From 4348d3b255862993dfac23335404af1d62c12ba7 Mon Sep 17 00:00:00 2001 From: Dankrad Feist Date: Wed, 16 Dec 2020 14:14:21 +0000 Subject: [PATCH] Add data availability coding rate as a constant (makes it more explicit what's going on) --- specs/phase1/beacon-chain.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/specs/phase1/beacon-chain.md b/specs/phase1/beacon-chain.md index aa3d3e2c9..b49fb00f3 100644 --- a/specs/phase1/beacon-chain.md +++ b/specs/phase1/beacon-chain.md @@ -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` | `MAX_SHARDS * MAX_SHARD_HEADERS_PER_SHARD` | | | `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 @@ -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)` | | | `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