Contruct a protocol to determine if three secret keys are different, without revealing any of them? I am trying to find a protocol for this problem:

Three persons, $A$, $B$, and $C$, know secret numbers $s_{A}, s_{B}$, and $s_{C}$, respectively. They want to know whether their numbers are all different, but none of them wants to reveal his number to any of the others.

If there are equal numbers between the three, this fact should be known, but no one shall discover which numbers are equal.

There is no trusted center (i.e. they can't use a fourth party doing calculations or similar), they only can communicate with each other.
You should easily be able to do this using a generic multi-party computation framework. For more info on what frameworks are available see Practical implementations of Multiparty computations.

From what I have seen, VIFF is pretty easy to get up and running to experiment with.