zero-knowledge systems

Zero-knowledge systems, rooted in zero-knowledge proofs (ZKPs), are cryptographic protocols that allow one party (the prover) to prove to another (the verifier) that a statement is true without revealing any additional information beyond the statement's validity. These systems ensure privacy, security, and verifiability in applications like blockchain transactions, identity verification, and secure voting. Key properties include completeness (true statements are accepted), soundness (false statements are rejected), and zero-knowledge (no extra information is leaked). Common implementations include zk-SNARKs and zk-STARKs, used in privacy-focused blockchains like Zcash.

Example: A zero-knowledge system can enable private transactions on a blockchain. For instance, a user wants to prove they have sufficient funds to send 10 tokens to another user without revealing their total balance. Using zk-SNARKs, the user generates a proof that validates the transaction's legitimacy (e.g., sufficient funds and correct computation) without disclosing their balance or transaction details. The blockchain verifies the proof, ensuring privacy and integrity.