25 KiB
25 KiB
Ethereum 2.0 Phase 1 -- The Beacon Chain for Shards
Notice: This document is a work-in-progress for researchers and implementers.
Table of contents
TODO
Introduction
This document describes the extensions made to the Phase 0 design of The Beacon Chain to facilitate the new shards as part of Phase 1 of Eth2.
Configuration
Configuration is not namespaced. Instead it is strictly an extension; no constants of phase 0 change, but new constants are adopted for changing behaviors.
Misc
| Name | Value | Unit | Duration |
|---|---|---|---|
MAX_SHARDS |
2**10 (= 1024) |
||
ACTIVE_SHARDS |
2**6 (= 64) |
||
ONLINE_PERIOD |
2**3 (= 8) |
epochs | ~51 min |
LIGHT_CLIENT_COMMITTEE_SIZE |
2**7 (= 128) |
||
LIGHT_CLIENT_COMMITTEE_PERIOD |
2**8 (= 256) |
epochs | ~27 hours |
SHARD_COMMITTEE_PERIOD |
2**8 (= 256) |
epochs | ~27 hours |
SHARD_BLOCK_CHUNK_SIZE |
2**18 (= 262,144) |
||
MAX_SHARD_BLOCK_CHUNKS |
2**2 (= 4) |
||
BLOCK_SIZE_TARGET |
3 * 2**16 (= 196,608) |
||
SHARD_BLOCK_OFFSETS |
[1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233] |
||
MAX_SHARD_BLOCKS_PER_ATTESTATION |
len(SHARD_BLOCK_OFFSETS) |
||
EMPTY_CHUNK_ROOT |
hash_tree_root(BytesN[SHARD_BLOCK_CHUNK_SIZE]()) |
||
MAX_GASPRICE |
2**14 (= 16,384) |
Gwei | |
MIN_GASPRICE |
2**5 (= 32) |
Gwei | |
GASPRICE_ADJUSTMENT_COEFFICIENT |
2**3 (= 8) |
||
DOMAIN_SHARD_LIGHT_CLIENT |
192 |
||
DOMAIN_SHARD_COMMITTEE |
192 |
||
DOMAIN_SHARD_PROPOSAL |
193 |
Containers
ShardBlockWrapper
Wrapper for being broadcasted over the network.
class ShardBlockWrapper(Container):
shard_parent_root: Hash
beacon_parent_root: Hash
slot: Slot
body: BytesN[SHARD_BLOCK_CHUNK_SIZE]
signature: BLSSignature
ShardSignableHeader
class ShardSignableHeader(Container):
shard_parent_root: Hash
beacon_parent_root: Hash
slot: Slot
body_root: Hash
ShardState
class ShardState(Container):
slot: Slot
gasprice: Gwei
data: Hash
latest_block_root: Hash
New AttestationData
class AttestationData(Container):
slot: Slot
index: CommitteeIndex
# LMD GHOST vote
beacon_block_root: Hash
# FFG vote
source: Checkpoint
target: Checkpoint
# Current-slot shard block root
head_shard_root: Hash
# Shard transition root
shard_transition_root: Hash
ShardTransition
class ShardTransition(Container):
# Starting from slot
start_slot: Slot
# Shard block lengths
shard_block_lengths: List[uint64, MAX_SHARD_BLOCKS_PER_ATTESTATION]
# Shard data roots
shard_data_roots: List[List[Hash, MAX_SHARD_BLOCK_CHUNKS], MAX_SHARD_BLOCKS_PER_ATTESTATION]
# Intermediate shard states
shard_states: List[ShardState, MAX_SHARD_BLOCKS_PER_ATTESTATION]
# Proposer signature aggregate
proposer_signature_aggregate: BLSSignature
New Attestation
class Attestation(Container):
aggregation_bits: Bitlist[MAX_VALIDATORS_PER_COMMITTEE]
data: AttestationData
custody_bits: List[Bitlist[MAX_VALIDATORS_PER_COMMITTEE], MAX_SHARD_BLOCKS_PER_ATTESTATION]
signature: BLSSignature
AttestationAndCommittee
class AttestationAndCommittee(Container):
committee: List[ValidatorIndex, MAX_VALIDATORS_PER_COMMITTEE]
attestation: Attestation
CompactCommittee
class CompactCommittee(Container):
pubkeys: List[BLSPubkey, MAX_VALIDATORS_PER_COMMITTEE]
compact_validators: List[uint64, MAX_VALIDATORS_PER_COMMITTEE]
AttestationCustodyBitWrapper
class AttestationCustodyBitWrapper(Container):
attestation_root: Hash
block_index: uint64
bit: boolean
New extended PendingAttestation
class PendingAttestation(phase0.PendingAttestation):
aggregation_bits: Bitlist[MAX_VALIDATORS_PER_COMMITTEE]
data: AttestationData
inclusion_delay: Slot
proposer_index: ValidatorIndex
crosslink_success: boolean
New extended Validator
class Validator(phase0.Validator):
pubkey: BLSPubkey
withdrawal_credentials: Hash # Commitment to pubkey for withdrawals
effective_balance: Gwei # Balance at stake
slashed: boolean
# Status epochs
activation_eligibility_epoch: Epoch # When criteria for activation were met
activation_epoch: Epoch
exit_epoch: Epoch
withdrawable_epoch: Epoch # When validator can withdraw funds
# Custody game
# next_custody_secret_to_reveal is initialised to the custody period
# (of the particular validator) in which the validator is activated
# = get_custody_period_for_validator(...)
next_custody_secret_to_reveal: uint64
max_reveal_lateness: Epoch
New extended BeaconBlockBody
class BeaconBlockBody(phase0.BeaconBlockBody):
randao_reveal: BLSSignature
eth1_data: Eth1Data # Eth1 data vote
graffiti: Bytes32 # Arbitrary data
# Slashings
proposer_slashings: List[ProposerSlashing, MAX_PROPOSER_SLASHINGS]
attester_slashings: List[AttesterSlashing, MAX_ATTESTER_SLASHINGS]
# Attesting
attestations: List[Attestation, MAX_ATTESTATIONS]
# Entry & exit
deposits: List[Deposit, MAX_DEPOSITS]
voluntary_exits: List[VoluntaryExit, MAX_VOLUNTARY_EXITS]
# Custody game
custody_chunk_challenges: List[CustodyChunkChallenge, MAX_CUSTODY_CHUNK_CHALLENGES]
custody_bit_challenges: List[CustodyBitChallenge, MAX_CUSTODY_BIT_CHALLENGES]
custody_key_reveals: List[CustodyKeyReveal, MAX_CUSTODY_KEY_REVEALS]
early_derived_secret_reveals: List[EarlyDerivedSecretReveal, MAX_EARLY_DERIVED_SECRET_REVEALS]
# Shards
shard_transitions: Vector[ShardTransition, MAX_SHARDS]
# Light clients
light_client_signature_bitfield: Bitlist[LIGHT_CLIENT_COMMITTEE_SIZE]
light_client_signature: BLSSignature
New extended BeaconBlock
Note that the body has a new BeaconBlockBody definition.
class BeaconBlock(phase0.BeaconBlock):
slot: Slot
parent_root: Hash
state_root: Hash
body: BeaconBlockBody
signature: BLSSignature
New extended BeaconState
Note that aside from the new additions, Validator and PendingAttestation have new definitions.
class BeaconState(phase0.BeaconState):
# Versioning
genesis_time: uint64
slot: Slot
fork: Fork
# History
latest_block_header: BeaconBlockHeader
block_roots: Vector[Hash, SLOTS_PER_HISTORICAL_ROOT]
state_roots: Vector[Hash, SLOTS_PER_HISTORICAL_ROOT]
historical_roots: List[Hash, HISTORICAL_ROOTS_LIMIT]
# Eth1
eth1_data: Eth1Data
eth1_data_votes: List[Eth1Data, SLOTS_PER_ETH1_VOTING_PERIOD]
eth1_deposit_index: uint64
# Registry
validators: List[Validator, VALIDATOR_REGISTRY_LIMIT]
balances: List[Gwei, VALIDATOR_REGISTRY_LIMIT]
# Randomness
randao_mixes: Vector[Hash, EPOCHS_PER_HISTORICAL_VECTOR]
# Slashings
slashings: Vector[Gwei, EPOCHS_PER_SLASHINGS_VECTOR] # Per-epoch sums of slashed effective balances
# Attestations
previous_epoch_attestations: List[PendingAttestation, MAX_ATTESTATIONS * SLOTS_PER_EPOCH]
current_epoch_attestations: List[PendingAttestation, MAX_ATTESTATIONS * SLOTS_PER_EPOCH]
# Finality
justification_bits: Bitvector[JUSTIFICATION_BITS_LENGTH] # Bit set for every recent justified epoch
previous_justified_checkpoint: Checkpoint # Previous epoch snapshot
current_justified_checkpoint: Checkpoint
finalized_checkpoint: Checkpoint
# Phase 1
shard_states: List[ShardState, MAX_SHARDS]
online_countdown: Bytes[VALIDATOR_REGISTRY_LIMIT]
current_light_committee: CompactCommittee
next_light_committee: CompactCommittee
# Custody game
# TODO: custody game refactor, no challenge-records, immediate processing.
custody_challenge_index: uint64
# Future derived secrets already exposed; contains the indices of the exposed validator
# at RANDAO reveal period % EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS
exposed_derived_secrets: Vector[List[ValidatorIndex, PLACEHOLDER],
EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS]
Helper functions
Crypto
bls_verify_multiple
bls_verify_multiple is a function for verifying a BLS signature constructed from multiple messages, as defined in the BLS Signature spec.
Misc
pack_compact_validator
def pack_compact_validator(index: int, slashed: bool, balance_in_increments: int) -> int:
"""
Creates a compact validator object representing index, slashed status, and compressed balance.
Takes as input balance-in-increments (// EFFECTIVE_BALANCE_INCREMENT) to preserve symmetry with
the unpacking function.
"""
return (index << 16) + (slashed << 15) + balance_in_increments
committee_to_compact_committee
def committee_to_compact_committee(state: BeaconState, committee: Sequence[ValidatorIndex]) -> CompactCommittee:
"""
Given a state and a list of validator indices, outputs the CompactCommittee representing them.
"""
validators = [state.validators[i] for i in committee]
compact_validators = [
pack_compact_validator(i, v.slashed, v.effective_balance // EFFECTIVE_BALANCE_INCREMENT)
for i, v in zip(committee, validators)
]
pubkeys = [v.pubkey for v in validators]
return CompactCommittee(pubkeys=pubkeys, compact_validators=compact_validators)
chunks_to_body_root
def chunks_to_body_root(chunks):
return hash_tree_root(chunks + [EMPTY_CHUNK_ROOT] * (MAX_SHARD_BLOCK_CHUNKS - len(chunks)))
Beacon state accessors
get_online_validator_indices
def get_online_validator_indices(state: BeaconState) -> Set[ValidatorIndex]:
active_validators = get_active_validator_indices(state, get_current_epoch(state))
return set([i for i in active_validators if state.online_countdown[i] != 0])
get_shard_committee
def get_shard_committee(beacon_state: BeaconState, epoch: Epoch, shard: Shard) -> Sequence[ValidatorIndex]:
source_epoch = epoch - epoch % SHARD_COMMITTEE_PERIOD
if source_epoch > 0:
source_epoch -= SHARD_COMMITTEE_PERIOD
active_validator_indices = get_active_validator_indices(beacon_state, source_epoch)
seed = get_seed(beacon_state, source_epoch, DOMAIN_SHARD_COMMITTEE)
return compute_committee(active_validator_indices, seed, 0, ACTIVE_SHARDS)
get_shard_proposer_index
def get_shard_proposer_index(beacon_state: BeaconState, slot: Slot, shard: Shard) -> ValidatorIndex:
committee = get_shard_committee(beacon_state, slot_to_epoch(slot), shard)
r = bytes_to_int(get_seed(beacon_state, get_current_epoch(state), DOMAIN_SHARD_COMMITTEE)[:8])
return committee[r % len(committee)]
get_light_client_committee
def get_light_client_committee(beacon_state: BeaconState, epoch: Epoch) -> Sequence[ValidatorIndex]:
source_epoch = epoch - epoch % LIGHT_CLIENT_COMMITTEE_PERIOD
if source_epoch > 0:
source_epoch -= LIGHT_CLIENT_COMMITTEE_PERIOD
active_validator_indices = get_active_validator_indices(beacon_state, source_epoch)
seed = get_seed(beacon_state, source_epoch, DOMAIN_SHARD_LIGHT_CLIENT)
return compute_committee(active_validator_indices, seed, 0, ACTIVE_SHARDS)[:TARGET_COMMITTEE_SIZE]
get_indexed_attestation
def get_indexed_attestation(beacon_state: BeaconState, attestation: Attestation) -> AttestationAndCommittee:
committee = get_beacon_committee(beacon_state, attestation.data.slot, attestation.data.index)
return AttestationAndCommittee(committee, attestation)
get_updated_gasprice
def get_updated_gasprice(prev_gasprice: Gwei, length: uint8) -> Gwei:
if length > BLOCK_SIZE_TARGET:
delta = prev_gasprice * (length - BLOCK_SIZE_TARGET) // BLOCK_SIZE_TARGET // GASPRICE_ADJUSTMENT_COEFFICIENT
return min(prev_gasprice + delta, MAX_GASPRICE)
else:
delta = prev_gasprice * (BLOCK_SIZE_TARGET - length) // BLOCK_SIZE_TARGET // GASPRICE_ADJUSTMENT_COEFFICIENT
return max(prev_gasprice, MIN_GASPRICE + delta) - delta
get_shard
def get_shard(state: BeaconState, attestation: Attestation) -> Shard:
return Shard((attestation.data.index + get_start_shard(state, attestation.data.slot)) % ACTIVE_SHARDS)
get_offset_slots
def get_offset_slots(state: BeaconState, start_slot: Slot) -> Sequence[Slot]:
return [start_slot + x for x in SHARD_BLOCK_OFFSETS if start_slot + x < state.slot]
Predicates
Updated is_valid_indexed_attestation
Note that this replaces the Phase 0 is_valid_indexed_attestation.
def is_valid_indexed_attestation(state: BeaconState, indexed_attestation: AttestationAndCommittee) -> bool:
"""
Check if ``indexed_attestation`` has valid indices and signature.
"""
# Verify aggregate signature
all_pubkeys = []
all_message_hashes = []
aggregation_bits = indexed_attestation.attestation.aggregation_bits
assert len(aggregation_bits) == len(indexed_attestation.committee)
for i, custody_bits in enumerate(indexed_attestation.attestation.custody_bits):
assert len(custody_bits) == len(indexed_attestation.committee)
for participant, abit, cbit in zip(indexed_attestation.committee, aggregation_bits, custody_bits):
if abit:
all_pubkeys.append(state.validators[participant].pubkey)
# Note: only 2N distinct message hashes
all_message_hashes.append(hash_tree_root(
AttestationCustodyBitWrapper(hash_tree_root(indexed_attestation.data), i, cbit)
))
else:
assert cbit == False
return bls_verify_multiple(
pubkeys=all_pubkeys,
message_hashes=all_message_hashes,
signature=indexed_attestation.signature,
domain=get_domain(state, DOMAIN_BEACON_ATTESTER, indexed_attestation.data.target.epoch),
)
Block processing
def process_block(state: BeaconState, block: BeaconBlock) -> None:
process_block_header(state, block)
process_randao(state, block.body)
process_eth1_data(state, block.body)
verify_shard_transition_false_positives(state, block)
process_light_client_signatures(state, block)
process_operations(state, block.body)
Operations
def process_operations(state: BeaconState, body: BeaconBlockBody) -> None:
# Verify that outstanding deposits are processed up to the maximum number of deposits
assert len(body.deposits) == min(MAX_DEPOSITS, state.eth1_data.deposit_count - state.eth1_deposit_index)
def for_ops(operations, fn):
for operation in operations:
fn(state, operation)
for_ops(body.proposer_slashings, process_proposer_slashing)
for_ops(body.attester_slashings, process_attester_slashing)
# New attestation processing
process_attestations(state, body, body.attestations)
for_ops(body.deposits, process_deposit)
for_ops(body.voluntary_exits, process_voluntary_exit)
# See custody game spec.
process_custody_game_operations(state, body)
# TODO process_operations(body.shard_receipt_proofs, process_shard_receipt_proofs)
New Attestation processing
validate_attestation
def validate_attestation(state: BeaconState, attestation: Attestation) -> None:
data = attestation.data
assert data.index < ACTIVE_SHARDS
shard = get_shard(state, attestation)
proposer_index = get_beacon_proposer_index(state)
# Signature check
assert is_valid_indexed_attestation(state, get_indexed_attestation(state, attestation))
# Type 1: on-time attestations
if attestation.custody_bits != []:
# Correct slot
assert data.slot == state.slot
# Correct data root count
assert len(attestation.custody_bits) == len(get_offset_slots(state, state.shard_next_slots[shard]))
# Correct parent block root
assert data.beacon_block_root == get_block_root_at_slot(state, state.slot - 1)
# Type 2: delayed attestations
else:
assert state.slot - compute_start_slot_at_epoch(slot_to_epoch(data.slot)) < EPOCH_LENGTH
assert data.shard_transition_root == Hash()
apply_shard_transition
def apply_shard_transition(state: BeaconState, shard: Shard, transition: ShardTransition) -> None:
# Slot the attestation starts counting from
start_slot = state.shard_next_slots[shard]
# Correct data root count
offset_slots = get_offset_slots(state, start_slot)
assert len(transition.shard_data_roots) == len(transition.shard_states) == len(transition.shard_block_lengths) == len(offset_slots)
assert transition.start_slot == start_slot
# Reonstruct shard headers
headers = []
proposers = []
shard_parent_root = state.shard_states[shard].latest_block_root
for i in range(len(offset_slots)):
if any(transition.shard_data_roots):
headers.append(ShardSignableHeader(
shard_parent_root=shard_parent_root,
parent_hash=get_block_root_at_slot(state, state.slot-1),
slot=offset_slots[i],
body_root=chunks_to_body_root(transition.shard_data_roots[i])
))
proposers.append(get_shard_proposer_index(state, shard, offset_slots[i]))
shard_parent_root = hash_tree_root(headers[-1])
# Verify correct calculation of gas prices and slots and chunk roots
prev_gasprice = state.shard_states[shard].gasprice
for i in range(len(offset_slots)):
shard_state, block_length, chunks = transition.shard_states[i], transition.shard_block_lengths[i], transition.shard_data_roots[i]
assert shard_state.gasprice == get_updated_gasprice(prev_gasprice, block_length)
assert shard_state.slot == offset_slots[i]
assert len(chunks) == block_length // SHARD_BLOCK_CHUNK_SIZE
prev_gasprice = shard_state.gasprice
# Verify combined proposer signature
assert bls_verify_multiple(
pubkeys=[state.validators[proposer].pubkey for proposer in proposers],
message_hashes=[hash_tree_root(header) for header in headers],
signature=transition.proposer_signature_aggregate,
domain=DOMAIN_SHARD_PROPOSAL
)
# Save updated state
state.shard_states[shard] = transition.shard_states[-1]
state.shard_states[shard].slot = state.slot - 1
process_attestations
def process_attestations(state: BeaconState, block_body: BeaconBlockBody, attestations: Sequence[Attestation]) -> None:
# Basic validation
for attestation in attestations:
validate_attestation(state, attestation)
# Process crosslinks
online_indices = get_online_validator_indices(state)
winners = set()
for shard in range(ACTIVE_SHARDS):
success = False
# All attestations in the block for this shard
this_shard_attestations = [attestation for attestation in attestations if get_shard(state, attestation) == shard and attestation.data.slot == state.slot]
# The committee for this shard
this_shard_committee = get_beacon_committee(state, get_current_epoch(state), shard)
# Loop over all shard transition roots
for shard_transition_root in sorted(set([attestation.data.shard_transition_root for attestation in this_shard_attestations])):
all_participants = set()
participating_attestations = []
for attestation in this_shard_attestations:
participating_attestations.append(attestation)
if attestation.data.shard_transition_root == shard_transition_root:
all_participants = all_participants.union(get_attesting_indices(state, attestation.data, attestation.aggregation_bits))
if (
get_total_balance(state, online_indices.intersection(all_participants)) * 3 >=
get_total_balance(state, online_indices.intersection(this_shard_committee)) * 2
and success is False
):
# Attestation <-> shard transition consistency
assert shard_transition_root == hash_tree_root(block_body.shard_transition)
assert attestation.data.head_shard_root == chunks_to_body_root(block_body.shard_transition.shard_data_roots[-1])
# Apply transition
apply_shard_transition(state, shard, block_body.shard_transition)
# Apply proposer reward and cost
estimated_attester_reward = sum([get_base_reward(state, attester) for attester in all_participants])
increase_balance(state, proposer, estimated_attester_reward // PROPOSER_REWARD_COEFFICIENT)
for shard_state, slot, length in zip(block_body.shard_transition.shard_states, offset_slots, block_body.shard_transition.shard_block_lengths):
decrease_balance(state, get_shard_proposer_index(state, shard, slot), shard_state.gasprice * length)
winners.add((shard, shard_transition_root))
success = True
if not success:
assert block_body.shard_transitions[shard] == ShardTransition()
for attestation in attestations:
pending_attestation = PendingAttestation(
aggregation_bits=attestation.aggregation_bits,
data=attestation.data,
inclusion_delay=state.slot - data.slot,
crosslink_success=(get_shard(state, attestation), attestation.shard_transition_root) in winners and attestation.data.slot == state.slot,
proposer_index=proposer_index
)
if attestation.data.target.epoch == get_current_epoch(state):
assert attestation.data.source == state.current_justified_checkpoint
state.current_epoch_attestations.append(pending_attestation)
else:
assert attestation.data.source == state.previous_justified_checkpoint
state.previous_epoch_attestations.append(pending_attestation)
Shard transition false positives
def verify_shard_transition_false_positives(state: BeaconState, block_body: BeaconBlockBody) -> None:
# Verify that a `shard_transition` in a block is empty if an attestation was not processed for it
for shard in range(ACTIVE_SHARDS):
if state.shard_states[shard].slot != state.slot - 1:
assert block_body.shard_transition[shard] == ShardTransition()
Light client processing
def process_light_client_signatures(state: BeaconState, block_body: BeaconBlockBody) -> None:
committee = get_light_client_committee(state, get_current_epoch(state))
assert len(block_body.light_client_signature_bitfield) == len(committee)
total_reward = Gwei(0)
signer_keys = []
for i, bit in enumerate(block_body.light_client_signature_bitfield):
if bit:
signer_keys.append(state.validators[committee[i]].pubkey)
increase_balance(state, committee[i], get_base_reward(state, committee[i]))
total_reward += get_base_reward(state, committee[i])
increase_balance(state, get_beacon_proposer_index(state), total_reward // PROPOSER_REWARD_COEFFICIENT)
assert bls_verify(
pubkey=bls_aggregate_pubkeys(signer_keys),
message_hash=get_block_root_at_slot(state, state.slot - 1),
signature=block_body.light_client_signature,
domain=DOMAIN_LIGHT_CLIENT
)
Epoch transition
This epoch transition overrides the phase0 epoch transition:
def process_epoch(state: BeaconState) -> None:
process_justification_and_finalization(state)
process_rewards_and_penalties(state)
process_registry_updates(state)
process_reveal_deadlines(state)
process_slashings(state)
process_final_updates(state)
process_custody_final_updates(state)
process_online_tracking(state)
process_light_client_committee_updates(state)
Custody game updates
process_reveal_deadlines and process_custody_final_updates are defined in the Custody Game spec,
Online-tracking
def process_online_tracking(state: BeaconState) -> None:
# Slowly remove validators from the "online" set if they do not show up
for index in range(len(state.validators)):
if state.online_countdown[index] != 0:
state.online_countdown[index] = state.online_countdown[index] - 1
# Process pending attestations
for pending_attestation in state.current_epoch_attestations + state.previous_epoch_attestations:
for index in get_attesting_indices(state, pending_attestation.data, pending_attestation.aggregation_bits):
state.online_countdown[index] = ONLINE_PERIOD
Light client committee updates
def process_light_client_committee_updates(state: BeaconState) -> None:
# Update light client committees
if get_current_epoch(state) % LIGHT_CLIENT_COMMITTEE_PERIOD == 0:
state.current_light_committee = state.next_light_committee
new_committee = get_light_client_committee(state, get_current_epoch(state) + LIGHT_CLIENT_COMMITTEE_PERIOD)
state.next_light_committee = committee_to_compact_committee(state, new_committee)