KZG commitment

Named after Aniket Kate, Gregory Zaverucha and Ian Goldberg, who introduced it in 2010, the scheme lets a prover commit to a polynomial with a single elliptic curve point. Later, they can prove that the polynomial takes a certain value at any point with a proof of constant size, regardless of how large the polynomial is. Verification uses pairings on curves such as BLS12-381.

Ethereum adopted KZG commitments for blob transactions introduced by EIP-4844 in 2024. Each blob of rollup data is treated as a polynomial and committed with KZG, so nodes can check that data matches the commitment and, in later upgrades, sample small pieces to verify data availability without downloading everything. KZG commitments are also a core component of many SNARK proof systems.

KZG requires a trusted setup, which Ethereum addressed with a large public ceremony, and it relies on pairing-based assumptions that a quantum computer could break. Alternatives such as hash-based commitments avoid both issues at the cost of larger proofs, and the long-term roadmap considers them for quantum resistance.