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 1, . . . , securely implement ideal functionalities F1, . . . , F according to our security definition, then any purely classical two-party protocol, which makes sequential calls to F1, . . . , F , is equally secure as the protocol obtained by replacing the calls to F1, . . . , F with the respective quantum protocols 1, . . . , . 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 ...