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Proof of knowledge — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Proof_of_knowledge
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-23T15:24:24.028Z
SHA-256 of the archived text: babeb042575c03dabdfc37c768216d80e867bcba6ac5cfaaf245dfeba5e856ec
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Proof of knowledge — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Proof_of_knowledge (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_cfafb4500151 (Metraipolis archive dc_cfafb4500151, sha256 babeb042575c03dabdfc37c768216d80e867bcba6ac5cfaaf245dfeba5e856ec)

BibTeX

@misc{dccfafb4500151,
  title = {Proof of knowledge — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Proof_of_knowledge},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_cfafb4500151; sha256 babeb042575c03dabdfc37c768216d80e867bcba6ac5cfaaf245dfeba5e856ec},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Proof_of_knowledge. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In cryptography, a proof of knowledge is an interactive proof in which the prover succeeds in 'convincing' a verifier that the prover knows something. What it means for a machine to 'know something' is defined in terms of computation. A machine 'knows something', if this something can be computed, given the machine as an input. As the program of the prover does not necessarily spit out the knowledge itself (as is the case for zero-knowledge proofs), a machine with a different program, called the knowledge extractor is introduced to capture this idea. This is mostly limited to what can be proven by polynomial time bounded machines. In this case, the set of knowledge elements is limited to a set of witnesses of some language in NP. Let x {\displaystyle x} be a statement of language L {\displaystyle L} in NP, and W ( x ) {\displaystyle W(x)} the set of witnesses for x that should be accepted in the proof. This allows to define the following relation: R = { ( x , w ) : x ∈ L , w ∈ W ( x ) } {\displaystyle R=\{(x,w):x\in L,w\in W(x)\}} . A proof of knowledge for relation R {\displaystyle R} with knowledge error κ {\displaystyle \kappa } is a two party protocol with a prover P {\displaystyle P} and a verifier V {\displaystyle V} with the following two properties: Completeness: If ( x , w ) ∈ R {\displaystyle (x,w)\in R} , then the prover P {\displaystyle P} who knows witness w {\displaystyle w} for x {\displaystyle x} succeeds in convincing the verifier V {\displaystyle V} of his knowledge. More formally: Pr ( P ( x , w ) ↔ V ( x ) → 1 ) = 1 {\displaystyle \Pr(P(x,w)\leftrightarrow V(x)\rightarrow 1)=1} , i.e. given the interaction between the prover P and the verifier V, the probability that the verifier is convinced is 1. Validity: Validity requires that the success probability of a knowledge extractor E {\displaystyle E} in extracting the witness, given oracle access to a possibly malicious prover P ~ {\displaystyle {\tilde {P}}} , must be at least as high as the success probability of the prover P ~ {\displaystyle {\tilde {P}}} in convincing the verifier. This property guarantees that no prover that doesn't know the witness can succeed in convincing the verifier.

Tema degli esploratori: fiducia digitale e crittografia (deposito sistematico; ricerca «zero-knowledge proof»).
Fonte: Wikipedia in inglese, voce «Proof of knowledge» — https://en.wikipedia.org/wiki/Proof_of_knowledge
Wikidata Q7250015 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q7250015
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Proof_of_knowledge?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1376498673, consultata il 2026-10-23T15:10:21.941Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 4d6273d9f8b9735dc469ec60deb8b7c8a6adf7209c705e3053ed299de8d44cc2