zero-knowledge proof，中文名为零知识证明，是零币(Zcoin)使用的共识算法，由S.Goldwasser、S.Micali及C.Rackoff在20世纪80年代初提出的。它指的是证明者能够在不向验证者提供任何有用的信息的情况下，使验证者相信某个论断是正确的。
Zero-knowledge proof, a Chinese-named zero-knowledge certificate, is the consensus algorithm used by Zcoin, proposed by S. Goldwasser, S. Micali and C. Rackoff in the early 1980s. It refers to the ability of the certifying officer to convince the certifying authority that a certain assertion is correct without providing any useful information to the certifying officer.
零知识证明实质上是一种涉及两方或更多方的协议，即两方或更多方完成一项任务所需采取的一系列步骤。证明者向验证者证明并使其相信自己知道或拥有某一消息，但证明过程不能向验证者泄漏任何关于被证明消息的信息。
The proof of zero knowledge is in essence an agreement involving two or more parties, i.e. a series of steps that two or more parties need to take to complete a mission. The certifying person proves to the certifying party that he or she knows or owns a certain information, but the certification process does not disclose to the certifying party any information about the proven information.
在零知识证明中，证明者和验证者之间必须进行交互，这样的零知识证明被称为“交互零知识证明”。80年代末，Blum等人进一步提出了“非交互零知识证明”的概念，用一个短随机串代替交互过程并实现了零知识证明。非交互零知识证明的一个重要应用场合是需要执行大量密码协议的大型网络。
At the end of the 1980s, Blum et al. further developed the concept of “non-interactive zero knowledge” by replacing the interactive process with a short random string and achieving zero knowledge. An important application of non-interactive zero knowledge is the large network that requires the implementation of a large number of password protocols.
在零知识证明中，个人(或器件)可以在不泄漏任何秘密的情况下，证明他知道这个秘密。如果能够将零知识证明用于验证，将可以有效解决许多问题。
In a zero knowledge certificate, a person (or device) can prove that he knows the secret without disclosing any secret. If the zero knowledge certificate can be used for verification, many problems can be solved effectively.
零知识证明并不是数学意义上的证明，因为它存在小概率的误差，欺骗者有可能通过虚假陈述骗过证明者。换句话来说，零知识证明是概率证明而不是确定性证明。但是也存在有技术能将误差降低到可以忽略的值。
In other words, proof of zero knowledge is proof of probability rather than certainty. But there is also technology to reduce errors to negligible values.
零知识的形式定义必须使用一些计算模型，最常见的是图灵机的计算模型。
A formal definition of zero knowledge must use a number of computational models, most commonly those of Turing machines.
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