>It's more like this: you and I have some process we're collaborating on, and we both have an interest in getting accurate outputs from some kind of computation related to that process. But the only way to get really accurate outputs is to feed in proprietary, "secret" data from both your company and mine, and while we both have an interest in those outputs, neither of us wants to share our proprietary data with the other.

Ahh, that makes a little more sense. Seems like I could get your "secret" data by simply reversing the operation that gives us our shared result, though, doesn't it? Unless it's some kind of modulo type thing.