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Add data availability coding rate as a constant (makes it more explicit what's going on)

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Dankrad Feist 2020-12-16 14:14:21 +00:00 committed by protolambda
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specs/phase1/beacon-chain.md
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@ -76,6 +76,8 @@ We define the following Python custom types for type hinting and readability:
| `MAX_SHARD_HEADERS_PER_SHARD` | `4` | | | `MAX_SHARD_HEADERS_PER_SHARD` | `4` | |
| `MAX_SHARD_HEADERS` | `MAX_SHARDS * MAX_SHARD_HEADERS_PER_SHARD` | | | `MAX_SHARD_HEADERS` | `MAX_SHARDS * MAX_SHARD_HEADERS_PER_SHARD` | |
| `PRIMITIVE_ROOT_OF_UNITY` | `5` | Primitive root of unity of the BLS12_381 (inner) modulus | | `PRIMITIVE_ROOT_OF_UNITY` | `5` | Primitive root of unity of the BLS12_381 (inner) modulus |
| `DATA_AVAILABILITY_INVERSE_CODING_RATE` | `2**1` (=2) | Factor by which samples are extended for data availability encoding |
### Shard block configs ### Shard block configs
@ -93,7 +95,7 @@ We define the following Python custom types for type hinting and readability:
| `ROOT_OF_UNITY` | `pow(PRIMITIVE_ROOT_OF_UNITY, (MODULUS - 1) // (MAX_SAMPLES_PER_BLOCK * POINTS_PER_SAMPLE, MODULUS)` | | | `ROOT_OF_UNITY` | `pow(PRIMITIVE_ROOT_OF_UNITY, (MODULUS - 1) // (MAX_SAMPLES_PER_BLOCK * POINTS_PER_SAMPLE, MODULUS)` | |
| `SIZE_CHECK_POINTS` | Type `List[G2, MAX_SAMPLES_PER_BLOCK + 1]`; TO BE COMPUTED | | `SIZE_CHECK_POINTS` | Type `List[G2, MAX_SAMPLES_PER_BLOCK + 1]`; TO BE COMPUTED |
These points are the G2-side Kate commitments to `product[a in i...MAX_SAMPLES_PER_BLOCK-1] (X ** POINTS_PER_SAMPLE - w ** (reverse_bit_order(a, MAX_SAMPLES_PER_BLOCK * 2) * POINTS_PER_SAMPLE))` for each `i` in `[0...MAX_SAMPLES_PER_BLOCK]`, where `w = ROOT_OF_UNITY`. They are used to verify block size proofs. They can be computed with a one-time O(N^2/log(N)) calculation using fast-linear-combinations in G2. These points are the G2-side Kate commitments to `product[a in i...MAX_SAMPLES_PER_BLOCK-1] (X ** POINTS_PER_SAMPLE - w ** (reverse_bit_order(a, MAX_SAMPLES_PER_BLOCK * DATA_AVAILABILITY_INVERSE_CODING_RATE) * POINTS_PER_SAMPLE))` for each `i` in `[0...MAX_SAMPLES_PER_BLOCK]`, where `w = ROOT_OF_UNITY`. They are used to verify block size proofs. They can be computed with a one-time O(N^2/log(N)) calculation using fast-linear-combinations in G2.
### Gwei values ### Gwei values