Appendix \[sec proofs\].

#### Related works.

The field of secure two (and multi) party (classical) computation started with Yao’s paper [@Yao86], which was proven secure against malicious adversaries in [@GMW87] using generic Zero-Knowledge proofs and in [@LinPin07] with the Cut-and-Choose technique. Covert adversaries were introduced in [@AumLin07] where again the Cut-and-Choose technique was used to achieve an even more efficient protocol. Yao’s protocol has been used for a number of other functionalities, such as constructing non-interactive verifiable computing [@GGB10]. In the early days of quantum computation, researchers believed that quantum properties could lead to a breakthrough and achieve, with unconditional security, several (clasical) multi-party cryptographic primitives. However a series of no-go theorems, first proving that bit commitment is impossible [@commit1; @commit2] , then oblivious transfer [@OT_nogo] and finally [@SSS09] showed that any non-trivial functionality leaks some information to adversaries. Since then, it is established that any such protocol is either only computationally secure or requires the existence of certain (quantum secure) simple cryptographic primitives.

Closely related is the question of what assumptions are required if one wants to perform a secure *quantum* computation involving multiple parties. The case of 2PQC was addressed in [@DNS10] for quantum honest-but-curious and in [@DNS12] 