Update 0_beacon-chain.md
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@ -30,7 +30,7 @@
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- [Attestations](#attestations)
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- [`Attestation`](#attestation)
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- [`AttestationData`](#attestationdata)
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- [`AttestationDataWrapped`](#attestationdatawrapped)
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- [`AttestationDataAndCustodyBit`](#attestationdataandcustodybit)
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- [Deposits](#deposits)
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- [`Deposit`](#deposit)
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- [`DepositData`](#depositdata)
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@ -80,10 +80,13 @@
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- [`get_effective_balance`](#get_effective_balance)
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- [`get_fork_version`](#get_fork_version)
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- [`get_domain`](#get_domain)
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- [`get_bitfield_bit`](#get_bitfield_bit)
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- [`verify_bitfield`](#verify_bitfield)
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- [`verify_slashable_vote_data`](#verify_slashable_vote_data)
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- [`is_double_vote`](#is_double_vote)
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- [`is_surround_vote`](#is_surround_vote)
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- [`integer_squareroot`](#integer_squareroot)
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- [`indices`](#indices)
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- [`bls_verify`](#bls_verify)
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- [`bls_verify_multiple`](#bls_verify_multiple)
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- [`bls_aggregate_pubkeys`](#bls_aggregate_pubkeys)
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@ -251,6 +254,13 @@ Code snippets appearing in `this style` are to be interpreted as Python code. Be
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| `DOMAIN_EXIT` | `3` |
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| `DOMAIN_RANDAO` | `4` |
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### Custody bits
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| Name | Value |
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| - | - |
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| `CUSTODY_BIT_ZERO` | `False` |
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| `CUSTODY_BIT_ONE` | `True` |
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## Data structures
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### Beacon chain operations
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@ -291,12 +301,14 @@ Code snippets appearing in `this style` are to be interpreted as Python code. Be
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```python
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{
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# Validator indices with custody bit equal to 0
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'custody_bit_0_indices': ['uint24'],
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# Validator indices with custody bit equal to 1
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'custody_bit_1_indices': ['uint24'],
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# Attestation data
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'data': AttestationData,
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# Aggregate signature
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'aggregate_signature': 'bytes96',
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# Validator indices
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'validator_indices': ['uint24'],
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}
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```
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@ -310,6 +322,8 @@ Code snippets appearing in `this style` are to be interpreted as Python code. Be
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'data': AttestationData,
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# Attester aggregation bitfield
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'aggregation_bitfield': 'bytes',
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# Custody bitfield
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'custody_bitfield': 'bytes',
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# BLS aggregate signature
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'aggregate_signature': 'bytes96',
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}
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@ -338,12 +352,14 @@ Code snippets appearing in `this style` are to be interpreted as Python code. Be
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}
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```
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#### `AttestationDataWrapped`
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##### `AttestationDataAndCustodyBit`
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```python
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{
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# Attestation data
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'data': AttestationData,
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# Custody bit
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'custody_bit': bool,
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}
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```
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@ -537,6 +553,8 @@ Code snippets appearing in `this style` are to be interpreted as Python code. Be
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'data': AttestationData,
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# Attester aggregation bitfield
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'aggregation_bitfield': 'bytes',
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# Custody bitfield
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'custody_bitfield': 'bytes',
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# Slot the attestation was included
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'slot_included': 'uint64',
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}
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@ -1008,22 +1026,20 @@ def merkle_root(values: List[Bytes32]) -> Bytes32:
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```python
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def get_attestation_participants(state: BeaconState,
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attestation_data: AttestationData,
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aggregation_bitfield: bytes) -> List[int]:
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bitfield: bytes) -> List[int]:
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"""
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Returns the participant indices at for the ``attestation_data`` and ``aggregation_bitfield``.
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Returns the participant indices at for the ``attestation_data`` and ``bitfield``.
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"""
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# Find the committee in the list with the desired shard
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crosslink_committees = get_crosslink_committees_at_slot(state, attestation_data.slot)
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assert attestation_data.shard in [shard for _, shard in crosslink_committees]
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crosslink_committee = [committee for committee, shard in crosslink_committees if shard == attestation_data.shard][0]
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assert len(aggregation_bitfield) == (len(committee) + 7) // 8
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# Find the participating attesters in the committee
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participants = []
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for i, validator_index in enumerate(crosslink_committee):
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aggregation_bit = (aggregation_bitfield[i // 8] >> (7 - (i % 8))) % 2
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aggregation_bit = get_bitfield_bit(bitfield, i)
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if aggregation_bit == 1:
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participants.append(validator_index)
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return participants
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@ -1066,18 +1082,51 @@ def get_domain(fork: Fork,
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) * 2**32 + domain_type
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```
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#### `get_bitfield_bit`
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```python
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def get_bitfield_bit(bitfield: bytes, i: int) -> int:
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return (bitfield[i // 8] >> (7 - (i % 8))) % 2
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```
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#### `verify_bitfield`
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```python
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def verify_bitfield(bitfield: bytes, size: int) -> bool:
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```
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Verify ``bitfield`` against the ``size``.
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if len(bitfield) != (size + 7) // 8:
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return False
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for i in range(size + 1, size + size % 8 + 8):
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if get_bitfield_bit(bitfield, i) != 0:
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return False
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return True
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```
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#### `verify_slashable_vote_data`
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```python
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def verify_slashable_vote_data(state: BeaconState, vote_data: SlashableVoteData) -> bool:
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if len(vote_data.validator_indices) > MAX_CASPER_VOTES:
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def verify_slashable_vote_data(state: BeaconState, slashable_vote_data: SlashableVoteData) -> bool:
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# [TO BE REMOVED IN PHASE 1]
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if len(slashable_vote_data.custody_bit_1_indices) > 0:
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return False
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if len(indices(slashable_vote_data)) > MAX_CASPER_VOTES:
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return False
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return bls_verify(
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pubkey=bls_aggregate_pubkeys([state.validator_registry[i].pubkey for i in vote_data.validator_indices]),
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message=hash_tree_root(AttestationDataWrapped(data=vote_data.data)),
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signature=vote_data.aggregate_signature,
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domain=get_domain(state.fork, vote_data.data.slot, DOMAIN_ATTESTATION),
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pubkeys=[
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bls_aggregate_pubkeys([state.validator_registry[i].pubkey for i in slashable_vote_data.custody_bit_0_indices]),
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bls_aggregate_pubkeys([state.validator_registry[i].pubkey for i in slashable_vote_data.custody_bit_1_indices]),
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],
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messages=[
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hash_tree_root(AttestationDataAndCustodyBit(slashable_vote_data.data, CUSTODY_BIT_ZERO)),
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hash_tree_root(AttestationDataAndCustodyBit(slashable_vote_data.data, CUSTODY_BIT_ONE)),
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],
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signature=slashable_vote_data.aggregate_signature,
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domain=get_domain(state.fork, slashable_vote_data.data.slot, DOMAIN_ATTESTATION),
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)
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```
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@ -1135,6 +1184,16 @@ def integer_squareroot(n: int) -> int:
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return x
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```
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#### `indices`
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```python
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def indices(slashable_vote_data: SlashableVoteData) -> List[int]:
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"""
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Return all indicies in ``slashable_vote_data``.
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"""
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return slashable_vote_data.custody_bit_0_indices + slashable_vote_data.custody_bit_1_indices
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```
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#### `bls_verify`
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`bls_verify` is a function for verifying a BLS signature, defined in the [BLS Signature spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/bls_signature.md#bls_verify).
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@ -1448,7 +1507,7 @@ For each `casper_slashing` in `block.body.casper_slashings`:
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* Let `slashable_vote_data_1 = casper_slashing.slashable_vote_data_1`.
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* Let `slashable_vote_data_2 = casper_slashing.slashable_vote_data_2`.
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* Let `intersection = [x for x in slashable_vote_data_1.validator_indices if x in slashable_vote_data_2.validator_indices]`.
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* Let `intersection = [x for x in indices(slashable_vote_data_1) if x in indices(slashable_vote_data_2)]`.
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* Verify that `len(intersection) >= 1`.
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* Verify that `slashable_vote_data_1.data != slashable_vote_data_2.data`.
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* Verify that `is_double_vote(slashable_vote_data_1.data, slashable_vote_data_2.data)` or `is_surround_vote(slashable_vote_data_1.data, slashable_vote_data_2.data)`.
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@ -1467,10 +1526,32 @@ For each `attestation` in `block.body.attestations`:
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* Verify that `attestation.data.justified_slot` is equal to `state.justified_slot if attestation.data.slot >= state.slot - (state.slot % EPOCH_LENGTH) else state.previous_justified_slot`.
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* Verify that `attestation.data.justified_block_root` is equal to `get_block_root(state, attestation.data.justified_slot)`.
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* Verify that either `attestation.data.latest_crosslink_root` or `attestation.data.shard_block_root` equals `state.latest_crosslinks[shard].shard_block_root`.
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* `aggregate_signature` verification:
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* Let `participants = get_attestation_participants(state, attestation.data, attestation.aggregation_bitfield)`.
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* Let `group_public_key = bls_aggregate_pubkeys([state.validator_registry[v].pubkey for v in participants])`.
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* Verify that `bls_verify(pubkey=group_public_key, message=hash_tree_root(AttestationDataWrapped(data=attestation.data)), signature=attestation.aggregate_signature, domain=get_domain(state.fork, attestation.data.slot, DOMAIN_ATTESTATION))`.
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* `attestation.aggregate_signature` verification:
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```python
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assert verify_bitfield(attestation.aggregation_bitfield)
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assert verify_bitfield(attestation.custody_bitfield)
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assert attestation.custody_bitfield & attestation.aggregation_bitfield == attestation.custody_bitfield
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participants = get_attestation_participants(state, attestation.data, attestation.aggregation_bitfield)
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custody_bit_0_participants = get_attestation_participants(state, attestation.data, attestation.custody_bitfield)
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custody_bit_1_participants = [i in participants for i not in custody_bit_0_participants]
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assert bls_verify_multiple(
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pubkeys=[
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bls_aggregate_pubkeys([state.validator_registry[i].pubkey for i in custody_bit_0_participants]),
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bls_aggregate_pubkeys([state.validator_registry[i].pubkey for i in custody_bit_1_participants]),
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],
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messages=[
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hash_tree_root(AttestationDataAndCustodyBit(data=attestation.data, custody_bit=CUSTODY_BIT_ZERO)),
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hash_tree_root(AttestationDataAndCustodyBit(data=attestation.data, custody_bit=CUSTODY_BIT_ONE)),
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],
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signature=attestation.aggregate_signature,
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domain=get_domain(state.fork, attestation.data.slot, DOMAIN_ATTESTATION),
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)
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```
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* [TO BE REMOVED IN PHASE 1] Verify that `attestation.data.shard_block_root == ZERO_HASH`.
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* Append `PendingAttestation(data=attestation.data, aggregation_bitfield=attestation.aggregation_bitfield, slot_included=state.slot)` to `state.latest_attestations`.
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