# 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 **Table of Contents** - [Introduction](#introduction) - [Custom types](#custom-types) - [Configuration](#configuration) - [Misc](#misc) - [Updated containers](#updated-containers) - [Extended `AttestationData`](#extended-attestationdata) - [Extended `Attestation`](#extended-attestation) - [Extended `PendingAttestation`](#extended-pendingattestation) - [`IndexedAttestation`](#indexedattestation) - [Extended `AttesterSlashing`](#extended-attesterslashing) - [Extended `Validator`](#extended-validator) - [Extended `BeaconBlockBody`](#extended-beaconblockbody) - [Extended `BeaconBlock`](#extended-beaconblock) - [Extended `SignedBeaconBlock`](#extended-signedbeaconblock) - [Extended `BeaconState`](#extended-beaconstate) - [New containers](#new-containers) - [`ShardBlock`](#shardblock) - [`SignedShardBlock`](#signedshardblock) - [`ShardBlockHeader`](#shardblockheader) - [`ShardState`](#shardstate) - [`ShardTransition`](#shardtransition) - [`CompactCommittee`](#compactcommittee) - [`AttestationCustodyBitWrapper`](#attestationcustodybitwrapper) - [Helper functions](#helper-functions) - [Misc](#misc-1) - [`compute_previous_slot`](#compute_previous_slot) - [`pack_compact_validator`](#pack_compact_validator) - [`unpack_compact_validator`](#unpack_compact_validator) - [`committee_to_compact_committee`](#committee_to_compact_committee) - [`compute_shard_from_committee_index`](#compute_shard_from_committee_index) - [`compute_offset_slots`](#compute_offset_slots) - [`compute_updated_gasprice`](#compute_updated_gasprice) - [Beacon state accessors](#beacon-state-accessors) - [`get_active_shard_count`](#get_active_shard_count) - [`get_online_validator_indices`](#get_online_validator_indices) - [`get_shard_committee`](#get_shard_committee) - [`get_light_client_committee`](#get_light_client_committee) - [`get_shard_proposer_index`](#get_shard_proposer_index) - [`get_indexed_attestation`](#get_indexed_attestation) - [`get_start_shard`](#get_start_shard) - [`get_shard`](#get_shard) - [`get_latest_slot_for_shard`](#get_latest_slot_for_shard) - [`get_offset_slots`](#get_offset_slots) - [Predicates](#predicates) - [`is_shard_attestation`](#is_shard_attestation) - [`is_winning_attestation`](#is_winning_attestation) - [Updated `is_valid_indexed_attestation`](#updated-is_valid_indexed_attestation) - [Block processing](#block-processing) - [Operations](#operations) - [New Attestation processing](#new-attestation-processing) - [`validate_attestation`](#validate_attestation) - [`apply_shard_transition`](#apply_shard_transition) - [`process_crosslink_for_shard`](#process_crosslink_for_shard) - [`process_crosslinks`](#process_crosslinks) - [`process_attestation`](#process_attestation) - [New Attester slashing processing](#new-attester-slashing-processing) - [Shard transition false positives](#shard-transition-false-positives) - [Light client processing](#light-client-processing) - [Epoch transition](#epoch-transition) - [Custody game updates](#custody-game-updates) - [Online-tracking](#online-tracking) - [Light client committee updates](#light-client-committee-updates) ## 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. ## Custom types We define the following Python custom types for type hinting and readability: | Name | SSZ equivalent | Description | | - | - | - | | `Shard` | `uint64` | a shard number | | `OnlineEpochs` | `uint8` | online countdown epochs | ## 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) | | `ONLINE_PERIOD` | `OnlineEpochs(2**3)` (= 8) | online epochs | ~51 min | | `LIGHT_CLIENT_COMMITTEE_SIZE` | `2**7` (= 128) | | `LIGHT_CLIENT_COMMITTEE_PERIOD` | `Epoch(2**8)` (= 256) | epochs | ~27 hours | | `SHARD_COMMITTEE_PERIOD` | `Epoch(2**8)` (= 256) | epochs | ~27 hours | | `MAX_SHARD_BLOCK_SIZE` | `2**20` (= 1,048,576) | | | `TARGET_SHARD_BLOCK_SIZE` | `2**18` (= 262,144) | | | `SHARD_BLOCK_OFFSETS` | `[1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233]` | | | `MAX_SHARD_BLOCKS_PER_ATTESTATION` | `len(SHARD_BLOCK_OFFSETS)` | | | `MAX_GASPRICE` | `Gwei(2**14)` (= 16,384) | Gwei | | | `MIN_GASPRICE` | `Gwei(2**3)` (= 8) | Gwei | | | `GASPRICE_ADJUSTMENT_COEFFICIENT` | `2**3` (= 8) | | | `DOMAIN_SHARD_PROPOSAL` | `DomainType('0x80000000')` | | | `DOMAIN_SHARD_COMMITTEE` | `DomainType('0x81000000')` | | | `DOMAIN_LIGHT_CLIENT` | `DomainType('0x82000000')` | | ## Updated containers The following containers have updated definitions in Phase 1. ### Extended `AttestationData` ```python class AttestationData(Container): slot: Slot index: CommitteeIndex # LMD GHOST vote beacon_block_root: Root # FFG vote source: Checkpoint target: Checkpoint # Current-slot shard block root head_shard_root: Root # Shard transition root shard_transition_root: Root ``` ### Extended `Attestation` ```python class Attestation(Container): aggregation_bits: Bitlist[MAX_VALIDATORS_PER_COMMITTEE] data: AttestationData custody_bits_blocks: List[Bitlist[MAX_VALIDATORS_PER_COMMITTEE], MAX_SHARD_BLOCKS_PER_ATTESTATION] signature: BLSSignature ``` ### Extended `PendingAttestation` ```python class PendingAttestation(Container): aggregation_bits: Bitlist[MAX_VALIDATORS_PER_COMMITTEE] data: AttestationData inclusion_delay: Slot proposer_index: ValidatorIndex crosslink_success: boolean ``` ### `IndexedAttestation` ```python class IndexedAttestation(Container): committee: List[ValidatorIndex, MAX_VALIDATORS_PER_COMMITTEE] attestation: Attestation ``` #### Extended `AttesterSlashing` Note that the `attestation_1` and `attestation_2` have a new `IndexedAttestation` definition. ```python class AttesterSlashing(Container): attestation_1: IndexedAttestation attestation_2: IndexedAttestation ``` ### Extended `Validator` ```python class Validator(Container): pubkey: BLSPubkey withdrawal_credentials: Bytes32 # 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 ``` ### Extended `BeaconBlockBody` ```python class BeaconBlockBody(Container): 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[SignedVoluntaryExit, MAX_VOLUNTARY_EXITS] # Custody game custody_slashings: List[SignedCustodySlashing, MAX_CUSTODY_SLASHINGS] 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: Bitvector[LIGHT_CLIENT_COMMITTEE_SIZE] light_client_signature: BLSSignature ``` ### Extended `BeaconBlock` Note that the `body` has a new `BeaconBlockBody` definition. ```python class BeaconBlock(Container): slot: Slot proposer_index: ValidatorIndex parent_root: Root state_root: Root body: BeaconBlockBody ``` #### Extended `SignedBeaconBlock` Note that the `message` has a new `BeaconBlock` definition. ```python class SignedBeaconBlock(Container): message: BeaconBlock signature: BLSSignature ``` ### Extended `BeaconState` Note that aside from the new additions, `Validator` and `PendingAttestation` have new definitions. ```python class BeaconState(Container): # Versioning genesis_time: uint64 genesis_validators_root: Root slot: Slot fork: Fork # History latest_block_header: BeaconBlockHeader block_roots: Vector[Root, SLOTS_PER_HISTORICAL_ROOT] state_roots: Vector[Root, SLOTS_PER_HISTORICAL_ROOT] historical_roots: List[Root, HISTORICAL_ROOTS_LIMIT] # Eth1 eth1_data: Eth1Data eth1_data_votes: List[Eth1Data, EPOCHS_PER_ETH1_VOTING_PERIOD * SLOTS_PER_EPOCH] eth1_deposit_index: uint64 # Registry validators: List[Validator, VALIDATOR_REGISTRY_LIMIT] balances: List[Gwei, VALIDATOR_REGISTRY_LIMIT] # Randomness randao_mixes: Vector[Root, 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: List[OnlineEpochs, VALIDATOR_REGISTRY_LIMIT] # not a raw byte array, considered its large size. current_light_committee: CompactCommittee next_light_committee: CompactCommittee # Custody game # 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, MAX_EARLY_DERIVED_SECRET_REVEALS * SLOTS_PER_EPOCH], EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS] ``` ## New containers The following containers are new in Phase 1. ### `ShardBlock` ```python class ShardBlock(Container): shard_parent_root: Root beacon_parent_root: Root slot: Slot proposer_index: ValidatorIndex body: ByteList[MAX_SHARD_BLOCK_SIZE] ``` ### `SignedShardBlock` ```python class SignedShardBlock(Container): message: ShardBlock signature: BLSSignature ``` ### `ShardBlockHeader` ```python class ShardBlockHeader(Container): shard_parent_root: Root beacon_parent_root: Root slot: Slot proposer_index: ValidatorIndex body_root: Root ``` ### `ShardState` ```python class ShardState(Container): slot: Slot gasprice: Gwei transition_digest: Bytes32 latest_block_root: Root ``` ### `ShardTransition` ```python 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[Bytes32, MAX_SHARD_BLOCKS_PER_ATTESTATION] # Intermediate shard states shard_states: List[ShardState, MAX_SHARD_BLOCKS_PER_ATTESTATION] # Proposer signature aggregate proposer_signature_aggregate: BLSSignature ``` ### `CompactCommittee` ```python class CompactCommittee(Container): pubkeys: List[BLSPubkey, MAX_VALIDATORS_PER_COMMITTEE] compact_validators: List[uint64, MAX_VALIDATORS_PER_COMMITTEE] ``` ### `AttestationCustodyBitWrapper` ```python class AttestationCustodyBitWrapper(Container): attestation_data_root: Root block_index: uint64 bit: boolean ``` ## Helper functions ### Misc #### `compute_previous_slot` ```python def compute_previous_slot(slot: Slot) -> Slot: if slot > 0: return Slot(slot - 1) else: return Slot(0) ``` #### `pack_compact_validator` ```python def pack_compact_validator(index: ValidatorIndex, slashed: bool, balance_in_increments: uint64) -> uint64: """ Create 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 ``` #### `unpack_compact_validator` ```python def unpack_compact_validator(compact_validator: uint64) -> Tuple[ValidatorIndex, bool, uint64]: """ Return validator index, slashed, balance // EFFECTIVE_BALANCE_INCREMENT """ return ( ValidatorIndex(compact_validator >> 16), bool((compact_validator >> 15) % 2), compact_validator & (2**15 - 1), ) ``` #### `committee_to_compact_committee` ```python 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) ``` #### `compute_shard_from_committee_index` ```python def compute_shard_from_committee_index(state: BeaconState, index: CommitteeIndex, slot: Slot) -> Shard: active_shards = get_active_shard_count(state) return Shard((index + get_start_shard(state, slot)) % active_shards) ``` #### `compute_offset_slots` ```python def compute_offset_slots(start_slot: Slot, end_slot: Slot) -> Sequence[Slot]: """ Return the offset slots that are greater than ``start_slot`` and less than ``end_slot``. """ return [Slot(start_slot + x) for x in SHARD_BLOCK_OFFSETS if start_slot + x < end_slot] ``` #### `compute_updated_gasprice` ```python def compute_updated_gasprice(prev_gasprice: Gwei, length: uint8) -> Gwei: if length > TARGET_SHARD_BLOCK_SIZE: delta = (prev_gasprice * (length - TARGET_SHARD_BLOCK_SIZE) // TARGET_SHARD_BLOCK_SIZE // GASPRICE_ADJUSTMENT_COEFFICIENT) return min(prev_gasprice + delta, MAX_GASPRICE) else: delta = (prev_gasprice * (TARGET_SHARD_BLOCK_SIZE - length) // TARGET_SHARD_BLOCK_SIZE // GASPRICE_ADJUSTMENT_COEFFICIENT) return max(prev_gasprice, MIN_GASPRICE + delta) - delta ``` ### Beacon state accessors #### `get_active_shard_count` ```python def get_active_shard_count(state: BeaconState) -> uint64: return len(state.shard_states) # May adapt in the future, or change over time. ``` #### `get_online_validator_indices` ```python 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` ```python 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) active_shard_count = get_active_shard_count(beacon_state) return compute_committee( indices=active_validator_indices, seed=seed, index=shard, count=active_shard_count, ) ``` #### `get_light_client_committee` ```python 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_LIGHT_CLIENT) return compute_committee( indices=active_validator_indices, seed=seed, index=0, count=get_active_shard_count(beacon_state), )[:TARGET_COMMITTEE_SIZE] ``` #### `get_shard_proposer_index` ```python def get_shard_proposer_index(beacon_state: BeaconState, slot: Slot, shard: Shard) -> ValidatorIndex: committee = get_shard_committee(beacon_state, compute_epoch_at_slot(slot), shard) r = bytes_to_int(get_seed(beacon_state, get_current_epoch(beacon_state), DOMAIN_SHARD_COMMITTEE)[:8]) return committee[r % len(committee)] ``` #### `get_indexed_attestation` ```python def get_indexed_attestation(beacon_state: BeaconState, attestation: Attestation) -> IndexedAttestation: committee = get_beacon_committee(beacon_state, attestation.data.slot, attestation.data.index) return IndexedAttestation( committee=committee, attestation=attestation, ) ``` #### `get_start_shard` ```python def get_start_shard(state: BeaconState, slot: Slot) -> Shard: # TODO: implement start shard logic return Shard(0) ``` #### `get_shard` ```python def get_shard(state: BeaconState, attestation: Attestation) -> Shard: return compute_shard_from_committee_index(state, attestation.data.index, attestation.data.slot) ``` #### `get_latest_slot_for_shard` ```python def get_latest_slot_for_shard(state: BeaconState, shard: Shard) -> Slot: return state.shard_states[shard].slot ``` #### `get_offset_slots` ```python def get_offset_slots(state: BeaconState, shard: Shard) -> Sequence[Slot]: return compute_offset_slots(state.shard_states[shard].slot, state.slot) ``` ### Predicates #### `is_shard_attestation` ```python def is_shard_attestation(state: BeaconState, attestation: Attestation, committee_index: CommitteeIndex) -> bool: if not ( attestation.data.index == committee_index and attestation.data.slot + MIN_ATTESTATION_INCLUSION_DELAY == state.slot ): return False return True ``` #### `is_winning_attestation` ```python def is_winning_attestation(state: BeaconState, attestation: PendingAttestation, committee_index: CommitteeIndex, winning_root: Root) -> bool: """ Check if ``attestation`` helped contribute to the successful crosslink of ``winning_root`` formed by ``committee_index`` committee at the current slot. """ return ( attestation.data.slot == state.slot and attestation.data.index == committee_index and attestation.data.shard_transition_root == winning_root ) ``` #### Updated `is_valid_indexed_attestation` Note that this replaces the Phase 0 `is_valid_indexed_attestation`. ```python def is_valid_indexed_attestation(state: BeaconState, indexed_attestation: IndexedAttestation) -> bool: """ Check if ``indexed_attestation`` has valid indices and signature. """ # Verify aggregate signature all_pubkeys = [] all_signing_roots = [] attestation = indexed_attestation.attestation domain = get_domain(state, DOMAIN_BEACON_ATTESTER, attestation.data.target.epoch) aggregation_bits = attestation.aggregation_bits assert len(aggregation_bits) == len(indexed_attestation.committee) if len(attestation.custody_bits_blocks) == 0: # fall back on phase0 behavior if there is no shard data. for participant, abit in zip(indexed_attestation.committee, aggregation_bits): if abit: all_pubkeys.append(state.validators[participant].pubkey) signing_root = compute_signing_root(indexed_attestation.attestation.data, domain) return bls.FastAggregateVerify(all_pubkeys, signing_root, signature=attestation.signature) else: for i, custody_bits in enumerate(attestation.custody_bits_blocks): 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 attestation_wrapper = AttestationCustodyBitWrapper( attestation_data_root=hash_tree_root(attestation.data), block_index=i, bit=cbit ) all_signing_roots.append(compute_signing_root(attestation_wrapper, domain)) else: assert not cbit return bls.AggregateVerify(zip(all_pubkeys, all_signing_roots), signature=attestation.signature) ``` ### Block processing ```python def process_block(state: BeaconState, block: BeaconBlock) -> None: process_block_header(state, block) process_randao(state, block.body) process_eth1_data(state, block.body) process_light_client_signatures(state, block.body) process_operations(state, block.body) verify_shard_transition_false_positives(state, block.body) ``` #### Operations ```python 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: Sequence[Any], fn: Callable[[BeaconState, Any], None]) -> None: 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 for_ops(body.attestations, process_attestation) for_ops(body.deposits, process_deposit) for_ops(body.voluntary_exits, process_voluntary_exit) # See custody game spec. process_custody_game_operations(state, body) process_crosslinks(state, body.shard_transitions, body.attestations) # TODO process_operations(body.shard_receipt_proofs, process_shard_receipt_proofs) ``` ##### New Attestation processing ###### `validate_attestation` ```python def validate_attestation(state: BeaconState, attestation: Attestation) -> None: data = attestation.data assert data.index < get_committee_count_at_slot(state, data.slot) assert data.index < get_active_shard_count(state) assert data.target.epoch in (get_previous_epoch(state), get_current_epoch(state)) assert data.target.epoch == compute_epoch_at_slot(data.slot) assert data.slot + MIN_ATTESTATION_INCLUSION_DELAY <= state.slot <= data.slot + SLOTS_PER_EPOCH committee = get_beacon_committee(state, data.slot, data.index) assert len(attestation.aggregation_bits) == len(committee) if attestation.data.target.epoch == get_current_epoch(state): assert attestation.data.source == state.current_justified_checkpoint else: assert attestation.data.source == state.previous_justified_checkpoint shard = get_shard(state, attestation) # Type 1: on-time attestations, the custody bits should be non-empty. if attestation.custody_bits_blocks != []: # Ensure on-time attestation assert data.slot + MIN_ATTESTATION_INCLUSION_DELAY == state.slot # Correct data root count assert len(attestation.custody_bits_blocks) == len(get_offset_slots(state, shard)) # Correct parent block root assert data.beacon_block_root == get_block_root_at_slot(state, compute_previous_slot(state.slot)) # Type 2: no shard transition, no custody bits else: # Ensure delayed attestation assert data.slot + MIN_ATTESTATION_INCLUSION_DELAY < state.slot # Late attestations cannot have a shard transition root assert data.shard_transition_root == Root() # Signature check assert is_valid_indexed_attestation(state, get_indexed_attestation(state, attestation)) ``` ###### `apply_shard_transition` ```python def apply_shard_transition(state: BeaconState, shard: Shard, transition: ShardTransition) -> None: # TODO: only need to check it once when phase 1 starts assert state.slot > PHASE_1_GENESIS_SLOT # Correct data root count offset_slots = get_offset_slots(state, shard) assert ( len(transition.shard_data_roots) == len(transition.shard_states) == len(transition.shard_block_lengths) == len(offset_slots) ) assert transition.start_slot == offset_slots[0] headers = [] proposers = [] prev_gasprice = state.shard_states[shard].gasprice shard_parent_root = state.shard_states[shard].latest_block_root for i in range(len(offset_slots)): shard_block_length = transition.shard_block_lengths[i] is_empty_proposal = shard_block_length == 0 shard_state = transition.shard_states[i] if not is_empty_proposal: proposal_index = get_shard_proposer_index(state, offset_slots[i], shard) # Reconstruct shard headers header = ShardBlockHeader( shard_parent_root=shard_parent_root, beacon_parent_root=get_block_root_at_slot(state, offset_slots[i]), proposer_index=proposal_index, slot=offset_slots[i], body_root=transition.shard_data_roots[i] ) shard_parent_root = hash_tree_root(header) headers.append(header) proposers.append(proposal_index) # Verify correct calculation of gas prices and slots assert shard_state.gasprice == compute_updated_gasprice(prev_gasprice, shard_block_length) assert shard_state.slot == offset_slots[i] prev_gasprice = shard_state.gasprice pubkeys = [state.validators[proposer].pubkey for proposer in proposers] signing_roots = [ compute_signing_root(header, get_domain(state, DOMAIN_SHARD_PROPOSAL, compute_epoch_at_slot(header.slot))) for header in headers ] # Verify combined proposer signature assert bls.AggregateVerify(zip(pubkeys, signing_roots), signature=transition.proposer_signature_aggregate) # Save updated state state.shard_states[shard] = transition.shard_states[len(transition.shard_states) - 1] state.shard_states[shard].slot = state.slot - 1 ``` ###### `process_crosslink_for_shard` ```python def process_crosslink_for_shard(state: BeaconState, committee_index: CommitteeIndex, shard_transition: ShardTransition, attestations: Sequence[Attestation]) -> Root: committee = get_beacon_committee(state, state.slot, committee_index) online_indices = get_online_validator_indices(state) shard = compute_shard_from_committee_index(state, committee_index, state.slot) # Loop over all shard transition roots shard_transition_roots = set([a.data.shard_transition_root for a in attestations]) for shard_transition_root in sorted(shard_transition_roots): transition_attestations = [a for a in attestations if a.data.shard_transition_root == shard_transition_root] transition_participants: Set[ValidatorIndex] = set() for attestation in transition_attestations: participants = get_attesting_indices(state, attestation.data, attestation.aggregation_bits) transition_participants = transition_participants.union(participants) assert attestation.data.head_shard_root == shard_transition.shard_data_roots[ len(shard_transition.shard_data_roots) - 1 ] enough_online_stake = ( get_total_balance(state, online_indices.intersection(transition_participants)) * 3 >= get_total_balance(state, online_indices.intersection(committee)) * 2 ) # If not enough stake, try next transition root if not enough_online_stake: continue # Attestation <-> shard transition consistency assert shard_transition_root == hash_tree_root(shard_transition) # Apply transition apply_shard_transition(state, shard, shard_transition) # Apply proposer reward and cost beacon_proposer_index = get_beacon_proposer_index(state) estimated_attester_reward = sum([get_base_reward(state, attester) for attester in transition_participants]) proposer_reward = Gwei(estimated_attester_reward // PROPOSER_REWARD_QUOTIENT) increase_balance(state, beacon_proposer_index, proposer_reward) states_slots_lengths = zip( shard_transition.shard_states, get_offset_slots(state, shard), shard_transition.shard_block_lengths ) for shard_state, slot, length in states_slots_lengths: proposer_index = get_shard_proposer_index(state, slot, shard) decrease_balance(state, proposer_index, shard_state.gasprice * length) # Return winning transition root return shard_transition_root # No winning transition root, ensure empty and return empty root assert shard_transition == ShardTransition() return Root() ``` ###### `process_crosslinks` ```python def process_crosslinks(state: BeaconState, shard_transitions: Sequence[ShardTransition], attestations: Sequence[Attestation]) -> None: committee_count = get_committee_count_at_slot(state, state.slot) for committee_index in map(CommitteeIndex, range(committee_count)): shard = compute_shard_from_committee_index(state, committee_index, state.slot) # All attestations in the block for this committee/shard and current slot shard_transition = shard_transitions[shard] shard_attestations = [ attestation for attestation in attestations if is_shard_attestation(state, attestation, committee_index) ] winning_root = process_crosslink_for_shard(state, committee_index, shard_transition, shard_attestations) if winning_root != Root(): # Mark relevant pending attestations as creating a successful crosslink for pending_attestation in state.current_epoch_attestations: if is_winning_attestation(state, pending_attestation, committee_index, winning_root): pending_attestation.crosslink_success = True ``` ###### `process_attestation` ```python def process_attestation(state: BeaconState, attestation: Attestation) -> None: validate_attestation(state, attestation) # Store pending attestation for epoch processing pending_attestation = PendingAttestation( aggregation_bits=attestation.aggregation_bits, data=attestation.data, inclusion_delay=state.slot - attestation.data.slot, proposer_index=get_beacon_proposer_index(state), crosslink_success=False, # To be filled in during process_crosslinks ) if attestation.data.target.epoch == get_current_epoch(state): state.current_epoch_attestations.append(pending_attestation) else: state.previous_epoch_attestations.append(pending_attestation) ``` ##### New Attester slashing processing ```python def get_indices_from_committee( committee: List[ValidatorIndex, MAX_VALIDATORS_PER_COMMITTEE], bits: Bitlist[MAX_VALIDATORS_PER_COMMITTEE]) -> List[ValidatorIndex, MAX_VALIDATORS_PER_COMMITTEE]: assert len(bits) == len(committee) return List[ValidatorIndex, MAX_VALIDATORS_PER_COMMITTEE]( [validator_index for i, validator_index in enumerate(committee) if bits[i]] ) ``` ```python def process_attester_slashing(state: BeaconState, attester_slashing: AttesterSlashing) -> None: indexed_attestation_1 = attester_slashing.attestation_1 indexed_attestation_2 = attester_slashing.attestation_2 assert is_slashable_attestation_data( indexed_attestation_1.attestation.data, indexed_attestation_2.attestation.data, ) assert is_valid_indexed_attestation(state, indexed_attestation_1) assert is_valid_indexed_attestation(state, indexed_attestation_2) indices_1 = get_indices_from_committee( indexed_attestation_1.committee, indexed_attestation_1.attestation.aggregation_bits, ) indices_2 = get_indices_from_committee( indexed_attestation_2.committee, indexed_attestation_2.attestation.aggregation_bits, ) slashed_any = False indices = set(indices_1).intersection(indices_2) for index in sorted(indices): if is_slashable_validator(state.validators[index], get_current_epoch(state)): slash_validator(state, index) slashed_any = True assert slashed_any ``` #### Shard transition false positives ```python 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(get_active_shard_count(state)): if state.shard_states[shard].slot != state.slot - 1: assert block_body.shard_transitions[shard] == ShardTransition() ``` #### Light client processing ```python def process_light_client_signatures(state: BeaconState, block_body: BeaconBlockBody) -> None: committee = get_light_client_committee(state, get_current_epoch(state)) total_reward = Gwei(0) signer_pubkeys = [] for bit_index, participant_index in enumerate(committee): if block_body.light_client_signature_bitfield[bit_index]: signer_pubkeys.append(state.validators[participant_index].pubkey) increase_balance(state, participant_index, get_base_reward(state, participant_index)) total_reward += get_base_reward(state, participant_index) increase_balance(state, get_beacon_proposer_index(state), Gwei(total_reward // PROPOSER_REWARD_QUOTIENT)) slot = compute_previous_slot(state.slot) signing_root = compute_signing_root(get_block_root_at_slot(state, slot), get_domain(state, DOMAIN_LIGHT_CLIENT, compute_epoch_at_slot(slot))) if len(signer_pubkeys) == 0: # TODO: Or disallow empty light_client_signature? return else: assert bls.FastAggregateVerify(signer_pubkeys, signing_root, signature=block_body.light_client_signature) ``` ### Epoch transition This epoch transition overrides the phase0 epoch transition: ```python 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](./1_custody-game.md), #### Online-tracking ```python 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 ```python 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) ```