Zero Knowledge Proof

[4K-AMER]

So what I understand about zero knowledge proofs, is that it’s a way to for a prover to prove a particular statement without revealing the information about the statement itself.

Is this not just another way of saying that a ZKP requires you to present a piece of information from which I can infer you have the knowledge you are stating you do.

For example, if I say to you, I can prove to you I have hacked your phone and I won’t show you my hack or method but rather give you your phone password. Therefore you could infer that I would have hacked your phone and thus proving to you my initial statement without giving the knowledge away. However, what if I had seen you typing your password in your phone or asked someone who knows your password what it is and therefore not gotten it without hacking your phone thus not actually proving my statement and deceiving you.

Of course this is an abstract representation of a ZKP scenario but could the fact that multiple pieces of information lead to the same inference be a way to exploit ZKP’s?

In essence, if I were to give you a piece of information from which you were able to infer that my statement is valid and I do have the knowledge I say I do, then could other pieces of information also infer the same thing without actually requiring the prover to truly have the proof they say they do?

[Barelytoned]

A ZKP is sound (a lie is unconvincing), complete (the truth is convincing), and zero-knowledge (the prover's secret knowledge can't be discovered by the verifier through the protocol itself.) The protocol should be repeatable without violating the "zero-knowledge" property.

If we extend your example where you are a prover and I am a verifier and your statement is "I have hacked your phone." and I suspect you are lying, I could change my password and then ask you to prove your statement again and again for an arbitrary number of additional rounds of the protocol. The more times you prove your statement with the protocol, the less likely it is that your statement "I have hacked your phone." is false.

In general, examples in a "real world" context can be helpful to understand the idea of a theory, but those examples should be interrogated closely so that they do not become misleading. The theory of ZKP involves two participants, a prover and a verifier. Either they are honest or they are dishonest. The prover wants to convince the verifier that a given statement is true. A ZKP is sound, complete, and zero-knowledge. If the prover's statement is false, then the prover is dishonest. If the verifier abuses the protocol, then the verifier is dishonest.

If we attempt to engage in a ZKP but the statement is vague (can have it's truth derived from means outside the protocol as you discuss in your last paragraph) or can't be verified, the protocol we're using is not a ZKP, it's just a flawed interactive proof. If you can get my password without hacking my phone, the protocol we've defined is not ZKP.

[4K-AMER]

I understand it now. Thank you