r/cryptography • u/Deep-Zucchini-2465 • 1d ago
Commitment Schemes in Zero Knowledge Proofs
Hi all,
I came across this subreddit because I think I finished the resources I could read regarding the topic.
Specifically, I know, in principle, what a commitment scheme is (a hiding-and-binding representation that can be opened or not at the verifier's discretion, so that the prover cannot change the value afterward). I am familiar with the whole envelope/safe analogy.
Now, I struggle to find any resource, or where to start in the first place, to understand the role of commitments in the context of ZKP (or Proof Systems in general), why we need them, and for what they are used.
Moreover, what is the difference between a simple commitment, vector commitments, and Pedersen commitments? Is there a resource that is able to reconcile this universe?
Also, why are they so important for systems such as LegoSNARK.
My "simple words" interpretation is "The commitment is a way the prover has to prove that the input used inside of the circuit is actually what has been used in the input. So there exists a value x such that Commit(x).Open = x, but I will not tell you x".
I know it might be a stupid question, but I cannot wrap my head around it. Maybe I just misunderstood the concept.
Thanks for your time, and for any guidance you might provide.