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If we should consider that in an MPC protocol, the confidential messages communicated between two parties can be eavesdropped on by adversaries? If so, should we build a secure channel for that?

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This is normally specified in the protocol description or in the theorem statement. The most common network assumptions are:

  • Secure point-to-point channels: all pairs of parties are linked by secure and authenticated channels.
  • Broadcast channel: the parties can broadcast (authenticated) messages to everyone (which eavesdroppers can of course see).

Many works characterize precisely how much MPC must rely on these network models, and some relaxations (with network delays, without authentication, etc) have been studied.

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