  Any two-party cryptographic primitive can be implemented using quantum
communication under the assumption that it is difficult to store a large number
of quantum states perfectly. However, achieving reliable quantum communication
over long distances remains a difficult problem. Here, we consider a large
network of nodes with only neighboring quantum links. We exploit properties of
this cloud of nodes to enable any two nodes to achieve security even if they
are not directly connected. Our results are based on techniques from classical
cryptography and do not resort to technologically difficult procedures like
entanglement swapping. More precisely, we show that oblivious transfer can be
achieved in such a network if and only if there exists a path in the network
between 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 the
assumption of an honest path. For example, we show that we can combine our
protocol for oblivious transfer with computational assumptions such that we
obtain security if either there exists an honest path, or, as a backup, at
least the adversary cannot solve a computational problem.
