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The key advantage of non-interactive [[zero-knowledge proof]]s is that they can be used in situations where there is no possibility of interaction between the prover and verifier, such as in online transactions where the two parties are not able to communicate in real time. This makes non-interactive zero-knowledge proofs particularly useful in decentralized systems like [[Blockchain|blockchains]], where transactions are verified by a network of [[nodes]] and there is no central authority to oversee the verification process.<ref name=":0">{{Cite book |last1=Gong |first1=Yinjie |last2=Jin |first2=Yifei |last3=Li |first3=Yuchan |last4=Liu |first4=Ziyi |last5=Zhu |first5=Zhiyi |title=2022 International Conference on Big Data, Information and Computer Network (BDICN) |chapter=Analysis and comparison of the main zero-knowledge proof scheme |date=January 2022 |chapter-url=https://ieeexplore.ieee.org/document/9758531 |pages=366–372 |doi=10.1109/BDICN55575.2022.00074|isbn=978-1-6654-8476-3 |s2cid=248267862 }}</ref>
Most non-interactive zero-knowledge proofs are based on mathematical constructs like [[elliptic curve cryptography]] or [[pairing-based cryptography]], which allow for the creation of short and easily verifiable proofs of the truth of a statement. Unlike [[interactive zero-knowledge proofs]], which require multiple rounds of interaction between the prover and verifier, non-interactive zero-knowledge proofs are designed to be efficient and can be used to verify a large number of statements simultaneously.<ref name=":0" />
== History ==<!-- really, as of Oct 2020, this is just the academic history of zero-knowledge proofs; needs expansion to include the history of use in real applications of software and apps -->
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