# `EEVM.Precompiles.Bls12381`
[🔗](https://github.com/mw2000/eevm/blob/v0.1.0/lib/eevm/precompiles/bls12381.ex#L1)

BLS12-381 precompiles — addresses `0x0B` through `0x11` (EIP-2537).

This module owns gas accounting, the EIP-2537 encoding, and input
validation for the Prague-gated BLS12-381 precompiles. The curve arithmetic
is `EEVM.Precompiles.Bls12381.Curve`, in pure Elixir.

### Encoding and validation

An Fp element is 64 bytes: 16 zero bytes, then a 48-byte big-endian value
below p. An Fp2 element c0 + c1·u is c0 then c1. A G1 point is x then y
(128 bytes), a G2 point x then y in Fp2 (256 bytes), and the point at
infinity is all zeros. A scalar is 32 big-endian bytes.

Every input point must be on its curve (ADD included); MSM and pairing
inputs must also be in the order-r subgroup. Any violation is an error,
which burns all gas supplied to the call.

# `execute_g1_add`

```elixir
@spec execute_g1_add(binary(), non_neg_integer()) ::
  {:ok, binary(), non_neg_integer()} | {:error, atom()}
```

BLS12_G1ADD (`0x0B`): adds two G1 points. Costs 375 gas.

# `execute_g1_msm`

```elixir
@spec execute_g1_msm(binary(), non_neg_integer()) ::
  {:ok, binary(), non_neg_integer()} | {:error, atom()}
```

BLS12_G1MSM (`0x0C`): returns Σ kᵢ·Pᵢ over (G1 point, scalar) pairs. Costs
12,000 gas per pair times the EIP-2537 discount for the pair count.

# `execute_g2_add`

```elixir
@spec execute_g2_add(binary(), non_neg_integer()) ::
  {:ok, binary(), non_neg_integer()} | {:error, atom()}
```

BLS12_G2ADD (`0x0D`): adds two G2 points. Costs 600 gas.

# `execute_g2_msm`

```elixir
@spec execute_g2_msm(binary(), non_neg_integer()) ::
  {:ok, binary(), non_neg_integer()} | {:error, atom()}
```

BLS12_G2MSM (`0x0E`): returns Σ kᵢ·Qᵢ over (G2 point, scalar) pairs. Costs
22,500 gas per pair times the EIP-2537 discount for the pair count.

# `execute_map_fp2_to_g2`

```elixir
@spec execute_map_fp2_to_g2(binary(), non_neg_integer()) ::
  {:ok, binary(), non_neg_integer()} | {:error, atom()}
```

BLS12_MAP_FP2_TO_G2 (`0x11`): maps an Fp2 element to G2. Costs 23,800 gas.

# `execute_map_fp_to_g1`

```elixir
@spec execute_map_fp_to_g1(binary(), non_neg_integer()) ::
  {:ok, binary(), non_neg_integer()} | {:error, atom()}
```

BLS12_MAP_FP_TO_G1 (`0x10`): maps an Fp element to G1. Costs 5,500 gas.

# `execute_pairing`

```elixir
@spec execute_pairing(binary(), non_neg_integer()) ::
  {:ok, binary(), non_neg_integer()} | {:error, atom()}
```

BLS12_PAIRING_CHECK (`0x0F`): returns 1 as a 32-byte word if the product of
the pairings of the given (G1, G2) pairs is 1, else 0. Costs
37,700 + 32,600 per pair.

---

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