Non-interactive zero-knowledge proof

As explained in Real-World Cryptography

A non-interactive zero-knowledge proof can be generated and verified without online interaction between the prover and verifier during the proof operation.

A non-interactive zero-knowledge proof lets a prover convince a verifier without requiring both parties to exchange messages during the proof operation. It replaces the verifier’s challenge with a hash of the protocol transcript, using the Fiat–Shamir transformation. section 7.2.2 section 7.5

The construction follows a practical chain:

• Hash the exchanged transcript to derive a challenge that appears random but cannot be freely chosen by the prover. section 7.2.2
• Include a message in the hash to bind that message cryptographically to proof of knowledge of the witness. section 7.2.2
• Recognize the resulting Schnorr construction as a digital signature, commonly represented by commitment R and response s. section 7.2.2

Figure 7.7 The left protocol is the Schnorr identification protocol previously discussed, which is an interactive protocol. The right protocol is a Schnorr signature, which is a non-interactive version of the left protocol (where the verifier message is replaced by a call to a hash function on the transcript).

Compare the interactive Schnorr identification protocol with its non-interactive signature form, where hashing replaces the verifier’s message. section 7.2.2

How Real-World Cryptography covers it

How deep it goes

Explains transcript hashing and Schnorr signatures, while treating general-purpose proof systems only as a broader extension.

Examples

Uses Schnorr signatures and a transcript-hash diagram to illustrate converting an interactive identification protocol into a non-interactive proof.

What it assumes

Builds from interactive zero-knowledge proofs, witnesses, transcripts, hash functions, and digital-signature concepts.

What you can do after

Apply it via Schnorr signatures to bind messages to proof of knowledge without requiring the verifier to be online during signing.

How it connects

Connects interactive zero-knowledge proofs, Fiat–Shamir transformation, Schnorr identification, digital signatures, and general-purpose ZKPs.

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Related concepts

• zero-knowledge proofcontrasts with · A zero-knowledge proof is a cryptographic protocol in which a prover demonstrates a statement’s truth without revealing information beyond its validity.
• Fiat-Shamir transformationproduced by · The Fiat-Shamir transformation converts an interactive proof into a non-interactive proof by deriving the verifier's challenge from a hash of the protocol transcript.
• digital signatureequivalent to · A digital signature is cryptographic data generated with a private key and verified with corresponding public information to authenticate data or its signer and detect alteration.
• zk-SNARKincludes · A zk-SNARK is a zero-knowledge, succinct, non-interactive argument of knowledge that enables efficient verification of a prover’s knowledge of a computation’s secret witness without revealing it.

This explainer was generated by Manning's knowledge graph from the text of Real-World Cryptography. The section links point to the parts of the book it draws on.