# `EEVM.Precompiles.KZGPointEval`
[🔗](https://github.com/mw2000/eevm/blob/v0.1.0/lib/eevm/precompiles/kzg_point_eval.ex#L1)

KZG point evaluation precompile — address `0x0A` (EIP-4844).

The precompile flow:

1. Validate the `versioned_hash` derived from the commitment.
2. Validate field element bounds for the evaluation point `z` and value `y`.
3. Verify the KZG proof for `(commitment, z, y, proof)`.

### Gas schedule

Flat **50,000 gas** per call.

### Input format (exactly 192 bytes)

- bytes `0..31`   — `versioned_hash` (32 bytes)
- bytes `32..63`  — `z` evaluation point (32 bytes, big-endian field element)
- bytes `64..95`  — `y` claimed evaluation (32 bytes, big-endian field element)
- bytes `96..143` — `commitment` (48 bytes)
- bytes `144..191` — `proof` (48 bytes)

### Output format

Exactly 64 bytes: two big-endian uint256 values:

- `FIELD_ELEMENTS_PER_BLOB` (`4096`)
- `BLS_MODULUS`

### Proof verification

The 48-byte commitment and proof are compressed G1 points (ZCash
serialization, as in the consensus specs' `bytes_to_kzg_commitment`). They
are decompressed and checked to be in G1, and the KZG check

    e(C − [y]G1, G2) = e(π, [τ]G2 − [z]G2)

is evaluated in the equivalent form e(C − [y]G1 + [z]π, −G2) · e(π, [τ]G2) = 1:
one G1 multi-scalar multiplication and one two-pair pairing check, both
from `EEVM.Precompiles.Bls12381.Curve`. Of the trusted setup, only [τ]G2 is
needed.

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*Consult [api-reference.md](api-reference.md) for complete listing*