[AgentME]

Say that all the other participants have revealed their pre-images, and you're the last one left you reveal your pre-image. Before you reveal it, you realize you alone have all the pre-images and can calculate the result. You calculate it, and realize you don't like the result. You could then decide to throw away your pre-image to force a new roll. If necessary, claim your computer crashed, your connection dropped, etc.

[AgentME]

I misworded the first sentence confusingly. Here's what I meant:

>Say that all the other participants have revealed their pre-images, and you're the last one left to your reveal your pre-image.

[mojomark]

Couldn't this be solved (or the risk of manipulation largely mitigated) using a trusted third party to witness, and perhaps hold, each candidates pre-image generation?

[AgentME]

If you have the trusted party reveal all of the pre-images, then you're just passing off the ability to decide not to reveal the pre-images to them. You could layer on the ability for all of the parties to reveal their pre-images if the third party fails to reveal them, though now you have the complication that the parties could reveal different pre-images than they gave to the third party. (Maybe one of the parties could realize the third party would defect because of a certain result that party doesn't want either, so that party could change their pre-image to avoid that result.)

The third party isn't any different than the main parties in the mix. If everyone can decide who the most trustworthy party in the mix is, you can have them reveal last.

[kannanvijayan]

Thanks for the succinct explanation - that makes sense.