ZK Proof Systems
Give designers a decision framework for choosing a zero-knowledge proof system on Ethereum. A zero-knowledge proof lets one party prove a statement is true without revealing the inputs. The system's commitment scheme (elliptic-curve pairings, discrete log over curves, collision-resistant hashes, or lattices) drives its post-quantum posture; the setup model drives its trust assumption; proof size and prover and verifier cost drive deployment economics.
Give designers a decision framework for choosing a zero-knowledge proof system on Ethereum. A zero-knowledge proof lets one party prove a statement is true without revealing the inputs. The system's commitment scheme (elliptic-curve pairings, discrete log over curves, collision-resistant hashes, or lattices) drives its post-quantum posture; the setup model drives its trust assumption; proof size and prover and verifier cost drive deployment economics.
- Pairing-based SNARKs rely on elliptic-curve pairings over curves such as BLS12-381 or BN254 and produce small constant-size proofs with low verifier cost. Groth16 requires a trusted setup per circuit; PLONK over KZG uses a universal setup.
- Elliptic-curve-based SNARKs rely on discrete log over an elliptic curve without pairings. Transparent setup, moderate proof size, medium verifier cost. PLONK over IPA and the Halo2 family sit here.
- Hash-based proof systems rely on collision-resistant hashes. STARKs over FRI and hash-based SNARKs (Plonky family, Binius) have transparent setup and remain sound against a CRQC, at the cost of larger proofs.
- Lattice-based SNARKs rely on Module-SIS or LWE hardness. Emerging, transparent, and PQ-safe; no production deployment yet.
- Hybrid systems compose a hash-based STARK with a pairing-based SNARK wrapper to achieve small on-chain proofs; the wrapper reintroduces pairing assumptions and the matching PQ exposure.
Guarantees:
- Completeness: an honest prover with a valid witness always convinces the verifier.
- Soundness: all listed systems offer computational soundness; a cheating prover cannot convince the verifier except with negligible probability under the stated cryptographic assumption.
- Zero-knowledge: each system hides the prover's private inputs from the verifier.
- Transparency (STARK, IPA, hash-based SNARK): no trusted party or ceremony is required.
- PQ safety: hash-based and lattice-based systems remain sound against quantum adversaries; pairing-based and elliptic-curve-based systems do not.
Threat model:
- Soundness holds only under the stated assumption: hardness of discrete log for EC-based systems, pairing-related assumptions for pairing-based systems, collision resistance for hash-based systems, Module-SIS or LWE for lattice-based systems.
- Trusted setups require that at least one ceremony participant was honest and that toxic waste was destroyed; a compromised ceremony allows proofs for false statements.
- Side-channel attacks on the prover or the signer for recursion are out of scope.
- Verifier contract bugs or mis-wired public inputs can accept proofs that the proof system itself rejects.
- PQ migration cost: existing pairing-based circuits must be re-implemented for hash-based or lattice-based backends; constraint systems differ (R1CS vs AIR) and field arithmetic differs.
- Proof size on-chain: hash-based proofs are roughly 100 to 1000 times larger than pairing-based proofs. EIP-4844 blobs help but on-chain verification remains more expensive.
- Hybrid complexity: wrapping a STARK in a pairing-based SNARK yields small on-chain proofs but reintroduces pairing assumptions and the matching PQ exposure.
- Ecosystem maturity: pairing-based tooling (Circom, Noir, Halo2) is more mature than STARK tooling, though the gap is closing.
A privacy L2 uses pairing-based PLONK for transaction proofs today. To prepare for post-quantum migration, the team evaluates moving to a FRI-based STARK backend. Proof size grows from about 400 bytes to about 100 kilobytes, but proofs become PQ-safe and require no trusted setup. Recursive composition keeps on-chain verification cost manageable, and EIP-4844 blobs carry proof Data Availability at lower cost than calldata.