Jan 22, 2014

example for Zeroo Knowledge proofs in cryptography

give me a cryptographyc examples for Zeroo Knowledge proofs

Zero-knowledge proof

"In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true, without conveying any additional information apart from the fact that the statement is indeed true. For cases where the ability to prove the statement requires some secret information on the part of the prover, the definition implies that the verifier will not be able to prove the statement to anyone else. Notice that the notion only applies if the statement being proven is the fact 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). This is a particular case known as zero-knowledge proof of knowledge, and it nicely illustrates the essence of the notion of zero-knowledge proofs: proving that one possesses a certain knowledge is in most cases trivial if one is allowed to simply reveal that knowledge; the challenge is proving that one has such knowledge without revealing it or without revealing 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 prove it to someone else, contradicting the fact that proving the statement requires knowledge of some secret on the part of the prover.

Some forms of non-interactive zero-knowledge proofs of knowledge exist,[1] but the validity of the proof relies on computational assumptions (typically the assumptions of an ideal cryptographic hash function)."

Strange question, is it thesis time? One zero knowlede proof example that almost everyone is familiar with is the two coloured balls example. Let’s see if I can remember it: You have two balls, one green and one red, identical in every way except colour. You have a colour-blind friend who sees them as identical, and he doesn’t believe you when you say that they are different. You want to prove that they are in fact different, but do not want to reveal which is green and which is red. So you give your mate the balls, one in each hand, and tell him to put the balls behind his back and mix them up (or not) while you can’t see them. You can then tell him with 100% accuracy whether he switched the balls (or not) each time simply by looking at the colour. If there was not a difference in colour, the best you could do over time would be guess with 50% accuracy. You can prove that the balls are different colours, but with this method, your mate didn’t gain any knowledge (zero knowledge, in other words) as to which ball is red and which is green.

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