In cryptography, azero-knowledge proof orzero-knowledge protocolis a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true, without conveying any information apart from the fact that the statement is indeed true.
Another way of understanding this would be: Interactive zero-knowledge proofs require interaction between the individual (or computer system) proving their knowledge and the individual validating the proof.
If proving the statement requires knowledge of some secret information onthe part of the prover, the definition implies that the verifier will not be able to prove the statement in turn to anyone else, since the verifier does not possess the secret information.
Notice that the statement being proved must include the assertion that the prover has such knowledge (otherwise, the statement would not be proved in zero-knowledge, since at the end of the protocol the verifier would gain the additional information that the prover has knowledge of the required secret information).
If the statement consists only of the fact that the prover possesses the secret information, it is a special case known as zero-knowledge proof of knowledge, and it nicely illustrates the essence of the notion of zero-knowledge proofs: proving that one has knowledge of certain information istrivial if one is allowed to simply reveal that information; the challenge is proving that one has such knowledge without revealing the secret information or anything else.
For zero-knowledge proofs of knowledge, the protocol must necessarily require interactive input from the verifier, usually in the form of a challenge or challenges such that the responses from the prover will convince the verifier if and only if the statement is true (i.e. if the prover does have the claimed knowledge).
This is clearly the case, since otherwise the verifier could record the execution of the protocol and replay it to someone else: if this were accepted by the new party as proof that the replaying party knows the secret information, then the new party’s acceptance is either justified—the replayer does know the secret information—which means that the protocol leaks knowledge and is not zero-knowledge, or it is spurious—i.e. leads to a party accepting someone’s proof of knowledge who does not actually possess it.
The artist has seen this red rose in her dreams for many years and in different shape and forms. The picture on the opening page of this website is yet another rendition by her of ‘the rose’. She recently discovered an artist on ‘Instagram’, who is always drawing the roses, but just in a different setting as her. His name is, David Brookton. Also, note the collage of the picture of the artist’s rose and David’s together. Both show identical water streams at the bottom of the rose.
See the attached picture link – David sold a copy of his picture of ‘the rose’, called: ‘Roses and trains of thought – Episode 2, in 2017’.
Listen to Michael Praetorius: ‘Es ist ein Ros entsprungen’, Voices of Music.