Secure Multi-Party Computation

What is secure multi-party computation?

A few companies want to compute something together — score credit risk jointly, train a shared model — but nobody wants to hand over their raw data. Secure multi-party computation (SMPC) lets several parties compute a correct result together without any of their data ever leaving the building.

How does it pull that off?

Split the data into "shares"
Each party first runs secret sharing, cutting its data into random pieces and distributing them to the others. Any single share reveals nothing about the original; only enough shares together can reconstruct it.
Compute on the shares
The parties do their math on the shares while everything stays hidden, then combine the pieces at the end. Nobody ever sees anyone else's raw data, yet everyone gets the correct result.

How does it relate to homomorphic encryption and federated learning?

Homomorphic encryption: one party, encrypted math
It's more about outsourcing encrypted data to a server to compute. SMPC is about several parties keeping secrets from each other.
Federated learning: share models, not data
Parties train separately and only exchange gradients; SMPC can also protect those exchanged gradients, so the two are often used together.

Where is it used?

Banks doing joint fraud detection, hospitals running cross-institution medical statistics, multi-party bidding and auctions — all fit SMPC. It's a way to get privacy and efficiency at once when people need to cooperate but fear leaks.

Bottom line: SMPC lets a group "compute together" while nobody gets to see anyone else's cards.