eth2.0-specs/specs/core/1_shard-data-chains.md

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# Ethereum 2.0 Phase 1 -- Shard Data Chains
**Notice**: This document is a work-in-progress for researchers and implementers.
## Table of contents
<!-- TOC -->
- [Ethereum 2.0 Phase 1 -- Shard Data Chains](#ethereum-20-phase-1----shard-data-chains)
- [Table of contents](#table-of-contents)
- [Introduction](#introduction)
- [Custom types](#custom-types)
- [Configuration](#configuration)
- [Misc](#misc)
- [Initial values](#initial-values)
- [Time parameters](#time-parameters)
- [State list lengths](#state-list-lengths)
- [Rewards and penalties](#rewards-and-penalties)
- [Signature domain types](#signature-domain-types)
- [TODO PLACEHOLDER](#todo-placeholder)
- [Data structures](#data-structures)
- [`ShardBlockHeader`](#shardblockheader)
- [`ShardBlock`](#shardblock)
- [`ShardBlockSignatures`](#shardblocksignatures)
- [`ShardBlockCore`](#shardblockcore)
- [`ExtendedShardBlockCore`](#extendedshardblockcore)
- [`ShardState`](#shardstate)
- [`ShardReceiptDelta`](#shardreceiptdelta)
- [Helper functions](#helper-functions)
- [`compute_slot_of_shard_slot`](#compute_slot_of_shard_slot)
- [`compute_epoch_of_shard_slot`](#compute_epoch_of_shard_slot)
- [`get_shard_period_start_epoch`](#get_shard_period_start_epoch)
- [`get_period_committee`](#get_period_committee)
- [`get_persistent_committee`](#get_persistent_committee)
- [`get_shard_block_proposer_index`](#get_shard_block_proposer_index)
- [`get_shard_header`](#get_shard_header)
- [`pad`](#pad)
- [`flatten_shard_header`](#flatten_shard_header)
- [`compute_crosslink_data_root`](#compute_crosslink_data_root)
- [`get_default_shard_state`](#get_default_shard_state)
- [Object validity](#object-validity)
- [Shard block validation: preliminary](#shard-block-validation-preliminary)
- [Shard state transition function helpers](#shard-state-transition-function-helpers)
- [Shard state transition function](#shard-state-transition-function)
- [Beacon attestations](#beacon-attestations)
- [Shard fork choice rule](#shard-fork-choice-rule)
<!-- /TOC -->
## Introduction
This document describes the shard data layer and the shard fork choice rule in Phase 1 of Ethereum 2.0.
## Custom types
We define the following Python custom types for type hinting and readability:
| Name | SSZ equivalent | Description |
| - | - | - |
| `ShardSlot` | `uint64` | a slot number in shard chain |
## Configuration
### Misc
| Name | Value |
| - | - |
| `SHARD_SLOTS_PER_BEACON_SLOT` | `2**1` (= 2) |
| `MAX_PERSISTENT_COMMITTEE_SIZE` | `2**7` (= 128) |
| `SHARD_HEADER_SIZE` | `2**9` (= 512) |
| `SHARD_BLOCK_SIZE_TARGET` | `2**14` (= 16,384) |
| `SHARD_BLOCK_SIZE_LIMIT` | `2**16` (= 65,536) |
### Initial values
| Name | Value |
| - | - |
| `PHASE_1_FORK_EPOCH` | **TBD** |
| `PHASE_1_FORK_SLOT` | **TBD** |
### Time parameters
| Name | Value | Unit | Duration |
| - | - | :-: | :-: |
| `CROSSLINK_LOOKBACK` | `2**0` (= 1) | epochs | 6.4 minutes |
| `EPOCHS_PER_SHARD_PERIOD` | `2**8` (= 256) | epochs | ~27 hours |
### State list lengths
| Name | Value | Unit |
| - | - | :-: |
| `HISTORY_ACCUMULATOR_VECTOR` | `2**6` (= 64) | state tree maximum depth |
### Rewards and penalties
| Name | Value |
| - | - |
| `BASEFEE_ADJUSTMENT_FACTOR` | `2**3` (= 8) |
| `REWARD_COEFFICIENT_BASE` | `2**20` ( = 1,048,576) |
### Signature domain types
The following types are defined, mapping into `DomainType` (little endian):
| Name | Value |
| - | - |
| `DOMAIN_SHARD_PROPOSER` | `128` |
| `DOMAIN_SHARD_ATTESTER` | `129` |
### TODO PLACEHOLDER
| Name | Value |
| - | - |
| `PLACEHOLDER` | `2**3` |
## Data structures
_Note: the shard block header structure is carefully designed so that all of the values have the same depth in a hash tree implementation, so `hash_tree_root(SSZ_partial(x)) == hash_tree_root(x)` (using the "left-to-right leaves" scheme [here](https://github.com/ethereum/eth2.0-specs/issues/1303)), which allows shard block headers to look like an SSZ object when in the crosslink structure. This is done by balancing it so that 7 or 8 items are on the left side (the "core") and two 96-byte (ie. 3*2 = 6 chunk) items are on the right side. Change with care._
### `ShardBlockHeader`
```python
class ShardBlockHeader(Container):
core: ShardBlockCore
signatures: ShardBlockSignatures
```
### `ShardBlock`
```python
class ShardBlock(Container):
core: ExtendedShardBlockCore
signatures: ShardBlockSignatures
```
### `ShardBlockSignatures`
```python
class ShardBlockSignatures(Container):
attestation_signature: BLSSignature
proposer_signature: BLSSignature
```
### `ShardBlockCore`
```python
class ShardBlockCore(Container):
slot: ShardSlot
beacon_chain_root: Hash
parent_root: Hash
data_root: Hash
state_root: Hash
total_bytes: uint64
attester_bitfield: Bitvector[MAX_PERSISTENT_COMMITTEE_SIZE * 2]
```
### `ExtendedShardBlockCore`
```python
class ExtendedShardBlockCore(Container):
slot: ShardSlot
beacon_chain_root: Hash
parent_root: Hash
data: Bytes[SHARD_BLOCK_SIZE_LIMIT - SHARD_HEADER_SIZE]
state_root: Hash
total_bytes: uint64
attester_bitfield: Bitvector[MAX_PERSISTENT_COMMITTEE_SIZE * 2]
```
### `ShardState`
```python
class ShardState(Container):
history_accumulator: Vector[Hash, HISTORY_ACCUMULATOR_VECTOR]
earlier_committee_rewards: List[uint64, MAX_PERSISTENT_COMMITTEE_SIZE]
later_committee_rewards: List[uint64, MAX_PERSISTENT_COMMITTEE_SIZE]
earlier_committee_fees: List[Gwei, MAX_PERSISTENT_COMMITTEE_SIZE]
later_committee_fees: List[Gwei, MAX_PERSISTENT_COMMITTEE_SIZE]
basefee: Gwei
slot: ShardSlot
shard: Shard
most_recent_block_core: ShardBlockCore
receipt_root: Hash
total_bytes: uint64
```
### `ShardReceiptDelta`
```python
class ShardReceiptDelta(Container):
index: ValidatorIndex
reward_coefficient: uint64
block_fee: Gwei
```
## Helper functions
### `compute_slot_of_shard_slot`
```python
def compute_slot_of_shard_slot(slot: ShardSlot) -> Epoch:
return Epoch(slot // SHARD_SLOTS_PER_BEACON_SLOT)
```
### `compute_epoch_of_shard_slot`
```python
def compute_epoch_of_shard_slot(slot: ShardSlot) -> Epoch:
return Epoch(slot // SHARD_SLOTS_PER_BEACON_SLOT // SLOTS_PER_EPOCH)
```
### `get_shard_period_start_epoch`
```python
def get_shard_period_start_epoch(epoch: Epoch, lookback: int=0) -> Epoch:
return Epoch(epoch - (epoch % EPOCHS_PER_SHARD_PERIOD) - lookback * EPOCHS_PER_SHARD_PERIOD)
```
### `get_period_committee`
```python
def get_period_committee(state: BeaconState, epoch: Epoch, shard: Shard) -> Sequence[ValidatorIndex]:
"""
Return committee for a period. Used to construct persistent committees.
"""
full_committee = compute_committee(
indices=get_active_validator_indices(state, epoch),
seed=get_seed(state, epoch),
index=shard,
count=SHARD_COUNT,
)
return full_committee[:MAX_PERSISTENT_COMMITTEE_SIZE]
```
### `get_persistent_committee`
```python
def get_persistent_committee(state: BeaconState,
shard: Shard,
slot: ShardSlot) -> Sequence[ValidatorIndex]:
"""
Return the persistent committee for the given ``shard`` at the given ``slot``.
"""
epoch = compute_epoch_of_shard_slot(slot)
earlier_committee = get_period_committee(state, get_shard_period_start_epoch(epoch, lookback=2), shard)
later_committee = get_period_committee(state, get_shard_period_start_epoch(epoch, lookback=1), shard)
# Take not-yet-cycled-out validators from earlier committee and already-cycled-in validators from
# later committee; return a sorted list of the union of the two, deduplicated
return sorted(set(
[i for i in earlier_committee if epoch % EPOCHS_PER_SHARD_PERIOD < i % EPOCHS_PER_SHARD_PERIOD]
+ [i for i in later_committee if epoch % EPOCHS_PER_SHARD_PERIOD >= i % EPOCHS_PER_SHARD_PERIOD]
))
```
### `get_shard_block_proposer_index`
```python
def get_shard_block_proposer_index(state: BeaconState,
shard: Shard,
slot: ShardSlot) -> Optional[ValidatorIndex]:
# Randomly shift persistent committee
persistent_committee = list(get_persistent_committee(state, shard, slot))
current_epoch = get_current_epoch(state)
active_indices = [i for i in persistent_committee if is_active_validator(state.validators[i], current_epoch)]
if not any(active_indices):
return None
MAX_RANDOM_BYTE = 2**8 - 1
seed = hash(get_seed(state, current_epoch) + int_to_bytes(shard, length=8) + int_to_bytes(slot, length=8))
i = 0
while True:
candidate_index = active_indices[(slot + i) % len(active_indices)]
random_byte = hash(seed + int_to_bytes(i // 32, length=8))[i % 32]
effective_balance = state.validators[candidate_index].effective_balance
if effective_balance * MAX_RANDOM_BYTE >= MAX_EFFECTIVE_BALANCE * random_byte:
return ValidatorIndex(candidate_index)
i += 1
```
### `get_shard_header`
```python
def get_shard_header(block: ShardBlock) -> ShardBlockHeader:
return ShardBlockHeader(
core=ShardBlockCore(
slot=block.core.slot,
beacon_chain_root=block.core.beacon_chain_root,
parent_root=block.core.parent_root,
data_root=hash_tree_root(block.core.data),
state_root=block.core.state_root,
total_bytes=block.core.total_bytes,
attester_bitfield=block.core.attester_bitfield,
),
signatures=block.signatures,
)
```
### `pad`
```python
def pad(x: bytes, length: int) -> bytes:
assert len(x) <= length
return x + b'\x00' * (length - len(x))
```
### `flatten_shard_header`
```python
def flatten_shard_header(header: ShardBlockHeader) -> Bytes[SHARD_HEADER_SIZE]:
"""
Converts a shard block header into a flat object with the same hash tree root. Used
in the crosslink construction.
"""
committee_size = len(header.core.attester_bitfield)
attester_bits = [header.core.attester_bitfield[i] if i < committee_size else 0 for i in range(256)]
attester_bytes = bytes([sum([attester_bits[i + j] << j for j in range(8)]) for i in range(0, 256, 8)])
return (
pad(int_to_bytes(header.core.slot, length=8), 32) +
header.core.beacon_chain_root +
header.core.parent_root +
header.core.data_root +
header.core.state_root +
pad(int_to_bytes(header.core.total_bytes, length=8), 32) +
attester_bytes +
b'\x00' * 32 +
pad(header.signatures.attestation_signature, 128) +
pad(header.signatures.proposer_signature, 128)
)
```
### `compute_crosslink_data_root`
```python
def compute_crosslink_data_root(blocks: Sequence[ShardBlock]) -> Hash:
header = b''.join([flatten_shard_header(get_shard_header(block)) for block in blocks])
footer = b''.join([block.core.data for block in blocks])
MAX_SIZE = SHARD_BLOCK_SIZE_LIMIT * SHARD_SLOTS_PER_BEACON_SLOT * SLOTS_PER_EPOCH * MAX_EPOCHS_PER_CROSSLINK
return hash_tree_root(BytesN[MAX_SIZE](pad(header + footer, MAX_SIZE)))
```
### `get_default_shard_state`
```python
def get_default_shard_state(beacon_state: BeaconState, shard: Shard) -> ShardState:
earlier_committee = get_period_committee(
beacon_state,
Epoch(PHASE_1_FORK_EPOCH - EPOCHS_PER_SHARD_PERIOD * 2),
shard,
)
later_committee = get_period_committee(
beacon_state,
Epoch(PHASE_1_FORK_EPOCH - EPOCHS_PER_SHARD_PERIOD),
shard,
)
return ShardState(
basefee=1,
shard=shard,
slot=PHASE_1_FORK_SLOT,
earlier_committee_rewards=[REWARD_COEFFICIENT_BASE for _ in range(len(earlier_committee))],
later_committee_rewards=[REWARD_COEFFICIENT_BASE for _ in range(len(later_committee))],
earlier_committee_fees=[Gwei(0) for _ in range(len(earlier_committee))],
later_committee_fees=[Gwei(0) for _ in range(len(later_committee))],
)
```
## Object validity
### Shard block validation: preliminary
Accept a shard block `block` only if all of the following are correct:
* Either `block.core.parent_root == Hash()` or a block `parent` such that `hash_tree_root(parent.core) == block.core.parent_root` has already been accepted.
* `block.core.beacon_chain_root == get_block_root(head_beacon_state, compute_epoch_of_shard_slot(parent.core.slot))` where `head_beacon_state` is the current beacon chain head state. Alternatively phrased, a beacon chain block `beacon_ref` such that `signing_root(beacon_ref) == block.core.beacon_chain_root` has already been accepted and is part of the canonical chain, and no block with slot `beacon_ref.slot < slot <= compute_start_slot_of_epoch(compute_epoch_of_shard_slot(parent.core.slot))` is part of the canonical chain.
* Let `beacon_state` be the state where `beacon_ref.state_root == hash_tree_root(beacon_state)`. Let `prev_state` be the post-state of the `parent` if the `parent` exists, otherwise let it be `get_default_shard_state(beacon_state, shard)` (defined below). `block.core.state_root` must equal the `hash_tree_root` of the state after applying `shard_state_transition(prev_state, beacon_state, block)`.
Note that these acceptance conditions depend on the canonical beacon chain; when the canonical beacon chain reorganizes, the eligibility of shard blocks should be re-evaluated.
### Shard state transition function helpers
```python
def add_reward(state: ShardState, beacon_state: BeaconState, index: ValidatorIndex, delta: int) -> None:
epoch = compute_epoch_of_shard_slot(state.slot)
earlier_committee = get_period_committee(
beacon_state,
get_shard_period_start_epoch(epoch, lookback=2),
state.shard,
)
later_committee = get_period_committee(beacon_state, get_shard_period_start_epoch(epoch, lookback=1), state.shard)
if index in earlier_committee:
state.earlier_committee_rewards[earlier_committee.index(index)] += delta
elif index in later_committee:
state.later_committee_rewards[later_committee.index(index)] += delta
else:
raise Exception("Should never be here")
```
```python
def add_fee(state: ShardState, beacon_state: BeaconState, index: ValidatorIndex, delta: int) -> None:
epoch = compute_epoch_of_shard_slot(state.slot)
earlier_committee = get_period_committee(beacon_state, get_shard_period_start_epoch(epoch, lookback=2), state.shard)
later_committee = get_period_committee(beacon_state, get_shard_period_start_epoch(epoch, lookback=1), state.shard)
if index in earlier_committee:
state.earlier_committee_fees[earlier_committee.index(index)] += delta
elif index in later_committee:
state.later_committee_fees[later_committee.index(index)] += delta
else:
raise Exception("Should never be here")
```
### Shard state transition function
```python
def shard_state_transition(state: ShardState,
beacon_state: BeaconState,
block: ShardBlock,
validate_state_root: bool=False) -> None:
assert block.core.slot > state.slot
for slot in range(state.slot, block.core.slot):
shard_slot_transition(state, beacon_state)
shard_block_transition(state, beacon_state, block, validate_state_root=validate_state_root)
```
```python
def shard_slot_transition(state: ShardState, beacon_state: BeaconState) -> None:
# Correct saved state root
if state.most_recent_block_core.state_root == Hash():
state.most_recent_block_core.state_root = hash_tree_root(state)
# Save states in history accumulator
depth = 0
h = hash_tree_root(state)
while state.slot % 2**depth == 0 and depth < HISTORY_ACCUMULATOR_VECTOR:
state.history_accumulator[depth] = h
depth += 1
# Period transitions
if (state.slot + 1) % (SHARD_SLOTS_PER_BEACON_SLOT * SLOTS_PER_EPOCH * EPOCHS_PER_SHARD_PERIOD) == 0:
epoch = compute_epoch_of_shard_slot(state.slot)
earlier_committee = get_period_committee(
beacon_state,
get_shard_period_start_epoch(epoch, lookback=2),
state.shard,
)
later_committee = get_period_committee(
beacon_state,
get_shard_period_start_epoch(epoch, lookback=1),
state.shard,
)
state.receipt_root = hash_tree_root(List[ShardReceiptDelta, PLACEHOLDER]([
ShardReceiptDelta(
index=validator_index,
reward_coefficient=state.earlier_committee_rewards[i],
block_fee=state.earlier_committee_fees[i],
)
for i, validator_index in enumerate(earlier_committee)
]))
state.earlier_committee_rewards = state.later_committee_rewards
state.earlier_committee_fees = state.later_committee_fees
state.later_committee_rewards = [REWARD_COEFFICIENT_BASE for _ in range(len(later_committee))],
state.later_committee_fees = [Gwei(0) for _ in range(len(later_committee))],
else:
state.receipt_root = Hash()
state.slot += ShardSlot(1)
```
```python
def shard_block_transition(state: ShardState,
beacon_state: BeaconState,
block: ShardBlock,
validate_state_root: bool) -> None:
# Check slot number
assert block.core.slot == state.slot
# Check parent block
if block.core.parent_root != Hash():
assert block.core.parent_root == hash_tree_root(state.most_recent_block_core)
# Calculate base reward
total_balance = get_total_active_balance(beacon_state)
base_reward = (
REWARD_COEFFICIENT_BASE * BASE_REWARD_FACTOR // integer_squareroot(total_balance) // BASE_REWARDS_PER_EPOCH
)
# Check attestations
attester_committee = get_persistent_committee(beacon_state, state.shard, block.core.slot)
pubkeys = []
attestations = 0
for i, validator_index in enumerate(attester_committee):
if block.core.attester_bitfield[i]:
pubkeys.append(beacon_state.validators[validator_index].pubkey)
add_reward(state, beacon_state, validator_index, base_reward)
attestations += 1
for i in range(len(attester_committee), MAX_PERSISTENT_COMMITTEE_SIZE):
assert block.core.attester_bitfield[i] is False or block.core.attester_bitfield[i] == 0 # TODO: FIX Bitvector
assert bls_verify(
pubkey=bls_aggregate_pubkeys(pubkeys),
message_hash=block.core.parent_root,
signature=block.signatures.attestation_signature,
domain=get_domain(beacon_state, DOMAIN_SHARD_ATTESTER, compute_epoch_of_shard_slot(block.core.slot))
)
# Check proposer
proposer_index = get_shard_block_proposer_index(beacon_state, state.shard, block.core.slot)
assert proposer_index is not None
add_reward(state, beacon_state, proposer_index, attestations * base_reward // PROPOSER_REWARD_QUOTIENT)
assert bls_verify(
pubkey=beacon_state.validators[proposer_index].pubkey,
message_hash=hash_tree_root(block.core),
signature=block.signatures.proposer_signature,
domain=get_domain(beacon_state, DOMAIN_SHARD_PROPOSER, compute_epoch_of_shard_slot(block.core.slot)),
)
# Process and update block data fees
add_fee(state, beacon_state, proposer_index, state.basefee * len(block.core.data) // SHARD_BLOCK_SIZE_LIMIT)
QUOTIENT = SHARD_BLOCK_SIZE_LIMIT * BASEFEE_ADJUSTMENT_FACTOR
if len(block.core.data) > SHARD_BLOCK_SIZE_TARGET:
state.basefee += Gwei(max(1, state.basefee * (len(block.core.data) - SHARD_BLOCK_SIZE_TARGET) // QUOTIENT))
elif len(block.core.data) < SHARD_BLOCK_SIZE_TARGET:
state.basefee -= Gwei(max(1, state.basefee * (len(block.core.data) - SHARD_BLOCK_SIZE_TARGET) // QUOTIENT))
state.basefee = Gwei(max(
1,
min(
EFFECTIVE_BALANCE_INCREMENT // EPOCHS_PER_SHARD_PERIOD // SHARD_SLOTS_PER_BEACON_SLOT * SLOTS_PER_EPOCH,
state.basefee,
)
))
# Check total bytes
state.total_bytes += len(block.core.data)
assert block.core.total_bytes == state.total_bytes
# Update in-state block header
state.most_recent_block_core = ShardBlockCore(
slot=block.core.slot,
beacon_chain_root=block.core.beacon_chain_root,
parent_root=block.core.parent_root,
data_root=hash_tree_root(block.core.data),
state_root=Hash(),
total_bytes=block.core.total_bytes,
attester_bitfield=block.core.attester_bitfield,
)
# Check state root
if validate_state_root:
assert block.core.state_root == hash_tree_root(state)
```
### Beacon attestations
Let:
- `pre_state` is the `ShardState` before processing any blocks
- `shard_blocks_or_state_roots` be the `Union[ShardBlock, Hash]` list such that `shard_blocks[slot]` is the canonical `ShardBlock` for shard `pre_state.shard` at slot `slot` if a block exists, or the post-state-root of processing state up to and including that slot if a block does not exist.
- `beacon_state` be the canonical `BeaconState`
- `valid_attestations` be the set of valid `Attestation` objects, recursively defined
- `candidate` be a candidate `Attestation` which is valid under Phase 0 rules, and for which validity is to be determined under Phase 1 rules by running `is_valid_beacon_attestation`
```python
def is_valid_beacon_attestation(pre_state: ShardState,
shard_blocks_or_state_roots: Sequence[Union[ShardBlock, Hash]],
beacon_state: BeaconState,
valid_attestations: Set[Attestation],
candidate: Attestation) -> bool:
# Check if attestation is already determined valid
for attestation in valid_attestations:
if candidate == attestation:
return True
# Check previous attestation
if candidate.data.previous_crosslink.epoch <= PHASE_1_FORK_EPOCH:
assert candidate.data.previous_crosslink.data_root == Hash()
else:
previous_attestation = next(
(attestation for attestation in valid_attestations
if attestation.data.crosslink.data_root == candidate.data.previous_crosslink.data_root),
None,
)
assert previous_attestation is not None
assert candidate.data.previous_attestation.epoch < compute_epoch_of_slot(candidate.data.slot)
# Check crosslink data root
start_epoch = beacon_state.crosslinks[pre_state.shard].epoch
end_epoch = min(compute_epoch_of_slot(candidate.data.slot) - CROSSLINK_LOOKBACK,
start_epoch + MAX_EPOCHS_PER_CROSSLINK)
blocks = []
for slot in range(start_epoch * SLOTS_PER_EPOCH, end_epoch * SLOTS_PER_EPOCH):
if isinstance(shard_blocks_or_state_roots[slot], ShardBlock):
blocks.append(shard_blocks_or_state_roots[slot])
else:
blocks.append(ShardBlock(
core=ExtendedShardBlockCore(
slot=slot,
state_root=shard_blocks_or_state_roots[slot],
total_bytes=pre_state.total_bytes,
),
signatures=ShardBlockSignatures(),
))
assert candidate.data.crosslink.data_root == compute_crosslink_data_root(blocks)
return True
```
## Shard fork choice rule
The fork choice rule for any shard is LMD GHOST using the shard attestations of the persistent 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. `state.crosslinks[shard].shard_block_root`). Only blocks whose `beacon_chain_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.)