# Ethereum 2.0 Phase 1 -- Shard Data Chains **Notice**: This document is a work-in-progress for researchers and implementers. ## Table of contents - [Ethereum 2.0 Phase 1 -- Shard Data Chains](#ethereum-20-phase-1----shard-data-chains) - [Table of contents](#table-of-contents) - [Introduction](#introduction) - [Constants](#constants) - [Misc](#misc) - [Time parameters](#time-parameters) - [Signature domains](#signature-domains) - [Data structures](#data-structures) - [`ShardBlockBody`](#shardblockbody) - [`ShardBlock`](#shardblock) - [`ShardBlockHeader`](#shardblockheader) - [`ShardAttestation`](#shardattestation) - [Helper functions](#helper-functions) - [`get_period_committee`](#get_period_committee) - [`get_switchover_epoch`](#get_switchover_epoch) - [`get_persistent_committee`](#get_persistent_committee) - [`get_shard_proposer_index`](#get_shard_proposer_index) - [`get_shard_header`](#get_shard_header) - [`verify_shard_attestation_signature`](#verify_shard_attestation_signature) - [`compute_crosslink_data_root`](#compute_crosslink_data_root) - [Object validity](#object-validity) - [Shard blocks](#shard-blocks) - [Shard attestations](#shard-attestations) - [Beacon attestations](#beacon-attestations) - [Shard fork choice rule](#shard-fork-choice-rule) ## Introduction This document describes the shard data layer and the shard fork choice rule in Phase 1 of Ethereum 2.0. ## Constants ### Misc | Name | Value | | - | - | | `BYTES_PER_SHARD_BLOCK_BODY` | `2**14` (= 16,384) | | `MAX_SHARD_ATTESTIONS` | `2**4` (= 16) | | `PHASE_1_GENESIS_EPOCH` | **TBD** | | `PHASE_1_GENESIS_SLOT` | get_epoch_start_slot(PHASE_1_GENESIS_EPOCH) | ### Time parameters | Name | Value | Unit | Duration | | - | - | :-: | :-: | | `CROSSLINK_LOOKBACK` | `2**0` (= 1) | epochs | 6.2 minutes | | `PERSISTENT_COMMITTEE_PERIOD` | `2**11` (= 2,048) | epochs | ~9 days | ### Signature domains | Name | Value | | - | - | | `DOMAIN_SHARD_PROPOSER` | `128` | | `DOMAIN_SHARD_ATTESTER` | `129` | ## Data structures ### `ShardBlockBody` ```python ['byte', BYTES_PER_SHARD_BLOCK_BODY] ``` ### `ShardBlock` ```python { 'slot': Slot, 'shard': Shard, 'beacon_chain_root': Hash, 'parent_block_root': Hash, 'data': ShardBlockBody, 'state_root': Hash, 'attestations': [ShardAttestation], 'signature': BLSSignature, } ``` ### `ShardBlockHeader` ```python { 'slot': Slot, 'shard': Shard, 'beacon_chain_root': Hash, 'parent_block_root': Hash, 'body_root': Hash, 'state_root': Hash, 'attestations': [ShardAttestation], 'signature': BLSSignature, } ``` ### `ShardAttestation` ```python { 'data': { 'slot': Slot, 'shard': Shard, 'shard_block_root': Hash, }, 'aggregation_bitfield': Bitfield, 'aggregate_signature': BLSSignature, } ``` ## Helper functions ### `get_period_committee` ```python def get_period_committee(state: BeaconState, epoch: Epoch, shard: Shard, index: int, count: int) -> List[ValidatorIndex]: """ Return committee for a period. Used to construct persistent committees. """ return compute_committee( indices=get_active_validator_indices(state, epoch), seed=generate_seed(state, epoch), index=shard * count + index, count=SHARD_COUNT * count, ) ``` ### `get_switchover_epoch` ```python def get_switchover_epoch(state: BeaconState, epoch: Epoch, index: ValidatorIndex): earlier_start_epoch = epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD * 2 return bytes_to_int(hash(generate_seed(state, earlier_start_epoch) + bytes3(index))[0:8]) % PERSISTENT_COMMITTEE_PERIOD ``` ### `get_persistent_committee` ```python def get_persistent_committee(state: BeaconState, shard: Shard, slot: Slot) -> List[ValidatorIndex]: """ Return the persistent committee for the given ``shard`` at the given ``slot``. """ epoch = slot_to_epoch(slot) earlier_start_epoch = epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD * 2 later_start_epoch = epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD committee_count = max( len(get_active_validator_indices(state.validator_registry, earlier_start_epoch)) // (SHARD_COUNT * TARGET_COMMITTEE_SIZE), len(get_active_validator_indices(state.validator_registry, later_start_epoch)) // (SHARD_COUNT * TARGET_COMMITTEE_SIZE), ) + 1 index = slot % committee_count earlier_committee = get_period_committee(state, shard, earlier_start_epoch, index, committee_count) later_committee = get_period_committee(state, shard, later_start_epoch, index, committee_count) # 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(list(set( [i for i in earlier_committee if epoch % PERSISTENT_COMMITTEE_PERIOD < get_switchover_epoch(state, epoch, i)] + [i for i in later_committee if epoch % PERSISTENT_COMMITTEE_PERIOD >= get_switchover_epoch(state, epoch, i)] ))) ``` ### `get_shard_proposer_index` ```python def get_shard_proposer_index(state: BeaconState, shard: Shard, slot: Slot) -> ValidatorIndex: # Randomly shift persistent committee persistent_committee = get_persistent_committee(state, shard, slot) seed = hash(state.current_shuffling_seed + int_to_bytes8(shard) + int_to_bytes8(slot)) random_index = bytes_to_int(seed[0:8]) % len(persistent_committee) persistent_committee = persistent_committee[random_index:] + persistent_committee[:random_index] # Search for an active proposer for index in persistent_committee: if is_active_validator(state.validator_registry[index], get_current_epoch(state)): return index # No block can be proposed if no validator is active return None ``` ### `get_shard_header` ```python def get_shard_header(block: ShardBlock) -> ShardBlockHeader: return ShardBlockHeader( slot: block.slot, shard: block.shard, beacon_chain_root: block.beacon_chain_root, parent_block_root: block.parent_block_root, body_root: hash_tree_root(block.body), state_root: block.state_root, attestations: block.attestations, signature: block.signature, ) ``` ### `verify_shard_attestation_signature` ```python def verify_shard_attestation_signature(state: BeaconState, attestation: ShardAttestation) -> None: data = attestation.data persistent_committee = get_persistent_committee(state, data.crosslink.shard, data.slot) assert verify_bitfield(attestation.aggregation_bitfield, len(persistent_committee)) pubkeys = [] for i, index in enumerate(persistent_committee): if get_bitfield_bit(attestation.aggregation_bitfield, i) == 0b1 validator = state.validator_registry[index] assert is_active_validator(validator, get_current_epoch(state)) pubkeys.append(validator.pubkey) assert bls_verify( pubkey=bls_aggregate_pubkeys(pubkeys), message_hash=data.crosslink.shard_block_root, signature=attestation.aggregate_signature, domain=get_domain(state, slot_to_epoch(data.slot), DOMAIN_SHARD_ATTESTER) ) ``` ### `compute_crosslink_data_root` ```python def compute_crosslink_data_root(blocks: List[ShardBlock]) -> Hash: def is_power_of_two(value: int) -> bool: return (value > 0) and (value & (value - 1) == 0) def pad_to_power_of_2(values: List[bytes]) -> List[bytes]: while not is_power_of_two(len(values)): values += [b'\x00' * BYTES_PER_SHARD_BLOCK_BODY] return values def merkle_root_of_bytes(data: bytes) -> bytes: return merkle_root([data[i:i + 32] for i in range(0, len(data), 32)]) return hash( merkle_root(pad_to_power_of_2([ merkle_root_of_bytes(zpad(serialize(get_shard_header(block)), BYTES_PER_SHARD_BLOCK_BODY)) for block in blocks ])) + merkle_root(pad_to_power_of_2([ merkle_root_of_bytes(block.body) for block in blocks ])) ) ``` ## Object validity ### Shard blocks Let: * `beacon_blocks` be the `BeaconBlock` list such that `beacon_blocks[slot]` is the canonical `BeaconBlock` at slot `slot` * `beacon_state` be the canonical `BeaconState` after processing `beacon_blocks[-1]` * `valid_shard_blocks` be the list of valid `ShardBlock`, recursively defined * `unix_time` be the current unix time * `candidate` be a candidate `ShardBlock` for which validity is to be determined by running `is_valid_shard_block` ```python def is_valid_shard_block(beacon_blocks: List[BeaconBlock], beacon_state: BeaconState, valid_shard_blocks: List[ShardBlock], unix_time: uint64, candidate: ShardBlock) -> bool # Check if block is already determined valid for _, block in enumerate(valid_shard_blocks): if candidate == block: return True # Check slot number assert block.slot >= PHASE_1_GENESIS_SLOT assert unix_time >= beacon_state.genesis_time + (block.slot - GENESIS_SLOT) * SECONDS_PER_SLOT # Check shard number assert block.shard <= SHARD_COUNT # Check beacon block beacon_block = beacon_blocks[block.slot] assert block.beacon_block_root == signing_root(beacon_block) assert beacon_block.slot <= block.slot: # Check state root assert block.state_root == ZERO_HASH # [to be removed in phase 2] # Check parent block if block.slot == PHASE_1_GENESIS_SLOT: assert candidate.parent_block_root == ZERO_HASH else: parent_block = next( block for block in valid_shard_blocks if signing_root(block) == candidate.parent_block_root , None) assert parent_block != None assert parent_block.shard == block.shard assert parent_block.slot < block.slot assert signing_root(beacon_blocks[parent_block.slot]) == parent_block.beacon_chain_root # Check attestations assert len(block.attestations) <= MAX_SHARD_ATTESTIONS for _, attestation in enumerate(block.attestations): assert max(GENESIS_SHARD_SLOT, block.slot - SLOTS_PER_EPOCH) <= attestation.data.slot assert attestation.data.slot <= block.slot - MIN_ATTESTATION_INCLUSION_DELAY assert attestation.data.crosslink.shard == block.shard verify_shard_attestation_signature(beacon_state, attestation) # Check signature proposer_index = get_shard_proposer_index(beacon_state, block.shard, block.slot) assert proposer_index is not None assert bls_verify( pubkey=validators[proposer_index].pubkey, message_hash=signing_root(block), signature=block.signature, domain=get_domain(beacon_state, slot_to_epoch(block.slot), DOMAIN_SHARD_PROPOSER) ) return True ``` ### Shard attestations Let: * `valid_shard_blocks` be the list of valid `ShardBlock` * `beacon_state` be the canonical `BeaconState` * `candidate` be a candidate `ShardAttestation` for which validity is to be determined by running `is_valid_shard_attestation` ```python def is_valid_shard_attestation(valid_shard_blocks: List[ShardBlock], beacon_state: BeaconState, candidate: Attestation) -> bool: # Check shard block shard_block = next( block for block in valid_shard_blocks if signing_root(block) == candidate.attestation.data.crosslink.shard_block_root , None) assert shard_block != None assert shard_block.slot == attestation.data.slot assert shard_block.shard == attestation.data.crosslink.shard # Check signature verify_shard_attestation_signature(beacon_state, attestation) return True ``` ### Beacon attestations Let: * `shard` be a valid `Shard` * `shard_blocks` be the `ShardBlock` list such that `shard_blocks[slot]` is the canonical `ShardBlock` for shard `shard` at slot `slot` * `beacon_state` be the canonical `BeaconState` * `valid_attestations` be the list of valid `Attestation`, 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(shard: Shard, shard_blocks: List[ShardBlock], beacon_state: BeaconState, valid_attestations: List[Attestation], candidate: Attestation) -> bool: # Check if attestation is already determined valid for _, attestation in enumerate(valid_attestations): if candidate == attestation: return True # Check previous attestation if candidate.data.previous_crosslink.epoch <= PHASE_1_GENESIS_EPOCH: assert candidate.data.previous_crosslink.data_root == ZERO_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 != None assert candidate.data.previous_attestation.epoch < slot_to_epoch(candidate.data.slot) # Check crosslink data root start_epoch = state.latest_crosslinks[shard].epoch end_epoch = min(slot_to_epoch(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): blocks.append(shard_blocks[slot]) 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.)