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MPC involves running calculations on numbers, perhaps from different parties, and sharing the result without anyone seeing the underlying data. Even the person operating the computer cannot access the information

How is this possible on ethereum?

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The iExec or Enigma projects might be what you are looking for.

A challenge of this sort of thing is verifying that the parties executed the job honestly and correctly without every node needing to repeat the job - because that would severely limit the complexity of what can be done and defeat the purpose of deligating a large job to a specific node.

iExec solves that by including an integrity check. It is a test of the properties of correct solutions even if the process is subjective. An example given is a face-blurring app that modifies images, and there is more than one "correct" result. Certain properties are defined - facial geometry, eyes not too clear, other stuff is still clear, and so on. Other nodes can evaluate the given solution to confirm it is acceptable.

Enigma is more challenging on a math and cryptography level. Within their system, parties can execute contracts without knowing what the contracts do, as I presently understand it. I suspect this project might be a closer match to your MPC requirement.

Hope it helps.

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