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Bellatrix -- The Beacon Chain

Table of contents

Introduction

This upgrade adds transaction execution to the beacon chain as part of Bellatrix upgrade.

Additionally, this upgrade introduces the following minor changes: * Penalty parameter updates to their planned maximally punitive values

Custom types

Note: The Transaction type is a stub which is not final.

Name SSZ equivalent Description
Transaction ByteList[MAX_BYTES_PER_TRANSACTION] either a typed transaction envelope or a legacy transaction
ExecutionAddress Bytes20 Address of account on the execution layer

Preset

Execution

Name Value
MAX_BYTES_PER_TRANSACTION uint64(2**30) (= 1,073,741,824)
MAX_TRANSACTIONS_PER_PAYLOAD uint64(2**20) (= 1,048,576)
BYTES_PER_LOGS_BLOOM uint64(2**8) (= 256)
MAX_EXTRA_DATA_BYTES 2**5 (= 32)

Updated penalty values

Bellatrix updates a few configuration values to move penalty parameters to their final, maximum security values.

Note: The spec does not override previous configuration values but instead creates new values and replaces usage throughout.

Name Value
INACTIVITY_PENALTY_QUOTIENT_BELLATRIX uint64(2**24) (= 16,777,216)
MIN_SLASHING_PENALTY_QUOTIENT_BELLATRIX uint64(2**5) (= 32)
PROPORTIONAL_SLASHING_MULTIPLIER_BELLATRIX uint64(3)

Configuration

Transition settings

Name Value
TERMINAL_TOTAL_DIFFICULTY 58750000000000000000000 (Estimated: Sept 15, 2022)
TERMINAL_BLOCK_HASH Hash32()
TERMINAL_BLOCK_HASH_ACTIVATION_EPOCH FAR_FUTURE_EPOCH

Containers

Extended containers

BeaconBlockBody

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class BeaconBlockBody(Container):
    randao_reveal: BLSSignature
    eth1_data: Eth1Data  # Eth1 data vote
    graffiti: Bytes32  # Arbitrary data
    # Operations
    proposer_slashings: List[ProposerSlashing, MAX_PROPOSER_SLASHINGS]
    attester_slashings: List[AttesterSlashing, MAX_ATTESTER_SLASHINGS]
    attestations: List[Attestation, MAX_ATTESTATIONS]
    deposits: List[Deposit, MAX_DEPOSITS]
    voluntary_exits: List[SignedVoluntaryExit, MAX_VOLUNTARY_EXITS]
    sync_aggregate: SyncAggregate
    # Execution
    execution_payload: ExecutionPayload  # [New in Bellatrix]

BeaconState

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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[Bytes32, EPOCHS_PER_HISTORICAL_VECTOR]
    # Slashings
    slashings: Vector[Gwei, EPOCHS_PER_SLASHINGS_VECTOR]  # Per-epoch sums of slashed effective balances
    # Participation
    previous_epoch_participation: List[ParticipationFlags, VALIDATOR_REGISTRY_LIMIT]
    current_epoch_participation: List[ParticipationFlags, VALIDATOR_REGISTRY_LIMIT]
    # Finality
    justification_bits: Bitvector[JUSTIFICATION_BITS_LENGTH]  # Bit set for every recent justified epoch
    previous_justified_checkpoint: Checkpoint
    current_justified_checkpoint: Checkpoint
    finalized_checkpoint: Checkpoint
    # Inactivity
    inactivity_scores: List[uint64, VALIDATOR_REGISTRY_LIMIT]
    # Sync
    current_sync_committee: SyncCommittee
    next_sync_committee: SyncCommittee
    # Execution
    latest_execution_payload_header: ExecutionPayloadHeader  # [New in Bellatrix]

New containers

ExecutionPayload

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class ExecutionPayload(Container):
    # Execution block header fields
    parent_hash: Hash32
    fee_recipient: ExecutionAddress  # 'beneficiary' in the yellow paper
    state_root: Bytes32
    receipts_root: Bytes32
    logs_bloom: ByteVector[BYTES_PER_LOGS_BLOOM]
    prev_randao: Bytes32  # 'difficulty' in the yellow paper
    block_number: uint64  # 'number' in the yellow paper
    gas_limit: uint64
    gas_used: uint64
    timestamp: uint64
    extra_data: ByteList[MAX_EXTRA_DATA_BYTES]
    base_fee_per_gas: uint256
    # Extra payload fields
    block_hash: Hash32  # Hash of execution block
    transactions: List[Transaction, MAX_TRANSACTIONS_PER_PAYLOAD]

ExecutionPayloadHeader

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class ExecutionPayloadHeader(Container):
    # Execution block header fields
    parent_hash: Hash32
    fee_recipient: ExecutionAddress
    state_root: Bytes32
    receipts_root: Bytes32
    logs_bloom: ByteVector[BYTES_PER_LOGS_BLOOM]
    prev_randao: Bytes32
    block_number: uint64
    gas_limit: uint64
    gas_used: uint64
    timestamp: uint64
    extra_data: ByteList[MAX_EXTRA_DATA_BYTES]
    base_fee_per_gas: uint256
    # Extra payload fields
    block_hash: Hash32  # Hash of execution block
    transactions_root: Root

Helper functions

Predicates

is_merge_transition_complete

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def is_merge_transition_complete(state: BeaconState) -> bool:
    return state.latest_execution_payload_header != ExecutionPayloadHeader()

is_merge_transition_block

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def is_merge_transition_block(state: BeaconState, body: BeaconBlockBody) -> bool:
    return not is_merge_transition_complete(state) and body.execution_payload != ExecutionPayload()

is_execution_enabled

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def is_execution_enabled(state: BeaconState, body: BeaconBlockBody) -> bool:
    return is_merge_transition_block(state, body) or is_merge_transition_complete(state)

Misc

compute_timestamp_at_slot

Note: This function is unsafe with respect to overflows and underflows.

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def compute_timestamp_at_slot(state: BeaconState, slot: Slot) -> uint64:
    slots_since_genesis = slot - GENESIS_SLOT
    return uint64(state.genesis_time + slots_since_genesis * SECONDS_PER_SLOT)

Beacon state accessors

Modified get_inactivity_penalty_deltas

Note: The function get_inactivity_penalty_deltas is modified to use INACTIVITY_PENALTY_QUOTIENT_BELLATRIX.

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def get_inactivity_penalty_deltas(state: BeaconState) -> Tuple[Sequence[Gwei], Sequence[Gwei]]:
    """
    Return the inactivity penalty deltas by considering timely target participation flags and inactivity scores.
    """
    rewards = [Gwei(0) for _ in range(len(state.validators))]
    penalties = [Gwei(0) for _ in range(len(state.validators))]
    previous_epoch = get_previous_epoch(state)
    matching_target_indices = get_unslashed_participating_indices(state, TIMELY_TARGET_FLAG_INDEX, previous_epoch)
    for index in get_eligible_validator_indices(state):
        if index not in matching_target_indices:
            penalty_numerator = state.validators[index].effective_balance * state.inactivity_scores[index]
            # [Modified in Bellatrix]
            penalty_denominator = INACTIVITY_SCORE_BIAS * INACTIVITY_PENALTY_QUOTIENT_BELLATRIX
            penalties[index] += Gwei(penalty_numerator // penalty_denominator)
    return rewards, penalties

Beacon state mutators

Modified slash_validator

Note: The function slash_validator is modified to use MIN_SLASHING_PENALTY_QUOTIENT_BELLATRIX.

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def slash_validator(state: BeaconState,
                    slashed_index: ValidatorIndex,
                    whistleblower_index: ValidatorIndex=None) -> None:
    """
    Slash the validator with index ``slashed_index``.
    """
    epoch = get_current_epoch(state)
    initiate_validator_exit(state, slashed_index)
    validator = state.validators[slashed_index]
    validator.slashed = True
    validator.withdrawable_epoch = max(validator.withdrawable_epoch, Epoch(epoch + EPOCHS_PER_SLASHINGS_VECTOR))
    state.slashings[epoch % EPOCHS_PER_SLASHINGS_VECTOR] += validator.effective_balance
    slashing_penalty = validator.effective_balance // MIN_SLASHING_PENALTY_QUOTIENT_BELLATRIX  # [Modified in Bellatrix]
    decrease_balance(state, slashed_index, slashing_penalty)

    # Apply proposer and whistleblower rewards
    proposer_index = get_beacon_proposer_index(state)
    if whistleblower_index is None:
        whistleblower_index = proposer_index
    whistleblower_reward = Gwei(validator.effective_balance // WHISTLEBLOWER_REWARD_QUOTIENT)
    proposer_reward = Gwei(whistleblower_reward * PROPOSER_WEIGHT // WEIGHT_DENOMINATOR)
    increase_balance(state, proposer_index, proposer_reward)
    increase_balance(state, whistleblower_index, Gwei(whistleblower_reward - proposer_reward))

Beacon chain state transition function

Execution engine

Request data

NewPayloadRequest
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@dataclass
class NewPayloadRequest(object):
    execution_payload: ExecutionPayload

Engine APIs

The implementation-dependent ExecutionEngine protocol encapsulates the execution sub-system logic via:

  • a state object self.execution_state of type ExecutionState
  • a notification function self.notify_new_payload which may apply changes to the self.execution_state

The body of these functions are implementation dependent. The Engine API may be used to implement this and similarly defined functions via an external execution engine.

notify_new_payload

notify_new_payload is a function accessed through the EXECUTION_ENGINE module which instantiates the ExecutionEngine protocol.

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def notify_new_payload(self: ExecutionEngine, execution_payload: ExecutionPayload) -> bool:
    """
    Return ``True`` if and only if ``execution_payload`` is valid with respect to ``self.execution_state``.
    """
    ...

is_valid_block_hash

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def is_valid_block_hash(self: ExecutionEngine, execution_payload: ExecutionPayload) -> bool:
    """
    Return ``True`` if and only if ``execution_payload.block_hash`` is computed correctly.
    """
    ...

verify_and_notify_new_payload

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def verify_and_notify_new_payload(self: ExecutionEngine,
                                  new_payload_request: NewPayloadRequest) -> bool:
    """
    Return ``True`` if and only if ``new_payload_request`` is valid with respect to ``self.execution_state``.
    """
    if not self.is_valid_block_hash(new_payload_request.execution_payload):
        return False
    if not self.notify_new_payload(new_payload_request.execution_payload):
        return False
    return True

Block processing

Note: The call to the process_execution_payload must happen before the call to the process_randao as the former depends on the randao_mix computed with the reveal of the previous block.

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def process_block(state: BeaconState, block: BeaconBlock) -> None:
    process_block_header(state, block)
    if is_execution_enabled(state, block.body):
        process_execution_payload(state, block.body, EXECUTION_ENGINE)  # [New in Bellatrix]
    process_randao(state, block.body)
    process_eth1_data(state, block.body)
    process_operations(state, block.body)
    process_sync_aggregate(state, block.body.sync_aggregate)

Execution payload

process_execution_payload
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def process_execution_payload(state: BeaconState, body: BeaconBlockBody, execution_engine: ExecutionEngine) -> None:
    payload = body.execution_payload

    # Verify consistency of the parent hash with respect to the previous execution payload header
    if is_merge_transition_complete(state):
        assert payload.parent_hash == state.latest_execution_payload_header.block_hash
    # Verify prev_randao
    assert payload.prev_randao == get_randao_mix(state, get_current_epoch(state))
    # Verify timestamp
    assert payload.timestamp == compute_timestamp_at_slot(state, state.slot)
    # Verify the execution payload is valid
    assert execution_engine.verify_and_notify_new_payload(NewPayloadRequest(execution_payload=payload))
    # Cache execution payload header
    state.latest_execution_payload_header = ExecutionPayloadHeader(
        parent_hash=payload.parent_hash,
        fee_recipient=payload.fee_recipient,
        state_root=payload.state_root,
        receipts_root=payload.receipts_root,
        logs_bloom=payload.logs_bloom,
        prev_randao=payload.prev_randao,
        block_number=payload.block_number,
        gas_limit=payload.gas_limit,
        gas_used=payload.gas_used,
        timestamp=payload.timestamp,
        extra_data=payload.extra_data,
        base_fee_per_gas=payload.base_fee_per_gas,
        block_hash=payload.block_hash,
        transactions_root=hash_tree_root(payload.transactions),
    )

Epoch processing

Slashings

Note: The function process_slashings is modified to use PROPORTIONAL_SLASHING_MULTIPLIER_BELLATRIX.

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def process_slashings(state: BeaconState) -> None:
    epoch = get_current_epoch(state)
    total_balance = get_total_active_balance(state)
    adjusted_total_slashing_balance = min(
        sum(state.slashings) * PROPORTIONAL_SLASHING_MULTIPLIER_BELLATRIX,  # [Modified in Bellatrix]
        total_balance
    )
    for index, validator in enumerate(state.validators):
        if validator.slashed and epoch + EPOCHS_PER_SLASHINGS_VECTOR // 2 == validator.withdrawable_epoch:
            increment = EFFECTIVE_BALANCE_INCREMENT  # Factored out from penalty numerator to avoid uint64 overflow
            penalty_numerator = validator.effective_balance // increment * adjusted_total_slashing_balance
            penalty = penalty_numerator // total_balance * increment
            decrease_balance(state, ValidatorIndex(index), penalty)

Testing

Note: The function initialize_beacon_state_from_eth1 is modified for pure Bellatrix testing only. Modifications include: 1. Use BELLATRIX_FORK_VERSION as the previous and current fork version. 2. Utilize the Bellatrix BeaconBlockBody when constructing the initial latest_block_header. 3. Initialize latest_execution_payload_header. If execution_payload_header == ExecutionPayloadHeader(), then the Merge has not yet occurred. Else, the Merge starts from genesis and the transition is incomplete.

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def initialize_beacon_state_from_eth1(eth1_block_hash: Hash32,
                                      eth1_timestamp: uint64,
                                      deposits: Sequence[Deposit],
                                      execution_payload_header: ExecutionPayloadHeader=ExecutionPayloadHeader()
                                      ) -> BeaconState:
    fork = Fork(
        previous_version=BELLATRIX_FORK_VERSION,  # [Modified in Bellatrix] for testing only
        current_version=BELLATRIX_FORK_VERSION,  # [Modified in Bellatrix]
        epoch=GENESIS_EPOCH,
    )
    state = BeaconState(
        genesis_time=eth1_timestamp + GENESIS_DELAY,
        fork=fork,
        eth1_data=Eth1Data(block_hash=eth1_block_hash, deposit_count=uint64(len(deposits))),
        latest_block_header=BeaconBlockHeader(body_root=hash_tree_root(BeaconBlockBody())),
        randao_mixes=[eth1_block_hash] * EPOCHS_PER_HISTORICAL_VECTOR,  # Seed RANDAO with Eth1 entropy
    )

    # Process deposits
    leaves = list(map(lambda deposit: deposit.data, deposits))
    for index, deposit in enumerate(deposits):
        deposit_data_list = List[DepositData, 2**DEPOSIT_CONTRACT_TREE_DEPTH](*leaves[:index + 1])
        state.eth1_data.deposit_root = hash_tree_root(deposit_data_list)
        process_deposit(state, deposit)

    # Process activations
    for index, validator in enumerate(state.validators):
        balance = state.balances[index]
        validator.effective_balance = min(balance - balance % EFFECTIVE_BALANCE_INCREMENT, MAX_EFFECTIVE_BALANCE)
        if validator.effective_balance == MAX_EFFECTIVE_BALANCE:
            validator.activation_eligibility_epoch = GENESIS_EPOCH
            validator.activation_epoch = GENESIS_EPOCH

    # Set genesis validators root for domain separation and chain versioning
    state.genesis_validators_root = hash_tree_root(state.validators)

    # Fill in sync committees
    # Note: A duplicate committee is assigned for the current and next committee at genesis
    state.current_sync_committee = get_next_sync_committee(state)
    state.next_sync_committee = get_next_sync_committee(state)

    # [New in Bellatrix] Initialize the execution payload header
    # If empty, will initialize a chain that has not yet gone through the Merge transition
    state.latest_execution_payload_header = execution_payload_header

    return state