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'''Non-interactive [[zero-knowledge proof]]s''' are [[cryptographic primitives]], where information between a prover and a verifier can be authenticated by the prover, without revealing any of the specific information beyond the validity of the statement itself. This [[Function (computer programming)|function]] of [[encryption]] makes direct communication between the prover and verifier unnecessary, effectively removing any intermediaries. The core trustless cryptography "proofing" involves a [[hash function]] generation of a random number, constrained within mathematical parameters (primarily to modulate hashing difficulties) determined by the prover and verifier.<ref>{{cite journal |last1=Goldreich |first1=Oded |last2=Krawczyk |first2=Hugo |date=1996 |title=On the Composition of Zero-Knowledge Proof Systems |url=https://epubs.siam.org/doi/abs/10.1137/S0097539791220688 |journal=SAIM |volume=25 |issue=1 |pages=169–192 |doi=10.1137/S0097539791220688 |access-date=4 November 2022}}</ref>
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 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>
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