Add `pi` to `BlobCommitment` to enable optimized kzg commitment verification

[litt3]

Problem

• Currently, the process for a client to verify the kzg commitment contained in the BlobCommitment involves recomputing the commitment, and checking whether the computed commitment matches the received commitment
• This is not always ideal, since computing the commitment requires the blob to have SRS data for the whole length of a blob (currently 32MiB, could be increased in the future)

Optimization

• The proposed optimization involves computing an opening pi of the kzg commitment, and including pi in the BlobCommitment
• Looking at this formula e(pi, s-z) = e(C-y, H):
  • z is the blob hash
  • C is the kzg commitment to the blob polynomial p
  • pi is the evaluation of C at z
  • s is the first public SRS point
  • y is the evaluation of p at z
  • H is the g2 generator
• With access to pi from the BlobCommitment, a client will be able to check the equality of these pairings, thus verifying the commitment without any SRS data

Implementation Details

• pi must be added to the BlobCommitment
• any party creating the BlobCommitment will be responsible for also computing pi
  • this is either the client doing the dispersal, or the disperser

[bxue-l2]

Related material. 4844 spec has a function definition for this purpose, see link here

But because 4844 treat the data as evaluation, the way to compute y is a bit different.

[bxue-l2]

We already have the rust code to verify a eigenda blob by verifying a KZG proof.

Here are the functions from the rust library that produce and verify the proof

• Computing https://github.com/Layr-Labs/rust-kzg-bn254/blob/788e13cd9fdbe3359d341489b42ca07999f5144a/prover/src/kzg.rs#L288
• Verifying https://github.com/Layr-Labs/rust-kzg-bn254/blob/788e13cd9fdbe3359d341489b42ca07999f5144a/verifier/src/batch.rs#L16

In hokulea our OP impl, we use it

• computing https://github.com/Layr-Labs/hokulea/blob/3e61825dca1be16e23078858e098a438ba744f85/crates/compute-proof/src/kzg_proof.rs#L32
• verifying https://github.com/Layr-Labs/hokulea/blob/3e61825dca1be16e23078858e098a438ba744f85/crates/proof/src/preloaded_eigenda_provider.rs#L178

Our go client also performs the check by committing the blob. This is not the most performant methods, but since it running in a regular computer host, the cost is not as significant as running it inside the zkvm host