Secure channels ⇒ MPC with honest majority ($t<n/3$) (Chaum–Crépeau–Damgård)

Free reduction · standard model · CCD88

Statement

If each pair of parties can communicate secretly (secure channels), every $n$-party functionality has a protocol secure against a malicious adversary corrupting any $t<n/3$ of the parties, with unconditional, statistical security and guaranteed output delivery: once the parties have committed to their inputs, fewer than a third of them cannot stop the protocol from completing correctly — CCD88. No complexity assumption is used.

Notes

• The result was obtained concurrently with a perfectly secure protocol for the same threshold (Secure channels ⇒ MPC with honest majority ($t<n/3$) (BGW)) — BGW88.
• For $t<n/3$ the broadcast channel can be emulated over the point-to-point channels in time polynomial in $n$, so none is needed — GM93.