Zero-Knowledge Proof (ZKP)

The guarantee that an honest prover can always convince an honest verifier that a true statement is valid. If the prover possesses the correct secret (witness) and follows the protocol faithfully, the verifier will accept the proof with probability 1. This property ensures the protocol is functional and usable for legitimate parties. A failure of completeness would mean a valid proof could be rejected, breaking the protocol's utility.

The guarantee that a malicious prover cannot convince an honest verifier of a false statement, except with negligible probability. Soundness binds the prover to the truth. There are two variants:

• Computational Soundness: Security holds against provers with bounded computational power (standard for most practical ZKPs).
• Statistical Soundness: Security holds against provers with unlimited computational power (a stronger property, found in zk-STARKs).

The defining property: the verifier learns absolutely nothing beyond the validity of the statement itself. This is formalized by demonstrating the existence of a simulator—an algorithm that can generate a transcript indistinguishable from a real interaction without access to the secret. If such a simulator exists, any information the verifier extracts could have been generated independently, proving no knowledge leakage occurred.

A stronger notion than soundness. A Proof of Knowledge demonstrates that the prover not only knows that a statement is true, but actually possesses the secret witness itself. This is formalized using an extractor—a hypothetical algorithm that, given special access to the prover (e.g., via rewinding), can extract the witness. This property is critical for authentication and identity systems where possession of a secret must be proven.

A practical property, not a core theoretical one, but essential for blockchain scaling. A succinct ZKP produces a proof that is:

• Small: Logarithmic or constant in size relative to the computation (e.g., a few hundred bytes).
• Fast to verify: Verifiable in milliseconds, regardless of the computation's complexity. This property defines zk-SNARKs (Succinct Non-interactive Arguments of Knowledge) and enables their use in rollups where thousands of transactions are compressed into a single tiny proof.

Classic ZKPs require multiple rounds of back-and-forth interaction between prover and verifier. Non-interactive ZKPs (NIZKs) collapse this into a single message: the prover generates a proof and sends it; the verifier checks it independently. This is achieved using the Fiat-Shamir heuristic, which replaces the verifier's random challenges with the output of a cryptographic hash function modeled as a random oracle. Non-interactivity is mandatory for public blockchain applications.

A mathematical framework that injects calibrated statistical noise into query results to guarantee that the presence or absence of a single individual cannot be inferred. Unlike ZKPs, which prove a statement about specific data without revealing it, differential privacy protects the aggregate output of a dataset.

• Uses the epsilon (ε) parameter to define the privacy budget.
• Essential for training machine learning models on sensitive user data.
• Complements ZKPs in privacy-preserving machine learning pipelines.

A cryptographic scheme that allows computation directly on encrypted ciphertext, generating an encrypted result that, when decrypted, matches the output of operations performed on the plaintext. This enables a third party to process data without ever seeing it.

• Fully Homomorphic Encryption (FHE) supports arbitrary computation.
• Eliminates the need for decryption during processing, unlike ZKPs which prove knowledge of plaintext properties.
• Critical for secure multi-party computation in cloud environments.

A data de-identification technique that replaces direct identifiers (e.g., name, email) with artificial pseudonyms or tokens. The data remains linkable for analysis but cannot be directly attributed without additional information held separately.

• Defined under GDPR Article 4(5) as a risk-reduction measure.
• Unlike ZKPs, pseudonymized data is not cryptographically hidden; it is merely obfuscated.
• Often used in conjunction with ZKPs to prove attributes about a pseudonymous identity.

A decentralized identity model where individuals hold and control their own digital credentials using verifiable data registries (often blockchains) without relying on a central issuing authority. ZKPs are the cryptographic engine enabling selective disclosure within SSI.

• Users can prove claims like 'I am over 18' without revealing their birthdate.
• Relies on Decentralized Identifiers (DIDs) and Verifiable Credentials (VCs).
• Eliminates the need for a centralized identity provider to vouch for claims.

A data subject's right under GDPR Recital 71 and Article 22 to obtain meaningful information about the logic involved in automated decisions, including the significance and envisaged consequences. ZKPs can provide cryptographic guarantees that a specific model logic was applied without exposing the model's proprietary weights.

• Addresses the 'black box' problem in AI governance.
• Enables auditable compliance with the EU AI Act's transparency mandates.
• ZKPs can prove that a decision was made by a certified model version.

Cryptographic methods ensuring the integrity and non-repudiation of AI system logs. ZKPs can be used to generate succinct proofs of log integrity without revealing the sensitive contents of the logs themselves.

• Ensures that audit records have not been tampered with post-generation.
• Uses Merkle trees and ZK-SNARKs to create verifiable log commitments.
• Critical for regulatory compliance under the EU AI Act's record-keeping requirements.