Zero knowledge proof of dependency Is there any ZK protocol that can be used to prove dependence of two entities. More specifically, if there are x(dependent) and y(independent), is there protocol to prove that x is dependent or function of y, without revealing the function it self.


  Edit: As replies below suggested, I thought to provide concrete form of dependent function. So for example x= 2+y another example can be x=ky, where k is yet another independent variable. In short, x can be even more complicated function of y.
Any NP statement can be proven in zero knowledge (not necessarily practically efficiently, but yes in polynomial time). So, if you can define what you want as an NP relation then it can be done. However, in order to do that, you must define what you mean by "dependent" and so on. 

Such statements can also be highly efficient. For example, it is possible to efficiently prove that a tuple of elements if of the "Diffie Hellman type". Informally, one can prove that for some $(g,h,u,v)$ there exists a value $r$ such that $u=g^r$ and $v=h^r$ (where $g$ is the group generator and all operations are in the group). Observe that this is exactly a proof that $u$ and $v$ are ''dependent'' variables.