Several people compute a result together, like their average salary, without anyone revealing their own number. It works with no math assumptions, as long as most of them are honest.
The idea: Each person splits their number into Shamir shares and gives one to everyone. Shares can be added directly: if everyone adds up the shares they hold, the results are shares of the total. So the group computes a sum without anyone seeing an input. Multiplying needs a short extra round of talking, and with additions and multiplications you can compute anything. Privacy holds as long as the cheaters are too few to pool enough shares.
Why it matters: Privacy-preserving teamwork can rest on honesty instead of hard math.
On the map: BGW, CCD
Secure multiparty computation (MPC) lets parties compute a function of their private inputs, say an average salary, without anyone seeing anyone else's input.
The BGW and CCD protocols (1988)[1, 2] do this with no computational assumptions at all, as long as more than half of the parties are honest (two thirds against actively cheating parties) and every pair can talk over a private channel. They work by computing directly on Shamir secret shares.
If any of these breaks, this breaks too.
If this breaks, these break with it.
Nothing on the map depends on it: it is an end point, something people use directly.