KZG

KZG (Kate-Zaverucha-Goldberg) commitment is a popular polynomial commitment scheme. This commitment scheme allows for proving and verifying the value obtained by summing any polynomial. In the dill system, KZG is used to commit to and verify blob data. To achieve the purpose of network sharding design, the dill system also introduces fast algorithms for computing KZG commitments.

In the earliest DAS (Data Availability Sampling) paper, Merkle commitments were used for data commitment, and sampling nodes needed to verify Merkle proofs to confirm the validity of the data.。

Compared to Merkle proofs, KZG commitments bring many advantages：

• For the same blob, its KZG commitment is also valid for its EC-extended data.
• For the data in the extended rows, both the KZG commitment and proof can be computed using EC algorithms. This eliminates the need for fraud proofs in the dill system.
• No matter how large the data is, the size of the KZG commitment and proof remains constant.