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Kate -> KZG10 (better in formal contexts)

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Dankrad Feist 2020-12-28 16:24:31 +00:00 committed by protolambda
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specs/phase1/beacon-chain.md
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@ -53,7 +53,7 @@
## Introduction
This document describes the extensions made to the Phase 0 design of The Beacon Chain to support data sharding, based on the ideas [here](https://hackmd.io/@HWeNw8hNRimMm2m2GH56Cw/B1YJPGkpD) and more broadly [here](https://arxiv.org/abs/1809.09044), using Kate commitments to commit to data to remove any need for fraud proofs (and hence, safety-critical synchrony assumptions) in the design.
This document describes the extensions made to the Phase 0 design of The Beacon Chain to support data sharding, based on the ideas [here](https://hackmd.io/@HWeNw8hNRimMm2m2GH56Cw/B1YJPGkpD) and more broadly [here](https://arxiv.org/abs/1809.09044), using KZG10 commitments to commit to data to remove any need for fraud proofs (and hence, safety-critical synchrony assumptions) in the design.
## Custom types
@ -96,7 +96,7 @@ 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)` |
| `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...next_power_of_two(i)] (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.
These points are the G2-side KZG10 commitments to `product[a in i...next_power_of_two(i)] (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
@ -166,7 +166,7 @@ The following containers are new in Phase 1.
```python
class DataCommitment(Container):
# Kate commitment to the data
# KZG10 commitment to the data
point: BLSCommitment
# Length of the data in samples
length: uint64
@ -193,7 +193,7 @@ class PendingShardHeader(Container):
# Slot and shard that this header is intended for
slot: Slot
shard: Shard
# Kate commitment to the data
# KZG10 commitment to the data
commitment: BLSCommitment
# hash_tree_root of the ShardHeader (stored so that attestations
# can be checked against it)