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Zero-knowledge proof
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Zero-knowledge proof
In cryptography, a zero-knowledge proof (also known as a ZK proof or ZKP) is a protocol in which one party (the prover) can convince another party (the verifier) that some given statement is true, without conveying to the verifier any information beyond the mere fact of that statement's truth. The intuition behind the nontriviality of zero-knowledge proofs is that it is trivial to prove possession of the relevant information simply by revealing it; the hard part is to prove this possession without revealing this information (or any aspect of it whatsoever).
In light of the fact that one should be able to generate a proof of some statement only when in possession of certain secret information connected to the statement, the verifier, even after having become convinced of the statement's truth by means of a zero-knowledge proof, should nonetheless remain unable to prove the statement to further third parties.
Zero-knowledge proofs can be interactive, meaning that the prover and verifier exchange messages according to some protocol, or noninteractive, meaning that the verifier is convinced by a single prover message and no other communication is needed. In the standard model, interaction is required, except for trivial proofs of BPP problems. In the common random string and random oracle models, non-interactive zero-knowledge proofs exist. The Fiat–Shamir heuristic can be used to transform certain interactive zero-knowledge proofs into noninteractive ones.
One example of a math-free zero knowledge proof is if Peggy wants to prove to Victor that she has drawn a red card from a standard deck of 52 playing cards, without revealing which specific red card she holds. Victor observes Peggy draw a card at random from the shuffled deck, but she keeps the card face-down so he cannot see it.
To prove her card is red without revealing its identity, Peggy takes the remaining 51 cards from the deck and systematically shows Victor all 26 black cards (the 13 spades and 13 clubs) one by one, placing them face-up on the table. Since a standard deck contains exactly 26 red cards and 26 black cards, and Peggy has demonstrated that all the black cards remain in the deck, Victor can conclude with certainty that Peggy's hidden card must be red.
This proof is zero-knowledge because Victor learns only that Peggy's card is red, but gains no information about whether it is a heart or diamond, or which specific red card she holds. The proof would be equally convincing whether Peggy held the Ace of Hearts or the Two of Diamonds. Furthermore, even if the interaction were recorded, the recording would not reveal Peggy's specific card to future observers, maintaining the zero-knowledge property.
If Peggy was lying and actually held a black card, she would be unable to produce all 26 black cards from the remaining deck, making deception impossible. This demonstrates the soundness of the proof system. This type of physical zero-knowledge proof using standard playing cards belongs to a broader class of card-based cryptographic protocols that allow participants to perform secure computations using everyday objects.
Another well-known example of a zero-knowledge proof is the "Where's Wally" example. In this example, the prover wants to prove to the verifier that they know where Wally is on a page in a Where's Wally? book, without revealing his location to the verifier.
Hub AI
Zero-knowledge proof AI simulator
(@Zero-knowledge proof_simulator)
Zero-knowledge proof
In cryptography, a zero-knowledge proof (also known as a ZK proof or ZKP) is a protocol in which one party (the prover) can convince another party (the verifier) that some given statement is true, without conveying to the verifier any information beyond the mere fact of that statement's truth. The intuition behind the nontriviality of zero-knowledge proofs is that it is trivial to prove possession of the relevant information simply by revealing it; the hard part is to prove this possession without revealing this information (or any aspect of it whatsoever).
In light of the fact that one should be able to generate a proof of some statement only when in possession of certain secret information connected to the statement, the verifier, even after having become convinced of the statement's truth by means of a zero-knowledge proof, should nonetheless remain unable to prove the statement to further third parties.
Zero-knowledge proofs can be interactive, meaning that the prover and verifier exchange messages according to some protocol, or noninteractive, meaning that the verifier is convinced by a single prover message and no other communication is needed. In the standard model, interaction is required, except for trivial proofs of BPP problems. In the common random string and random oracle models, non-interactive zero-knowledge proofs exist. The Fiat–Shamir heuristic can be used to transform certain interactive zero-knowledge proofs into noninteractive ones.
One example of a math-free zero knowledge proof is if Peggy wants to prove to Victor that she has drawn a red card from a standard deck of 52 playing cards, without revealing which specific red card she holds. Victor observes Peggy draw a card at random from the shuffled deck, but she keeps the card face-down so he cannot see it.
To prove her card is red without revealing its identity, Peggy takes the remaining 51 cards from the deck and systematically shows Victor all 26 black cards (the 13 spades and 13 clubs) one by one, placing them face-up on the table. Since a standard deck contains exactly 26 red cards and 26 black cards, and Peggy has demonstrated that all the black cards remain in the deck, Victor can conclude with certainty that Peggy's hidden card must be red.
This proof is zero-knowledge because Victor learns only that Peggy's card is red, but gains no information about whether it is a heart or diamond, or which specific red card she holds. The proof would be equally convincing whether Peggy held the Ace of Hearts or the Two of Diamonds. Furthermore, even if the interaction were recorded, the recording would not reveal Peggy's specific card to future observers, maintaining the zero-knowledge property.
If Peggy was lying and actually held a black card, she would be unable to produce all 26 black cards from the remaining deck, making deception impossible. This demonstrates the soundness of the proof system. This type of physical zero-knowledge proof using standard playing cards belongs to a broader class of card-based cryptographic protocols that allow participants to perform secure computations using everyday objects.
Another well-known example of a zero-knowledge proof is the "Where's Wally" example. In this example, the prover wants to prove to the verifier that they know where Wally is on a page in a Where's Wally? book, without revealing his location to the verifier.