 Zero-knowledge proof

A zero-knowledge proof is a proof protocol that convinces a verifier of a public statement's validity while revealing no additional information that the verifier could not efficiently obtain from that statement and its permitted prior information. The formal comparison uses a zero-knowledge simulator: an efficient randomized algorithm that reproduces the verifier's view without the prover's secret cryptographic witness.^[ref]

An interactive proof system separates three questions. Completeness of an interactive proof asks whether an honest prover can convince the verifier of a true statement. Soundness of an interactive proof bounds acceptance of false statements. Zero knowledge concerns information disclosure, so a protocol can pass a soundness test without being zero knowledge. The simulator comparison may require equality of distributions, statistical closeness or computational indistinguishability, depending on the definition.^[ref]

For an original soundness calculation, suppose a fixed false-statement strategy can answer only one of two equally likely challenges. Its acceptance probability is at most $1/2$. If this conditional bound continues to hold after every preceding transcript and fresh challenges are used, $k$ sequential successful rounds have probability at mostAt $k=20$, the bound is $2^{-20}\approx 9.54\times 10^{-7}$. This stipulated calculation does not prove that any particular protocol has the required per-round bound, nor does it establish zero knowledge.

The simulator supplies the separate privacy argument. It must reproduce the relevant distribution efficiently, rather than merely output one accepting transcript. A zero-knowledge proof can be interactive or a non-interactive zero-knowledge proof; its precise verifier and setup assumptions are part of its security claim.

A zero-knowledge proof is a method used in cryptography that allows one party (the prover) to convince another party (the verifier) that they know a certain piece of information (often a secret, such as a password or cryptographic key) without revealing the actual information itself. The key characteristics of a zero-knowledge proof include: 1. **Completeness**: If the statement is true and both parties follow the protocol correctly, the verifier will be convinced of this fact.