Unconditional

Private channels

In plain words

The assumption that every pair of participants can talk without being overheard.

Why it matters: In practice ordinary encryption provides it, which brings math assumptions back in.

The details

On the map: between every pair of parties, unconditional only with one-time-pad or QKD keys (in practice: TLS)

Unconditional MPC protocols assume every pair of parties can talk secretly and authentically^[1].

That is only truly unconditional if the channels are protected with one-time pads or QKD keys. In practice they run over TLS, which brings back computational assumptions, including quantum vulnerability unless the key exchange is hybrid.

Rests on

If any of these breaks, this breaks too.

Good randomness (needed by everything in the unconditional box (and everything else))

If it falls

If this breaks, these break with it.

MPC, honest majority

References

Michael Ben-Or and Avi Wigderson. Completeness theorems for non-cryptographic fault-tolerant distributed computation. Proceedings of the twentieth annual ACM symposium on Theory of computing - STOC '88, 1988. doi:10.1145/62212.62213