Hi, I would like to ask concerning zk-proofs,

I would like to know whether most of the proving can be side-stepped/cut-down given that an entity does not want to prove to a verifier that some execution is done correctly, but rather the result of some execution is tied to their identity (key pair) without revealing any other secret about it.

So basically we don't care about the correctness of the execution, only that the prover can prove that its identity is tied to the execution result without revealing any other secret.

Full context:

So I'm building a project, and in this system are a secretly chosen committee that executes some computational work secretly after being chosen secretly using VDF + VRF, this committee then send their result to the network, for which any node can then listen, compile and check that >2/3 of chosen nodes (committee) agreed on the result to conclude that the execution is correct. 

But a chosen committee node can wait for other committee nodes to expose their results before taking that result and submitting it as their own claiming part of whatever reward is shared for the execution. 

My goal is then to have each chosen committee node use zk-proofs to prove that their identity is connected to execution, or at least it spent the necessary gas in that execution, without having to prove execution correctness, as the network can do that.

Thank you.