Witness
A witness is private information that enables a prover to establish that a statement is true within a proof system.
Real-World Cryptography
A witness is secret information whose possession enables a prover to establish the truth of a statement in a proof system.
- How it is used
- Uses a secret witness to connect proof of knowledge, zero-knowledge proofs, Schnorr identification, and digital signatures.
- How deep it goes
- Explains witness hiding through Schnorr equations and failure cases, then connects the construction to signatures without detailing implementation standards.
- Examples
- Uses Peggy and Victor, Y = g^x, random k, hidden values s and R, and Schnorr signature components R and s.
- What you can do after
- Evaluate how a proof demonstrates knowledge while withholding its witness, and recognize the witness as a signature’s private key.
Elliptic Curve Cryptography for Developers
A witness variable is a secret wire value that supplies private information satisfying a proof statement.
- How it is used
- Uses private wire values to let a prover establish a public statement without disclosing the underlying information.
- How deep it goes
- Connects witnesses to QAP wires, multiplication gates, proof creation, randomization, and verification, but does not implement a prover.
- Examples
- Uses a medical record, secret patient number, medicine number, dose, QAP wires, and multiplication gates as concrete examples.
- What you can do after
- Understand how private inputs satisfy a QAP and support proof generation while remaining hidden from verification.
Read how Elliptic Curve Cryptography for Developers explains witness →
Related concepts
- proof statementcontrasts with · A proof statement is the public claim and associated public inputs whose validity a cryptographic proof establishes.
- proof of knowledgeused by · A proof of knowledge is a cryptographic proof in which a prover demonstrates knowledge of a witness satisfying a specified statement.
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