A zero-knowledge proof (ZKP) is a method by which one party (the prover) can prove to another party (the verifier) that a statement is true, without revealing any additional information. The key property of a ZKP is that the verifier learns nothing about the statement being proven other than whether it is true or false. This can be useful in situations where the prover wants to prove something without revealing any sensitive information.
This idea has wider implications when it applies to user authentication.
Zero-knowledge proofs can be used in user authentication in a number of ways. One example is password-less authentication, where the user proves possession of a secret, such as a private key, without revealing it to the verifier (e.g. a server). This can be done by using a zero-knowledge proof of knowledge of the secret, such as a zero-knowledge proof of knowledge of a discrete logarithm or a zero-knowledge proof of knowledge of a discrete logarithm of an elliptic curve.
Another example is attribute-based authentication, where the user proves possession of certain attributes, such as age or address, without revealing the specific values of those attributes. This can be done by using a zero-knowledge proof of knowledge of the attributes, such as a zero-knowledge proof of knowledge of a discrete logarithm of a commitment to the attribute.
Zero-knowledge proofs could be used in several other ways and it's becoming more and more popular in the field of privacy-enhancing technologies.
Zero-knowledge proofs can be used in payments to enable privacy-preserving transactions. One example is confidential transactions, which use zero-knowledge proofs to hide the amounts being transferred. This can be done by using a zero-knowledge proof of knowledge of the discrete logarithm of the sum of the input amounts to the sum of the output amounts. This way, the verifier can ensure that the inputs and outputs are valid without learning the specific amounts being transferred.
Another example is privacy-preserving token trading, where the user can prove that they own a certain number of tokens without revealing which specific tokens they own. This can be done by using a zero-knowledge proof of knowledge of the discrete logarithm of the commitment to the tokens. In addition to tokens, ZPKs could be used to verify account balances for a purchase or to verify a credit score without revealing the specific score to a creditor.
Zero-knowledge proofs could be used in payments to enhance the privacy and security of transactions. ZKPs can also be used in other payment related areas such as fraud detection, compliance, and regulatory reporting.