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I am studying about the zero knowledge proofs and I am looking for a practical (example based) approach to undrestand its process. I have studied the theory a little bit and I find it interesting yet confusing.

My exact question is given a prover A and verifier B. How can prover A prove that he is in the possession of some value 'X' without disclosing 'X' to B. 'X' could be A's last name or A's telephone number.

I am trying to compare this approach with commitment schemes (i.e. Hashing 'X' and comparing the hashes). I know that in the commitment schemes the value 'X' must be shared with B.

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    $\begingroup$ There are many standard references on ZK proofs (and on commitment schemes). I suggest studying them. $\endgroup$ – D.W. Oct 2 '17 at 2:35
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"is Zero knowledge Proof same as commitment schemes?"

No, although if one makes soundness be only computational
(i.e., arguments rather than proofs) , ​ then existence of such zero-knowledge protocols
is equivalent to existence of instance-dependent commitment schemes.



"How can prover A prove that he is in the possession of some value 'X'
without disclosing 'X' to B. 'X' could be A's last name or A's telephone number"


How would the verifier check validity of the claimed 'X' if A did disclose 'X' to B?

Your hashing remark suggests that what you're thinking
about is actually proving knowledge of a preimage:
i.e., both parties know 'Y', and A is proving knowledge of a 'W' such that ​ H(W) = Y .

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