Ethereum 2.0 Phase 1 -- Shard Data Chains
Notice: This document is a work-in-progress for researchers and implementers.
Table of contents
Introduction
This document describes the shard transition function (data layer only) and the shard fork choice rule as part of Phase 1 of Ethereum 2.0.
Custom types
| Name |
SSZ equivalent |
Description |
ShardSlot |
uint64 |
a shard slot number |
Configuration
Misc
| Name |
Value |
MIN_BLOCK_BODY_PRICE |
2**0 (= 1) |
MAX_PERIOD_COMMITTEE_SIZE |
2**7 (= 128) |
SHARD_HEADER_SIZE |
2**10 (= 1024) |
SHARD_BLOCK_SIZE_TARGET |
2**14 (= 16,384) |
MAX_SHARD_BLOCK_SIZE |
2**16 (= 65,536) |
Initial values
| Name | Value | Unit |
| - | - |
| SHARD_GENESIS_EPOCH | TBD | Epoch |
Time parameters
| Name |
Value |
Unit |
Duration |
SHARD_SLOTS_PER_EPOCH |
2**7 (= 128) |
shard slots |
6.4 minutes |
EPOCHS_PER_SHARD_PERIOD |
2**8 (= 256) |
epochs |
~27 hours |
State list lengths
| Name |
Value |
HISTORY_ACCUMULATOR_DEPTH |
2**6 (= 64) |
Rewards and penalties
| Name |
Value |
BLOCK_BODY_PRICE_QUOTIENT |
2**3 (= 8) |
Signature domain types
| Name |
Value |
DOMAIN_SHARD_PROPOSER |
128 |
DOMAIN_SHARD_ATTESTER |
129 |
Containers
ShardBlock
class ShardBlock(Container):
shard: Shard
slot: ShardSlot
beacon_block_root: Hash
parent_root: Hash
state_root: Hash
body: List[byte, MAX_SHARD_BLOCK_SIZE - SHARD_HEADER_SIZE]
block_size_sum: uint64
aggregation_bits: Bitvector[2 * MAX_PERIOD_COMMITTEE_SIZE]
attestations: BLSSignature
signature: BLSSignature
class ShardBlockHeader(Container):
shard: Shard
slot: ShardSlot
beacon_block_root: Hash
parent_root: Hash
state_root: Hash
body_root: Hash
block_size_sum: uint64
aggregation_bits: Bitvector[2 * MAX_PERIOD_COMMITTEE_SIZE]
attestations: BLSSignature
signature: BLSSignature
ShardState
class ShardState(Container):
shard: Shard
slot: ShardSlot
history_accumulator: Vector[Hash, HISTORY_ACCUMULATOR_DEPTH]
latest_block_header: ShardBlockHeader
block_size_sum: uint64
# Fees and rewards
block_body_price: Gwei
older_committee_positive_deltas: Vector[Gwei, MAX_PERIOD_COMMITTEE_SIZE]
older_committee_negative_deltas: Vector[Gwei, MAX_PERIOD_COMMITTEE_SIZE]
newer_committee_positive_deltas: Vector[Gwei, MAX_PERIOD_COMMITTEE_SIZE]
newer_committee_negative_deltas: Vector[Gwei, MAX_PERIOD_COMMITTEE_SIZE]
ShardAttestationData
class ShardAttestationData(Container):
slot: ShardSlot
parent_root: Hash
Helper functions
Misc
compute_epoch_of_shard_slot
def compute_epoch_of_shard_slot(slot: ShardSlot) -> Epoch:
return Epoch(slot // SHARD_SLOTS_PER_EPOCH)
compute_shard_period_start_epoch
def compute_shard_period_start_epoch(epoch: Epoch, lookback: uint64) -> Epoch:
return Epoch(epoch - (epoch % EPOCHS_PER_SHARD_PERIOD) - lookback * EPOCHS_PER_SHARD_PERIOD)
Beacon state accessors
get_period_committee
def get_period_committee(beacon_state: BeaconState, shard: Shard, epoch: Epoch) -> Sequence[ValidatorIndex]:
active_validator_indices = get_active_validator_indices(beacon_state, epoch)
seed = get_seed(beacon_state, epoch, DOMAIN_SHARD_ATTESTER)
return compute_committee(active_validator_indices, seed, shard, SHARD_COUNT)[:MAX_PERIOD_COMMITTEE_SIZE]
get_shard_committee
def get_shard_committee(beacon_state: BeaconState, shard: Shard, epoch: Epoch) -> Sequence[ValidatorIndex]:
older_committee = get_period_committee(beacon_state, shard, compute_shard_period_start_epoch(epoch, 2))
newer_committee = get_period_committee(beacon_state, shard, compute_shard_period_start_epoch(epoch, 1))
# Every epoch cycle out validators from the older committee and cycle in validators from the newer committee
older_subcommittee = [i for i in older_committee if i % EPOCHS_PER_SHARD_PERIOD > epoch % EPOCHS_PER_SHARD_PERIOD]
newer_subcommittee = [i for i in newer_committee if i % EPOCHS_PER_SHARD_PERIOD <= epoch % EPOCHS_PER_SHARD_PERIOD]
return older_subcommittee + newer_subcommittee
get_shard_proposer_index
def get_shard_proposer_index(beacon_state: BeaconState, shard: Shard, slot: ShardSlot) -> ValidatorIndex:
epoch = get_current_epoch(beacon_state)
shard_committee = get_shard_committee(beacon_state, shard, epoch)
active_indices = [i for i in shard_committee if is_active_validator(beacon_state.validators[i], epoch)]
assert any(active_indices)
epoch_seed = get_seed(beacon_state, epoch, DOMAIN_SHARD_PROPOSER)
seed = hash(epoch_seed + int_to_bytes(slot, length=8) + int_to_bytes(shard, length=8))
return compute_proposer_index(beacon_state, active_indices, seed)
Shard state mutators
process_delta
def process_delta(beacon_state: BeaconState,
shard_state: ShardState,
index: ValidatorIndex,
delta: Gwei,
positive: bool=True) -> None:
epoch = compute_epoch_of_shard_slot(shard_state.slot)
older_committee = get_period_committee(beacon_state, shard_state.shard, compute_shard_period_start_epoch(epoch, 2))
newer_committee = get_period_committee(beacon_state, shard_state.shard, compute_shard_period_start_epoch(epoch, 1))
if index in older_committee:
if positive:
shard_state.older_committee_positive_deltas[older_committee.index(index)] += delta
else:
shard_state.older_committee_negative_deltas[older_committee.index(index)] += delta
elif index in newer_committee:
if positive:
shard_state.newer_committee_positive_deltas[newer_committee.index(index)] += delta
else:
shard_state.newer_committee_negative_deltas[newer_committee.index(index)] += delta
Genesis
get_genesis_shard_state
def get_genesis_shard_state(shard: Shard) -> ShardState:
return ShardState(
shard=shard,
slot=ShardSlot(SHARD_GENESIS_EPOCH * SHARD_SLOTS_PER_EPOCH),
latest_block_header=ShardBlockHeader(
shard=shard,
slot=ShardSlot(SHARD_GENESIS_EPOCH * SHARD_SLOTS_PER_EPOCH),
body_root=hash_tree_root(List[byte, MAX_SHARD_BLOCK_SIZE - SHARD_HEADER_SIZE]()),
),
block_body_price=MIN_BLOCK_BODY_PRICE,
)
get_genesis_shard_block
def get_genesis_shard_block(shard: Shard) -> ShardBlock:
return ShardBlock(
shard=shard,
slot=ShardSlot(SHARD_GENESIS_EPOCH * SHARD_SLOTS_PER_EPOCH),
state_root=hash_tree_root(get_genesis_shard_state(shard)),
)
Shard state transition function
def shard_state_transition(beacon_state: BeaconState,
shard_state: ShardState,
block: ShardBlock,
validate_state_root: bool=False) -> ShardState:
# Process slots (including those with no blocks) since block
process_shard_slots(shard_state, block.slot)
# Process block
process_shard_block(beacon_state, shard_state, block)
# Validate state root (`validate_state_root == True` in production)
if validate_state_root:
assert block.state_root == hash_tree_root(shard_state)
# Return post-state
return shard_state
def process_shard_slots(shard_state: ShardState, slot: ShardSlot) -> None:
assert shard_state.slot <= slot
while shard_state.slot < slot:
process_shard_slot(shard_state)
# Process shard period on the start slot of the next shard period
if (shard_state.slot + 1) % (SHARD_SLOTS_PER_EPOCH * EPOCHS_PER_SHARD_PERIOD) == 0:
process_shard_period(shard_state)
shard_state.slot += ShardSlot(1)
def process_shard_slot(shard_state: ShardState) -> None:
# Cache state root
previous_state_root = hash_tree_root(shard_state)
if shard_state.latest_block_header.state_root == Bytes32():
shard_state.latest_block_header.state_root = previous_state_root
# Cache state root in history accumulator
depth = 0
while shard_state.slot % 2**depth == 0 and depth < HISTORY_ACCUMULATOR_DEPTH:
shard_state.history_accumulator[depth] = previous_state_root
depth += 1
Period processing
def process_shard_period(shard_state: ShardState) -> None:
# Rotate committee deltas
shard_state.older_committee_positive_deltas = shard_state.newer_committee_positive_deltas
shard_state.older_committee_negative_deltas = shard_state.newer_committee_negative_deltas
shard_state.newer_committee_positive_deltas = [Gwei(0) for _ in range(MAX_PERIOD_COMMITTEE_SIZE)]
shard_state.newer_committee_negative_deltas = [Gwei(0) for _ in range(MAX_PERIOD_COMMITTEE_SIZE)]
Block processing
def process_shard_block(beacon_state: BeaconState, shard_state: ShardState, block: ShardBlock) -> None:
process_shard_block_header(beacon_state, shard_state, block)
process_shard_attestations(beacon_state, shard_state, block)
process_shard_block_body(beacon_state, shard_state, block)
def process_shard_block_header(beacon_state: BeaconState, shard_state: ShardState, block: ShardBlock) -> None:
# Verify the shard number
assert block.shard == shard_state.shard
# Verify the slot number
assert block.slot == shard_state.slot
# Verify the beacon chain root
epoch = compute_epoch_of_shard_slot(shard_state.slot)
assert epoch * SLOTS_PER_EPOCH == beacon_state.slot
beacon_block_header = BeaconBlockHeader(
slot=beacon_state.latest_block_header.slot,
parent_root=beacon_state.latest_block_header.parent_root,
state_root=beacon_state.latest_block_header.state_root,
body_root=beacon_state.latest_block_header.body_root,
)
if beacon_block_header.state_root == Bytes32():
beacon_block_header.state_root = hash_tree_root(beacon_state)
assert block.beacon_block_root == signing_root(beacon_block_header)
# Verify the parent root
assert block.parent_root == signing_root(shard_state.latest_block_header)
# Save current block as the new latest block
shard_state.latest_block_header = ShardBlockHeader(
shard=block.shard,
slot=block.slot,
beacon_block_root=block.beacon_block_root,
parent_root=block.parent_root,
# `state_root` is zeroed and overwritten in the next `process_shard_slot` call
body_root=hash_tree_root(block.body),
block_size_sum=block.block_size_sum,
aggregation_bits=block.aggregation_bits,
attestations=block.attestations,
# `signature` is zeroed
)
# Verify the sum of the block sizes since genesis
shard_state.block_size_sum += SHARD_HEADER_SIZE + len(block.body)
assert block.block_size_sum == shard_state.block_size_sum
# Verify proposer is not slashed
proposer_index = get_shard_proposer_index(beacon_state, shard_state.shard, block.slot)
proposer = beacon_state.validators[proposer_index]
assert not proposer.slashed
# Verify proposer signature
domain = get_domain(beacon_state, DOMAIN_SHARD_PROPOSER, compute_epoch_of_shard_slot(block.slot))
assert bls_verify(proposer.pubkey, signing_root(block), block.signature, domain)
Attestations
def process_shard_attestations(beacon_state: BeaconState, shard_state: ShardState, block: ShardBlock) -> None:
pubkeys = []
attestation_count = 0
shard_committee = get_shard_committee(beacon_state, shard_state.shard, block.slot)
for i, validator_index in enumerate(shard_committee):
if block.aggregation_bits[i]:
pubkeys.append(beacon_state.validators[validator_index].pubkey)
process_delta(beacon_state, shard_state, validator_index, get_base_reward(beacon_state, validator_index))
attestation_count += 1
# Verify there are no extraneous bits set beyond the shard committee
for i in range(len(shard_committee), 2 * MAX_PERIOD_COMMITTEE_SIZE):
assert block.aggregation_bits[i] == 0b0
# Verify attester aggregate signature
domain = get_domain(beacon_state, DOMAIN_SHARD_ATTESTER, compute_epoch_of_shard_slot(block.slot))
message = hash_tree_root(ShardAttestationData(slot=shard_state.slot, parent_root=block.parent_root))
assert bls_verify(bls_aggregate_pubkeys(pubkeys), message, block.attestations, domain)
# Proposer micro-reward
proposer_index = get_shard_proposer_index(beacon_state, shard_state.shard, block.slot)
reward = attestation_count * get_base_reward(beacon_state, proposer_index) // PROPOSER_REWARD_QUOTIENT
process_delta(beacon_state, shard_state, proposer_index, Gwei(reward))
Block body
def process_shard_block_body(beacon_state: BeaconState, shard_state: ShardState, block: ShardBlock) -> None:
# Verify block body size is a multiple of the header size
assert len(block.body) % SHARD_HEADER_SIZE == 0
# Apply proposer block body fee
block_body_fee = shard_state.block_body_price * len(block.body) // MAX_SHARD_BLOCK_SIZE
proposer_index = get_shard_proposer_index(beacon_state, shard_state.shard, block.slot)
process_delta(beacon_state, shard_state, proposer_index, Gwei(block_body_fee), positive=False) # Burn
process_delta(beacon_state, shard_state, proposer_index, Gwei(block_body_fee // PROPOSER_REWARD_QUOTIENT)) # Reward
# Calculate new block body price
block_size = SHARD_HEADER_SIZE + len(block.body)
QUOTIENT = MAX_SHARD_BLOCK_SIZE * BLOCK_BODY_PRICE_QUOTIENT
if block_size > SHARD_BLOCK_SIZE_TARGET:
price_delta = Gwei(shard_state.block_body_price * (block_size - SHARD_BLOCK_SIZE_TARGET) // QUOTIENT)
# The maximum block body price caps the amount burnt on fees within a shard period
MAX_BLOCK_BODY_PRICE = MAX_EFFECTIVE_BALANCE // EPOCHS_PER_SHARD_PERIOD // SHARD_SLOTS_PER_EPOCH
shard_state.block_body_price = Gwei(min(MAX_BLOCK_BODY_PRICE, shard_state.block_body_price + price_delta))
else:
price_delta = Gwei(shard_state.block_body_price * (SHARD_BLOCK_SIZE_TARGET - block_size) // QUOTIENT)
shard_state.block_body_price = Gwei(max(MIN_BLOCK_BODY_PRICE, shard_state.block_body_price + price_delta))
Shard fork choice rule
The fork choice rule for any shard is LMD GHOST using the shard attestations of the shard committee and the beacon chain attestations of the crosslink committee currently assigned to that shard, but instead of being rooted in the genesis it is rooted in the block referenced in the most recent accepted crosslink (i.e. beacon_state.crosslinks[shard].shard_block_root). Only blocks whose beacon_block_root is the block in the main beacon chain at the specified slot should be considered. (If the beacon chain skips a slot, then the block at that slot is considered to be the block in the beacon chain at the highest slot lower than that slot.)