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256-bit custody atoms for better alignment with rest of the spec and greater efficiency

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Dankrad Feist 2020-04-05 14:39:00 +01:00
parent 6ea8f9c0d2
commit ca6af0c2e9
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GPG Key ID: 6815E6A20BEBBABA
1 changed files with 20 additions and 7 deletions
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specs/phase1/custody-game.md
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@ -49,8 +49,9 @@ This document details the beacon chain additions and changes in Phase 1 of Ether
| Name | Value | Unit |
| - | - | - |
| `BLS12_381_Q` | `4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787` | - |
| `BYTES_PER_CUSTODY_ATOM` | `48` | bytes |
| `CUSTODY_PRIME` | `2 ** 256 - 189` | - |
| `CUSTODY_SECRETS` | `3` | - |
| `BYTES_PER_CUSTODY_ATOM` | `32` | bytes |
## Configuration
@ -175,7 +176,7 @@ def legendre_bit(a: int, q: int) -> int:
return 0
```
### `custody_atoms`
### `get_custody_atoms`
Given one set of data, return the custody atoms: each atom will be combined with one legendre bit.
@ -186,16 +187,28 @@ def get_custody_atoms(bytez: bytes) -> Sequence[bytes]:
for i in range(0, len(bytez), BYTES_PER_CUSTODY_ATOM)]
```
### `get_custody_secrets`
Extract the custody secrets from the signature
```python
def get_custody_secrets(key: BLSSignature):
full_G2_element = bls.signature_to_G2(key)
signature = full_G2_element[0].coeffs
signature_bytes = sum(x.to_bytes(48, "little") for x in signature)
secrets = [int.from_bytes(x[i:i+BYTES_PER_CUSTODY_ATOM]) for i in range(0, len(signature_bytes), 32)]
return secrets
```
### `compute_custody_bit`
```python
def compute_custody_bit(key: BLSSignature, data: bytes) -> bit:
full_G2_element = bls.signature_to_G2(key)
s = full_G2_element[0].coeffs
secrets = get_custody_secrets(key)
custody_atoms = get_custody_atoms(data)
n = len(custody_atoms)
a = sum(s[i % 2]**i * int.from_bytes(atom, "little") for i, atom in enumerate(custody_atoms) + s[n % 2]**n)
return legendre_bit(a, BLS12_381_Q)
uhf = sum(secrets[i % CUSTORY_SECRETS]**i * int.from_bytes(atom, "little") for i, atom in enumerate(custody_atoms)) + secrets[n % CUSTORY_SECRETS]**n
return legendre_bit(uhf + secrets[0], BLS12_381_Q)
```
### `get_randao_epoch_for_custody_period`