Zero-Knowledge Proof (ZKP)

If the statement is true and both the prover and verifier follow the protocol honestly, the verifier will always be convinced of the proof's validity.

• Mechanism: The protocol's mathematical construction guarantees that a prover possessing the valid witness can generate a proof that passes the verifier's polynomial-time check.
• Practical Example: In a Schnorr identification protocol, a prover who knows the discrete logarithm x of a public value y = gˣ will always succeed in convincing the verifier.
• Failure Mode: A protocol lacking completeness would reject valid credentials, rendering it useless for authentication.

If the statement is false, no cheating prover can convince the honest verifier that it is true, except with some negligible probability.

• Computational Soundness: Security holds against provers limited to polynomial-time computation, relying on hard mathematical problems like the Discrete Logarithm Problem.
• Statistical Soundness: Unconditional security against even computationally unbounded provers, typical in zk-STARKs.
• Knowledge Soundness: A stronger variant requiring that a valid proof implies the prover actually knows the witness, not just that the statement is true. This is the foundation of zk-SNARKs.

The verifier learns absolutely nothing beyond the single bit of information: 'the statement is true.' No other data about the secret witness is leaked.

• Perfect Zero-Knowledge: The distribution of the verifier's view of the interaction can be simulated exactly without access to the witness, proving no information is transferred.
• Computational Zero-Knowledge: The simulated view is computationally indistinguishable from the real interaction, sufficient for most practical applications.
• Formal Guarantee: This property is proven via a simulator algorithm that can generate a transcript indistinguishable from a real protocol run, demonstrating the verifier could have generated the conversation alone.

While not a core theoretical property like the original three, succinctness is a critical practical requirement for modern ZKP systems, especially in blockchain scaling.

• Definition: The proof size is small (ideally constant or logarithmic) and verification time is exponentially faster than re-executing the computation.
• zk-SNARK Implementation: The 'S' in SNARK stands for Succinct. A proof for a complex smart contract execution can be verified in milliseconds regardless of the computation's complexity.
• Trade-off: Achieving succinctness often requires a trusted setup ceremony or reliance on the random oracle model, introducing different security assumptions.

Zero-Knowledge Succinct Non-Interactive Argument of Knowledge — a proof type that is both succinct (small proof size, fast verification) and non-interactive (no back-and-forth between prover and verifier).

• Requires a trusted setup ceremony to generate a Common Reference String (CRS)
• Proof size is typically just a few hundred bytes regardless of computation complexity
• Used extensively in privacy coins like Zcash and zk-rollup scaling solutions
• The "toxic waste" from the setup must be destroyed to prevent counterfeit proofs

Zero-Knowledge Scalable Transparent Argument of Knowledge — eliminates the trusted setup requirement by relying on collision-resistant hash functions instead of elliptic curve pairings.

• Post-quantum secure: resistant to attacks from both classical and quantum computers
• Proofs are larger than SNARKs (typically 40-200KB) but verification scales logarithmically
• Transparent setup means no "toxic waste" to manage
• Ideal for high-throughput applications where setup trust is unacceptable

A cryptographic primitive that allows a prover to commit to a value while keeping it hidden, then later reveal it with a guarantee that the value hasn't changed.

• Hiding property: the commitment reveals nothing about the committed value
• Binding property: the committer cannot change the value after committing
• Fundamental building block for constructing ZKPs
• Common constructions include Pedersen commitments and polynomial commitments like KZG

A technique that transforms any interactive proof (requiring multiple rounds of challenge-response) into a non-interactive proof by replacing the verifier's random challenges with the output of a cryptographic hash function.

• The prover hashes the transcript so far to generate the next challenge deterministically
• Enables ZKPs to be used asynchronously without a live verifier
• Security relies on the random oracle model
• Underpins most practical non-interactive ZKP systems in production today

A privacy-enhancing mechanism allowing a credential holder to reveal only a subset of claims to a verifier without exposing the entire credential.

• Prove you are over 21 without revealing your exact birthdate
• Prove you have a valid license without showing your address
• Built on ZKP techniques to generate a proof about specific attributes
• Core to W3C Verifiable Credentials and self-sovereign identity systems

A function that requires a specified number of sequential computational steps to evaluate — it cannot be parallelized — yet produces an output that can be verified efficiently.

• Prevents front-running in blockchain applications by enforcing time delays
• Used alongside ZKPs for unbiased randomness generation
• Verification is exponentially faster than computation
• Requires specialized hardware or ASICs for efficient sequential evaluation