with only neighboring quantum links. We exploit properties ofthis cloud of nodes to enable any two nodes to achieve security even if theyare not directly connected. Our results are based on techniques from classicalcryptography and do not resort to technologically difficult procedures likeentanglement swapping. More precisely, we show that oblivious transfer can beachieved in such a network if and only if there exists a path in the networkbetween the sender and the receiver along which all nodes are honest. Finally,we show that useful notions of security can still be achieved when we relax theassumption of an honest path. For example, we show that we can combine ourprotocol for oblivious transfer with computational assumptions such that weobtain security if either there exists an honest path, or, as a backup, atleast the adversary cannot solve a computational problem.

Long distance two-party quantum cryptography made simple