We propose a general security definition for cryptographic quantum protocols that implement classical non-reactive two-party tasks. The definition is expressed in terms of simple quantum-information-theoretic conditions which must be satisfied by the protocol to be secure. The conditions are uniquely determined by the ideal functionality F defining the cryptographic task to be implemented. We then show the following composition result. If quantum protocols π_1, ..., π_l securely implement ideal functionalities F_1, ..., F_l according to our security definition, then any purely classical two-party protocol, which makes sequential calls to F_1,..., F_l, is equally secure as the protocol obtained by replacing the calls to F_1, ..., F_l with the respective quantum protocols π_1,..., π_l. Hence, our approach yields the minimal security requirements which are strong enough for the typical use of quantum protocols as subroutines within larger classical schemes. Finally, we show that recently proposed quantum protocols for secure identification and oblivious transfer in the bounded-quantum-storage model satisfy our security definition, and thus compose in the above sense.
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