#ZKP #proof [[Hub/Theory/Category Theory/Logic/Proof/ZKP|Zero Knowledge Proof]] ([[Hub/Theory/Category Theory/Logic/Proof/ZKP]]) is a cryptographic technique that allows one party, the prover, to convince another party, the verifier, that a certain statement is true without revealing any additional information apart from the truth of the statement itself. In other words, it enables proving knowledge of a secret or solving a problem without disclosing any details about how it was done. ZKPs provide an important tool for enhancing privacy and security in various scenarios. For example, they can be used to authenticate users without revealing their passwords or other sensitive information. They also play a crucial role in blockchain technology by allowing participants to verify transactions and smart contracts without exposing confidential data. The concept of [[Hub/Theory/Category Theory/Logic/Proof/ZKP|Zero Knowledge Proofs]] was introduced by [[Shafi Goldwasser]], [[Silvio Micali]], and [[Charles Rackoff]] in 1985. Since then, various types of ZKPs have been developed, including interactive and non-interactive protocols. These protocols involve complex mathematical computations and rely on concepts such as commitment schemes and trapdoor functions to ensure the integrity and confidentiality of the proof. Zero Knowledge Proofs have widespread applications in cryptography, cybersecurity, authentication protocols, secure multiparty computation, digital signatures, secure voting systems, and more. They offer a powerful tool to establish trust and privacy in situations where parties need to share information but want to minimize the disclosure of sensitive data. # Examples of ZKP approaches 1. [[SNARK|Succinct Non-interactive ARguments of Knowledge]] ([[SNARK]]): SNARKs allow a prover to convince a verifier about the truth of a statement without revealing any additional information. They are efficient and compact, making them suitable for use in blockchain applications. 2. zk-SNARK: zk-SNARKs are a specific type of SNARK that utilize zero-knowledge proofs to prove knowledge of a solution to a computational problem without revealing the solution itself. They are widely used in privacy-focused cryptocurrencies like Zcash. 3. Bulletproofs: Bulletproofs are non-interactive zero-knowledge proofs that provide efficient and secure verification of range proofs for confidential transactions. They significantly reduce the size and computational overhead associated with range proofs, making them practical for use in blockchain systems. 4. zk-STARK: zk-STARK is an alternative to SNARK that offers post-quantum security by utilizing transparent and scalable zero-knowledge proofs. It allows for efficient verification of computational integrity and correctness without requiring any trusted setup. 5. Zero-Knowledge Sets (ZK-sets): ZK-sets enable the construction of cryptographic sets where one can prove membership or non-membership in the set without revealing any information about the set itself or other elements within it. This approach has applications in privacy-preserving authentication systems. 6. Zero-Knowledge Proofs of Knowledge (ZKPK): ZKPK protocols allow a prover to demonstrate knowledge of some secret information without revealing anything other than the fact that they possess this knowledge. They are often used for password authentication or key exchange protocols. 7. Zero-Knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARG): Similar to zk-SNARKs, zk-SNARGs provide non-interactive zero-knowledge proofs with succinctness and soundness properties. They have applications in privacy-preserving computations, authentication protocols, and more. 8. Sigma Protocols: Sigma protocols are interactive zero-knowledge proofs that allow a prover to convince a verifier about the truth of a statement without revealing any additional information. They are widely used in cryptographic protocols, such as digital signatures and secure key exchange. 9. Secure Multi-Party Computation (MPC): MPC protocols enable multiple parties to jointly compute a function over their private inputs without revealing any information about those inputs. While not strictly zero-knowledge proofs, they provide privacy guarantees by ensuring that only the desired output is revealed. 10. Zero-Knowledge Password Proof ([[ZKPP]]) is a cryptographic protocol that allows a user to prove knowledge of a password without actually revealing the password itself. This provides an extra layer of security and privacy, as the server or verifier does not have access to the actual password. # References ![[@computationalthinkingZeroKnowledgeProofs2022|Zero Knowledge Proofs]] [[@nicoZeroKnowledgeProof2023|One Page on zero knowledge proof]] [[@ingonyamaMagicZeroKnowledgeProofs2023|The Magic of Zero Knowledge Proofs]]