Zero-knowledge proof

A zero-knowledge proof (ZKP) is a cryptographic protocol by which a prover convinces a verifier that a statement is true without revealing any more information than that fact ¹.

It has three properties:

• Completeness. If the statement is true and both parties follow the protocol, the verifier accepts ².
• Soundness. If the statement is false, a verifier that follows the protocol is not convinced ².
• Zero knowledge. If the statement is true and the prover follows the protocol, the verifier learns no confidential information beyond the fact that the statement is true ².

The statement combines a public instance, known to both parties, with a private witness known only to the prover ². Strictly, a proof must be sound even against a computationally unbounded prover; an argument, such as a SNARK (succinct non-interactive argument of knowledge), need only be sound against bounded ones ². In zero-knowledge proofs of inference the witness is the model's weights: the prover publishes a commitment to them once, then proves for each query that the output equals the committed model applied to the input ³. zkLLM proved one 2,048-token forward pass of LLaMa-2-13B in 803 seconds on one A100 GPU, producing a 188 kB proof of a fixed-point approximation of the model ³. For zero-knowledge proofs of training constraints, a 2026 proposal notes that governance analyses judge such proofs currently impractical at frontier scale, and argues that this limit is not fundamental ⁴.