# A question about verifier in zero knowledge proof

I found an article about zero knowlegde authentication and I have question ethesis.nitrkl.ac.in/5755/1/110CS0371-2.pdf

It said "In Cryptography, the Zero Knowledge confirmation/convention is a sort of convention in which one entity (claimant) demonstrates an alternate entity (verifier) that a certain information is genuine separated from the way that it doesn't pass on that the data given is genuine or false."

Does this mean that the verifier does not (and will not) know whether the data from the claimant is true or false? Because using the cave analogy, the verifier will know about the genuineness of the data, since the verifier will see where the claimant will come out from (either from the wrong / right path).

From that paper, what I got is: The verifier doesn't know what the data is, and it also doesn't (and won't) know whether the data is genuine or not

Edit: English is not my first language, so maybe I got the wrong conclusion / translation from that bolded part...

• The quoted passage makes absolutely no sense to me. – fkraiem Feb 9 '17 at 1:15

The meaning of this has two aspects:

• After running the protocol successfully, the verifier is convinced (with overwhelming probability) that the information is genuine.
• The verifier can by no means extract the information from the protocol. It is simply impossible (not unlikely, actually impossible).

Very simplified a zero knowledge protocol goes like this:

• First, the prover sends some information to the verifier
• Then the verifier generates a random value (often just a single bit) and sends that to the prover
• The prover answers based on that random value, and the verifier can check that answer combined with the first value and his random value.

The protocol is set up such a way, that only if the prover truly knows the secret information, he can send the correct answer in the last step with certainty. Otherwise he has to rely on luck. So if the verifier used random values in the second step and the prover didn't know them in the first step, there is a certain chance (often probability $0.5$) that the verification in the end does not work out.

And lastly, the above steps are done multiple times and only if the prover passed all of them the verifier is convinced. With probability $1/2$ per round, the remaining uncertainty after $k$ rounds is $\frac{1}{2^k}$.

One would split Prover "data" into a statement (a theorem) and solution (witness to validity of the theorem). Please consider to read NP complexity class definition for a better view. Verifier will not learn the witness still he will be convinced that theorem is true (with high probability).