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Reducing accusations of rigged electronic dice

Posted By: Timothy Chow
Date: Wednesday, 23 August 2023, at 12:39 p.m.

In Response To: Reducing accusations of rigged electronic dice (Jason Lee)

Jason Lee wrote:

The hash function is rigged.

LOL.

I might as well take this opportunity to mention that some researchers have seriously considered whether even this loophole can be closed. That is, suppose you have a hash function f and I have a hash function g. You trust f  but not g, and I trust g but not f. Is there a way to combine f and g to produce a hash function that both of us trust?

This is a more difficult problem than it might seem. For example, an obvious attempt is to compose the hash functions; i.e., define h(x) to be f (g(x)). You could argue that if either f or g is hard to invert, then h should be hard to invert. But the trouble is that if I have a secret clever method of producing collisions for g, then that gives me a way to produce collisions for h, no matter how secure f is.

I'm not very familiar with all the literature on this particular problem, but the last time I checked, someone had proposed an extremely complicated solution to this problem, which nobody had been able to break. The trouble was that the solution was so complicated as to be impractical for real-world use.

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