# Ethereum 2.0 Phase 1 -- Shard Data Chains **Notice**: This document is a work-in-progress for researchers and implementers. ## 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) - [Containers](#containers) - [`Crosslink`](#crosslink) - [`ShardBlock`](#shardblock) - [`ShardBlockHeader`](#shardblockheader) - [`ShardState`](#shardstate) - [`ShardAttestationData`](#shardattestationdata) - [Helper functions](#helper-functions) - [Misc](#misc-1) - [`compute_epoch_of_shard_slot`](#compute_epoch_of_shard_slot) - [`compute_shard_period_start_epoch`](#compute_shard_period_start_epoch) - [Beacon state accessors](#beacon-state-accessors) - [`get_period_committee`](#get_period_committee) - [`get_shard_committee`](#get_shard_committee) - [`get_shard_proposer_index`](#get_shard_proposer_index) - [Shard state mutators](#shard-state-mutators) - [`process_delta`](#process_delta) - [Genesis](#genesis) - [`get_genesis_shard_state`](#get_genesis_shard_state) - [`get_genesis_shard_block`](#get_genesis_shard_block) - [Shard state transition function](#shard-state-transition-function) - [Period processing](#period-processing) - [Block processing](#block-processing) - [Block header](#block-header) - [Attestations](#attestations) - [Block body](#block-body) - [Shard fork choice rule](#shard-fork-choice-rule) ## 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 | | - | - | - | | `Shard` | `uint64` | a shard number | | `ShardSlot` | `uint64` | a shard slot number | ## Configuration ### Misc | Name | Value | | - | - | | `SHARD_COUNT` | `2**10` (= 1,024) | | `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` | `0x80000000` | | `DOMAIN_SHARD_ATTESTER` | `0x81000000` | ## Containers ### `Crosslink` ```python # Crosslink is a placeholder to appease the build script until phase 1 is reworked class Crosslink(Container): shard: Shard ``` ### `ShardBlock` ```python class ShardBlock(Container): shard: Shard slot: ShardSlot beacon_block_root: Root parent_root: Root state_root: Root 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 ``` ### `ShardBlockHeader` ```python class ShardBlockHeader(Container): shard: Shard slot: ShardSlot beacon_block_root: Root parent_root: Root state_root: Root body_root: Root block_size_sum: uint64 aggregation_bits: Bitvector[2 * MAX_PERIOD_COMMITTEE_SIZE] attestations: BLSSignature signature: BLSSignature ``` ### `ShardState` ```python class ShardState(Container): shard: Shard slot: ShardSlot history_accumulator: Vector[Bytes32, 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` ```python class ShardAttestationData(Container): slot: ShardSlot parent_root: Root ``` ## Helper functions ### Misc #### `compute_epoch_of_shard_slot` ```python def compute_epoch_of_shard_slot(slot: ShardSlot) -> Epoch: return Epoch(slot // SHARD_SLOTS_PER_EPOCH) ``` #### `compute_shard_period_start_epoch` ```python 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` ```python 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` ```python 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` ```python 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` ```python 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` ```python 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` ```python 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 ```python 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 ``` ```python 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) ``` ```python 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 ```python 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 ```python 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) ``` #### Block header ```python 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 == hash_tree_root(beacon_block_header) # Verify the parent root assert block.parent_root == hash_tree_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 Verify(proposer.pubkey, compute_domain_wrapper_root(block, domain), block.signature) ``` #### Attestations ```python 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)) shard_attestation_data = ShardAttestationData(slot=shard_state.slot, parent_root=block.parent_root) message = compute_domain_wrapper_root(shard_attestation_data, domain) assert FastAggregateVerify(pubkeys, message, block.attestations) # 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 ```python 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.)