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Non-local quantum computation (NLQC) is a cheating strategy forposition-verification schemes, and has appeared in the context of the AdS/CFTcorrespondence. Here, we connect NLQC to the wider context of informationtheoretic cryptography by relating it to a number of other cryptographicprimitives. We show one special case of NLQC, known as $f$-routing, isequivalent to the quantum analogue of the conditional disclosure of secrets(CDS) primitive, where by equivalent we mean that a protocol for one task givesa protocol for the other with only small overhead in resource costs. We furtherconsider another special case of position verification, which we call coherentfunction evaluation (CFE), and show CFE protocols induce similarly efficientprotocols for the private simultaneous message passing (PSM) scenario. Byrelating position-verification to these cryptographic primitives, a number ofresults in the cryptography literature give new implications for NLQC, and viceversa. These include the first sub-exponential upper bounds on the worst casecost of $f$-routing of $2^{O(\sqrt{n\log n})}$ entanglement, the first exampleof an efficient $f$-routing strategy for a problem believed to be outside$P/poly$, linear lower bounds on entanglement for CDS in the quantum setting,linear lower bounds on communication cost of CFE, and efficient protocols forCDS in the quantum setting for functions that can be computed with quantumcircuits of low $T$ depth.

Relating non-local quantum computation to information theoretic cryptography