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A signature is a zkp. So your example is also a good example :)

A signature is a PoK, but not ZK.
I was not clear enough, thanks. Whether it is a pok or zk depends on the chosen signature scheme. In any case, zk signature schemes exist and are implied by the existence of one way functions and publicly verifiable nizk
> zk signature schemes exist and are implied by the existence of one way functions and publicly verifiable nizk.

Almost. The result is from CRYPTO89 paper of Bellare and Goldwasser. They derive a signature scheme from a nizk. It is not known whether you can get a nizk from a signature scheme. Moreover, no signature scheme can be a ZK: https://crypto.stackexchange.com/questions/35177/is-using-di...

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