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Assume we have a multi-party computation protocol and the protocol definition, where both of them consider a semi-honest adversary, without explicitly assuming the type of channel the parties want to use.

Also, assume three parties are involved in the protocol: two clients and a server. Let a client encrypt its input under the public key of the other client and send it to the server, where the server somehow computes the result and send it to the other client.

The protocol is proven in the case where a party is corrupted at a time by a semi-honest adversary

Question: Can we say that the protocol is insecure because a corrupted client can eavesdrop the communication between the other client and server and learn some information? Or we can say that the protocol implicitly assumes the parties are using a secure channel (e.g. TLS)?

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Typically in the MPC literature it is assumed that there are pair-wise secure channels between all parties. So I would say it is the latter in the case of your question.

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  • $\begingroup$ thank you for the answer! I wondered if you have any paper/textbook in mind saying that? $\endgroup$
    – Ay.
    Apr 26, 2018 at 14:02
  • $\begingroup$ @AdrianAd, see the original BGW paper. It states The model of computation is a complete synchronou network of n processors. The pairwise communication channels between players are secure, i.e., they cannot be read or tempered [sic] with by other players. $\endgroup$
    – mikeazo
    Apr 26, 2018 at 14:33

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