A method for performing spacetime-constrained oblivious transfer between a party A and a party B. The method includes imposing relativistic signaling constraints on a cryptographic task of one out-of-m oblivious transfer involving parties A and B. The method further includes using quantum systems for the one-out of-m oblivious transfer. The method guarantees unconditional security of the spacetime-constrained oblivious transfer, based on the imposed relativistic signaling constraints and based on using quantum systems for the one-out of-m oblivious transfer.