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Zero-knowledge proof
In cryptography, a zero-knowledge proof 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.[1] The intuition underlying 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).[2]
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, 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.[3] 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.[4][5][6]
- ^ Aad, Imad (2023), Mulder, Valentin; Mermoud, Alain; Lenders, Vincent; Tellenbach, Bernhard (eds.), "Zero-Knowledge Proof", Trends in Data Protection and Encryption Technologies, Cham: Springer Nature Switzerland, pp. 25–30, doi:10.1007/978-3-031-33386-6_6, ISBN 978-3-031-33386-6
- ^ Goldreich, Oded (2001). Foundations of Cryptography Volume I. Cambridge University Press. p. 184. doi:10.1017/CBO9780511546891. ISBN 9780511546891.
- ^ Goldreich, Oded (2001). Foundations of Cryptography Volume I. Cambridge University Press. p. 247. doi:10.1017/CBO9780511546891. ISBN 9780511546891.
- ^ Goldreich, Oded (2001). Foundations of Cryptography Volume I. Cambridge University Press. p. 299. doi:10.1017/CBO9780511546891. ISBN 9780511546891.
- ^ Blum, Manuel; Feldman, Paul; Micali, Silvio (1988). "Non-interactive zero-knowledge and its applications". Proceedings of the twentieth annual ACM symposium on Theory of computing - STOC '88 (PDF). pp. 103–112. doi:10.1145/62212.62222. ISBN 978-0897912648. S2CID 7282320. Archived (PDF) from the original on December 14, 2018. Retrieved June 2, 2022.
- ^ Wu, Huixin; Wang, Feng (2014). "A Survey of Noninteractive Zero Knowledge Proof System and Its Applications". The Scientific World Journal. 2014: 560484. doi:10.1155/2014/560484. PMC 4032740. PMID 24883407.
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