Zero-knowledge proofs [ZKP]

Zero-knowledge proofs (ZKPs) are a category of cryptographic algorithms that allow one party (the prover) to prove to another party (the verifier) that they know a specific piece of information without revealing the information itself.

The fundamental properties of zero-knowledge proofs are:

1. Completeness: If the statement is true, the honest verifier (one who follows the protocol) will be convinced of this fact by an honest prover.
2. Soundness: If the statement is false, no cheating prover can convince the honest verifier that it is true, except with some small probability.
3. Zero-knowledge: If the statement is true, the verifier cannot learn anything beyond the fact that the statement is true.

Zero-knowledge proofs can be either interactive or non-interactive:

• Interactive ZKPs: The prover and verifier engage in a back-and-forth conversation. The prover attempts to convince the verifier that they possess knowledge of a secret without revealing it.
• Non-Interactive ZKPs (NIZKPs): In a non-interactive scheme, no back-and-forth communication is required. The proof consists of a single message sent from prover to verifier.

One of the main applications of ZKPs is in enhancing privacy and security in blockchain technology. For instance, Zcash, a cryptocurrency, uses a form of ZKP called zk-SNARKs (Zero-Knowledge Succinct Non-interactive Argument of Knowledge) to maintain the privacy of transactions. This allows the network to maintain a secure ledger of balances without disclosing the parties or amounts involved in transactions.