# Ethereum 2.0 Phase 0 -- The Beacon Chain **NOTICE**: This document is a work-in-progress for researchers and implementers. It reflects recent spec changes and takes precedence over the Python proof-of-concept implementation [[python-poc]](#ref-python-poc). ## Table of contents - [Ethereum 2.0 Phase 0 -- The Beacon Chain](#ethereum-20-phase-0----the-beacon-chain) - [Table of contents](#table-of-contents) - [Introduction](#introduction) - [Notation](#notation) - [Terminology](#terminology) - [Constants](#constants) - [Misc](#misc) - [Deposit contract](#deposit-contract) - [Gwei values](#gwei-values) - [Initial values](#initial-values) - [Time parameters](#time-parameters) - [State list lengths](#state-list-lengths) - [Reward and penalty quotients](#reward-and-penalty-quotients) - [Max transactions per block](#max-transactions-per-block) - [Signature domains](#signature-domains) - [Data structures](#data-structures) - [Misc dependencies](#misc-dependencies) - [`Fork`](#fork) - [`Crosslink`](#crosslink) - [`Eth1Data`](#eth1data) - [`Eth1DataVote`](#eth1datavote) - [`AttestationData`](#attestationdata) - [`AttestationDataAndCustodyBit`](#attestationdataandcustodybit) - [`SlashableAttestation`](#slashableattestation) - [`DepositInput`](#depositinput) - [`DepositData`](#depositdata) - [`BeaconBlockHeader`](#beaconblockheader) - [`Validator`](#validator) - [`PendingAttestation`](#pendingattestation) - [`HistoricalBatch`](#historicalbatch) - [Beacon transactions](#beacon-transactions) - [`ProposerSlashing`](#proposerslashing) - [`AttesterSlashing`](#attesterslashing) - [`Attestation`](#attestation) - [`Deposit`](#deposit) - [`VoluntaryExit`](#voluntaryexit) - [`Transfer`](#transfer) - [Beacon blocks](#beacon-blocks) - [`BeaconBlockBody`](#beaconblockbody) - [`BeaconBlock`](#beaconblock) - [Beacon state](#beacon-state) - [`BeaconState`](#beaconstate) - [Custom Types](#custom-types) - [Helper functions](#helper-functions) - [`xor`](#xor) - [`hash`](#hash) - [`hash_tree_root`](#hash_tree_root) - [`signed_root`](#signed_root) - [`get_temporary_block_header`](#get_temporary_block_header) - [`slot_to_epoch`](#slot_to_epoch) - [`get_previous_epoch`](#get_previous_epoch) - [`get_current_epoch`](#get_current_epoch) - [`get_epoch_start_slot`](#get_epoch_start_slot) - [`is_active_validator`](#is_active_validator) - [`get_active_validator_indices`](#get_active_validator_indices) - [`get_permuted_index`](#get_permuted_index) - [`get_split_offset`](#get_split_offset) - [`get_epoch_committee_count`](#get_epoch_committee_count) - [`compute_committee`](#compute_committee) - [`get_previous_epoch_committee_count`](#get_previous_epoch_committee_count) - [`get_current_epoch_committee_count`](#get_current_epoch_committee_count) - [`get_next_epoch_committee_count`](#get_next_epoch_committee_count) - [`get_crosslink_committees_at_slot`](#get_crosslink_committees_at_slot) - [`get_block_root`](#get_block_root) - [`get_state_root`](#get_state_root) - [`get_randao_mix`](#get_randao_mix) - [`get_active_index_root`](#get_active_index_root) - [`generate_seed`](#generate_seed) - [`get_beacon_proposer_index`](#get_beacon_proposer_index) - [`verify_merkle_branch`](#verify_merkle_branch) - [`get_attestation_participants`](#get_attestation_participants) - [`is_power_of_two`](#is_power_of_two) - [`int_to_bytes1`, `int_to_bytes2`, ...](#int_to_bytes1-int_to_bytes2-) - [`bytes_to_int`](#bytes_to_int) - [`get_effective_balance`](#get_effective_balance) - [`get_total_balance`](#get_total_balance) - [`get_fork_version`](#get_fork_version) - [`get_domain`](#get_domain) - [`get_bitfield_bit`](#get_bitfield_bit) - [`verify_bitfield`](#verify_bitfield) - [`verify_slashable_attestation`](#verify_slashable_attestation) - [`is_double_vote`](#is_double_vote) - [`is_surround_vote`](#is_surround_vote) - [`integer_squareroot`](#integer_squareroot) - [`get_delayed_activation_exit_epoch`](#get_delayed_activation_exit_epoch) - [`bls_verify`](#bls_verify) - [`bls_verify_multiple`](#bls_verify_multiple) - [`bls_aggregate_pubkeys`](#bls_aggregate_pubkeys) - [`process_deposit`](#process_deposit) - [Routines for updating validator status](#routines-for-updating-validator-status) - [`activate_validator`](#activate_validator) - [`initiate_validator_exit`](#initiate_validator_exit) - [`exit_validator`](#exit_validator) - [`slash_validator`](#slash_validator) - [`prepare_validator_for_withdrawal`](#prepare_validator_for_withdrawal) - [Ethereum 1.0 deposit contract](#ethereum-10-deposit-contract) - [Deposit arguments](#deposit-arguments) - [Withdrawal credentials](#withdrawal-credentials) - [`Deposit` logs](#deposit-logs) - [`Eth2Genesis` log](#eth2genesis-log) - [Vyper code](#vyper-code) - [On genesis](#on-genesis) - [Beacon chain processing](#beacon-chain-processing) - [Beacon chain fork choice rule](#beacon-chain-fork-choice-rule) - [Beacon chain state transition function](#beacon-chain-state-transition-function) - [State caching](#state-caching) - [Per-epoch processing](#per-epoch-processing) - [Helper functions](#helper-functions-1) - [Justification](#justification) - [Crosslinks](#crosslinks) - [Eth1 data](#eth1-data-1) - [Rewards and penalties](#rewards-and-penalties) - [Justification and finalization](#justification-and-finalization) - [Crosslinks](#crosslinks-1) - [Apply rewards](#apply-rewards) - [Ejections](#ejections) - [Validator registry and shuffling seed data](#validator-registry-and-shuffling-seed-data) - [Slashings and exit queue](#slashings-and-exit-queue) - [Final updates](#final-updates) - [Per-slot processing](#per-slot-processing) - [Per-block processing](#per-block-processing) - [Block header](#block-header) - [RANDAO](#randao) - [Eth1 data](#eth1-data) - [Transactions](#transactions) - [Proposer slashings](#proposer-slashings) - [Attester slashings](#attester-slashings) - [Attestations](#attestations) - [Deposits](#deposits) - [Voluntary exits](#voluntary-exits) - [Transfers](#transfers) - [State root verification](#state-root-verification) - [References](#references) - [Normative](#normative) - [Informative](#informative) - [Copyright](#copyright) ## Introduction This document represents the specification for Phase 0 of Ethereum 2.0 -- The Beacon Chain. At the core of Ethereum 2.0 is a system chain called the "beacon chain". The beacon chain stores and manages the registry of [validators](#dfn-validator). In the initial deployment phases of Ethereum 2.0 the only mechanism to become a [validator](#dfn-validator) is to make a one-way ETH transaction to a deposit contract on Ethereum 1.0. Activation as a [validator](#dfn-validator) happens when Ethereum 1.0 deposit receipts are processed by the beacon chain, the activation balance is reached, and after a queuing process. Exit is either voluntary or done forcibly as a penalty for misbehavior. The primary source of load on the beacon chain is "attestations". Attestations are availability votes for a shard block, and simultaneously proof of stake votes for a beacon block. A sufficient number of attestations for the same shard block create a "crosslink", confirming the shard segment up to that shard block into the beacon chain. Crosslinks also serve as infrastructure for asynchronous cross-shard communication. ## Notation Code snippets appearing in `this style` are to be interpreted as Python code. ## Terminology * **Validator** - a registered participant in the beacon chain. You can become one by sending Ether into the Ethereum 1.0 deposit contract. * **Active validator** - an active participant in the Ethereum 2.0 consensus invited to, among other things, propose and attest to blocks and vote for crosslinks. * **Committee** - a (pseudo-) randomly sampled subset of [active validators](#dfn-active-validator). When a committee is referred to collectively, as in "this committee attests to X", this is assumed to mean "some subset of that committee that contains enough [validators](#dfn-validator) that the protocol recognizes it as representing the committee". * **Proposer** - the [validator](#dfn-validator) that creates a beacon chain block * **Attester** - a [validator](#dfn-validator) that is part of a committee that needs to sign off on a beacon chain block while simultaneously creating a link (crosslink) to a recent shard block on a particular shard chain. * **Beacon chain** - the central PoS chain that is the base of the sharding system. * **Shard chain** - one of the chains on which user transactions take place and account data is stored. * **Block root** - a 32-byte Merkle root of a beacon chain block or shard chain block. Previously called "block hash". * **Crosslink** - a set of signatures from a committee attesting to a block in a shard chain, which can be included into the beacon chain. Crosslinks are the main means by which the beacon chain "learns about" the updated state of shard chains. * **Slot** - a period during which one proposer has the ability to create a beacon chain block and some attesters have the ability to make attestations * **Epoch** - an aligned span of slots during which all [validators](#dfn-validator) get exactly one chance to make an attestation * **Finalized**, **justified** - see Casper FFG finalization [[casper-ffg]](#ref-casper-ffg) * **Withdrawal period** - the number of slots between a [validator](#dfn-validator) exit and the [validator](#dfn-validator) balance being withdrawable * **Genesis time** - the Unix time of the genesis beacon chain block at slot 0 ## Constants ### Misc | Name | Value | | - | - | | `SHARD_COUNT` | `2**10` (= 1,024) | | `TARGET_COMMITTEE_SIZE` | `2**7` (= 128) | | `MAX_BALANCE_CHURN_QUOTIENT` | `2**5` (= 32) | | `MAX_INDICES_PER_SLASHABLE_VOTE` | `2**12` (= 4,096) | | `MAX_EXIT_DEQUEUES_PER_EPOCH` | `2**2` (= 4) | | `SHUFFLE_ROUND_COUNT` | 90 | * For the safety of crosslinks `TARGET_COMMITTEE_SIZE` exceeds [the recommended minimum committee size of 111](https://vitalik.ca/files/Ithaca201807_Sharding.pdf); with sufficient active validators (at least `SLOTS_PER_EPOCH * TARGET_COMMITTEE_SIZE`), the shuffling algorithm ensures committee sizes of at least `TARGET_COMMITTEE_SIZE`. (Unbiasable randomness with a Verifiable Delay Function (VDF) will improve committee robustness and lower the safe minimum committee size.) ### Deposit contract | Name | Value | | - | - | | `DEPOSIT_CONTRACT_ADDRESS` | **TBD** | | `DEPOSIT_CONTRACT_TREE_DEPTH` | `2**5` (= 32) | ### Gwei values | Name | Value | Unit | | - | - | :-: | | `MIN_DEPOSIT_AMOUNT` | `2**0 * 10**9` (= 1,000,000,000) | Gwei | | `MAX_DEPOSIT_AMOUNT` | `2**5 * 10**9` (= 32,000,000,000) | Gwei | | `FORK_CHOICE_BALANCE_INCREMENT` | `2**0 * 10**9` (= 1,000,000,000) | Gwei | | `EJECTION_BALANCE` | `2**4 * 10**9` (= 16,000,000,000) | Gwei | ### Initial values | Name | Value | | - | - | | `GENESIS_FORK_VERSION` | `int_to_bytes4(0)` | | `GENESIS_SLOT` | `2**32` | | `GENESIS_EPOCH` | `slot_to_epoch(GENESIS_SLOT)` | | `GENESIS_START_SHARD` | `0` | | `FAR_FUTURE_EPOCH` | `2**64 - 1` | | `ZERO_HASH` | `int_to_bytes32(0)` | | `EMPTY_SIGNATURE` | `int_to_bytes96(0)` | | `BLS_WITHDRAWAL_PREFIX_BYTE` | `int_to_bytes1(0)` | * `GENESIS_SLOT` should be at least as large in terms of time as the largest of the time parameters or state list lengths below (ie. it should be at least as large as any value measured in slots, and at least `SLOTS_PER_EPOCH` times as large as any value measured in epochs). ### Time parameters | Name | Value | Unit | Duration | | - | - | :-: | :-: | | `SECONDS_PER_SLOT` | `6` | seconds | 6 seconds | | `MIN_ATTESTATION_INCLUSION_DELAY` | `2**2` (= 4) | slots | 24 seconds | | `SLOTS_PER_EPOCH` | `2**6` (= 64) | slots | 6.4 minutes | | `MIN_SEED_LOOKAHEAD` | `2**0` (= 1) | epochs | 6.4 minutes | | `ACTIVATION_EXIT_DELAY` | `2**2` (= 4) | epochs | 25.6 minutes | | `EPOCHS_PER_ETH1_VOTING_PERIOD` | `2**4` (= 16) | epochs | ~1.7 hours | | `SLOTS_PER_HISTORICAL_ROOT` | `2**13` (= 8,192) | slots | ~13 hours | | `MIN_VALIDATOR_WITHDRAWABILITY_DELAY` | `2**8` (= 256) | epochs | ~27 hours | | `PERSISTENT_COMMITTEE_PERIOD` | `2**11` (= 2,048) | epochs | 9 days | ### State list lengths | Name | Value | Unit | Duration | | - | - | :-: | :-: | | `LATEST_RANDAO_MIXES_LENGTH` | `2**13` (= 8,192) | epochs | ~36 days | | `LATEST_ACTIVE_INDEX_ROOTS_LENGTH` | `2**13` (= 8,192) | epochs | ~36 days | | `LATEST_SLASHED_EXIT_LENGTH` | `2**13` (= 8,192) | epochs | ~36 days | ### Reward and penalty quotients | Name | Value | | - | - | | `BASE_REWARD_QUOTIENT` | `2**5` (= 32) | | `WHISTLEBLOWER_REWARD_QUOTIENT` | `2**9` (= 512) | | `ATTESTATION_INCLUSION_REWARD_QUOTIENT` | `2**3` (= 8) | | `INACTIVITY_PENALTY_QUOTIENT` | `2**24` (= 16,777,216) | | `MIN_PENALTY_QUOTIENT` | `2**5` (= 32) | * The `BASE_REWARD_QUOTIENT` parameter dictates the per-epoch reward. It corresponds to ~2.54% annual interest assuming 10 million participating ETH in every epoch. * The `INACTIVITY_PENALTY_QUOTIENT` equals `INVERSE_SQRT_E_DROP_TIME**2` where `INVERSE_SQRT_E_DROP_TIME := 2**12 epochs` (~18 days) is the time it takes the inactivity penalty to reduce the balance of non-participating [validators](#dfn-validator) to about `1/sqrt(e) ~= 60.6%`. Indeed, the balance retained by offline [validators](#dfn-validator) after `n` epochs is about `(1-1/INACTIVITY_PENALTY_QUOTIENT)**(n**2/2)` so after `INVERSE_SQRT_E_DROP_TIME` epochs it is roughly `(1-1/INACTIVITY_PENALTY_QUOTIENT)**(INACTIVITY_PENALTY_QUOTIENT/2) ~= 1/sqrt(e)`. ### Max transactions per block | Name | Value | | - | - | | `MAX_PROPOSER_SLASHINGS` | `2**4` (= 16) | | `MAX_ATTESTER_SLASHINGS` | `2**0` (= 1) | | `MAX_ATTESTATIONS` | `2**7` (= 128) | | `MAX_DEPOSITS` | `2**4` (= 16) | | `MAX_VOLUNTARY_EXITS` | `2**4` (= 16) | | `MAX_TRANSFERS` | `2**4` (= 16) | ### Signature domains | Name | Value | | - | - | | `DOMAIN_BEACON_BLOCK` | `0` | | `DOMAIN_RANDAO` | `1` | | `DOMAIN_ATTESTATION` | `2` | | `DOMAIN_DEPOSIT` | `3` | | `DOMAIN_VOLUNTARY_EXIT` | `4` | | `DOMAIN_TRANSFER` | `5` | ## Data structures The following data structures are defined as [SimpleSerialize (SSZ)](https://github.com/ethereum/eth2.0-specs/blob/master/specs/simple-serialize.md) objects. The types are defined topologically to aid in facilitating an executable version of the spec. ### Misc dependencies #### `Fork` ```python { # Previous fork version 'previous_version': 'bytes4', # Current fork version 'current_version': 'bytes4', # Fork epoch number 'epoch': 'uint64', } ``` #### `Crosslink` ```python { # Epoch number 'epoch': 'uint64', # Shard data since the previous crosslink 'crosslink_data_root': 'bytes32', } ``` #### `Eth1Data` ```python { # Root of the deposit tree 'deposit_root': 'bytes32', # Block hash 'block_hash': 'bytes32', } ``` #### `Eth1DataVote` ```python { # Data being voted for 'eth1_data': Eth1Data, # Vote count 'vote_count': 'uint64', } ``` #### `AttestationData` ```python { # LMD GHOST vote 'slot': 'uint64', 'beacon_block_root': 'bytes32', # FFG vote 'source_epoch': 'uint64', 'source_root': 'bytes32', 'target_root': 'bytes32', # Crosslink vote 'shard': 'uint64', 'previous_crosslink': Crosslink, 'crosslink_data_root': 'bytes32', } ``` #### `AttestationDataAndCustodyBit` ```python { # Attestation data 'data': AttestationData, # Custody bit 'custody_bit': 'bool', } ``` #### `SlashableAttestation` ```python { # Validator indices 'validator_indices': ['uint64'], # Attestation data 'data': AttestationData, # Custody bitfield 'custody_bitfield': 'bytes', # Aggregate signature 'aggregate_signature': 'bytes96', } ``` #### `DepositInput` ```python { # BLS pubkey 'pubkey': 'bytes48', # Withdrawal credentials 'withdrawal_credentials': 'bytes32', # A BLS signature of this `DepositInput` 'proof_of_possession': 'bytes96', } ``` #### `DepositData` ```python { # Amount in Gwei 'amount': 'uint64', # Timestamp from deposit contract 'timestamp': 'uint64', # Deposit input 'deposit_input': DepositInput, } ``` #### `BeaconBlockHeader` ```python { 'slot': 'uint64', 'previous_block_root': 'bytes32', 'state_root': 'bytes32', 'block_body_root': 'bytes32', 'signature': 'bytes96', } ``` #### `Validator` ```python { # BLS public key 'pubkey': 'bytes48', # Withdrawal credentials 'withdrawal_credentials': 'bytes32', # Epoch when validator activated 'activation_epoch': 'uint64', # Epoch when validator exited 'exit_epoch': 'uint64', # Epoch when validator is eligible to withdraw 'withdrawable_epoch': 'uint64', # Did the validator initiate an exit 'initiated_exit': 'bool', # Was the validator slashed 'slashed': 'bool', } ``` #### `PendingAttestation` ```python { # Attester aggregation bitfield 'aggregation_bitfield': 'bytes', # Attestation data 'data': AttestationData, # Custody bitfield 'custody_bitfield': 'bytes', # Inclusion slot 'inclusion_slot': 'uint64', } ``` #### `HistoricalBatch` ```python { # Block roots 'block_roots': ['bytes32', SLOTS_PER_HISTORICAL_ROOT], # State roots 'state_roots': ['bytes32', SLOTS_PER_HISTORICAL_ROOT], } ``` ### Beacon transactions #### `ProposerSlashing` ```python { # Proposer index 'proposer_index': 'uint64', # First block header 'header_1': BeaconBlockHeader, # Second block header 'header_2': BeaconBlockHeader, } ``` #### `AttesterSlashing` ```python { # First slashable attestation 'slashable_attestation_1': SlashableAttestation, # Second slashable attestation 'slashable_attestation_2': SlashableAttestation, } ``` #### `Attestation` ```python { # Attester aggregation bitfield 'aggregation_bitfield': 'bytes', # Attestation data 'data': AttestationData, # Custody bitfield 'custody_bitfield': 'bytes', # BLS aggregate signature 'aggregate_signature': 'bytes96', } ``` #### `Deposit` ```python { # Branch in the deposit tree 'proof': ['bytes32', DEPOSIT_CONTRACT_TREE_DEPTH], # Index in the deposit tree 'index': 'uint64', # Data 'deposit_data': DepositData, } ``` #### `VoluntaryExit` ```python { # Minimum epoch for processing exit 'epoch': 'uint64', # Index of the exiting validator 'validator_index': 'uint64', # Validator signature 'signature': 'bytes96', } ``` #### `Transfer` ```python { # Sender index 'sender': 'uint64', # Recipient index 'recipient': 'uint64', # Amount in Gwei 'amount': 'uint64', # Fee in Gwei for block proposer 'fee': 'uint64', # Inclusion slot 'slot': 'uint64', # Sender withdrawal pubkey 'pubkey': 'bytes48', # Sender signature 'signature': 'bytes96', } ``` ### Beacon blocks #### `BeaconBlockBody` ```python { 'randao_reveal': 'bytes96', 'eth1_data': Eth1Data, 'proposer_slashings': [ProposerSlashing], 'attester_slashings': [AttesterSlashing], 'attestations': [Attestation], 'deposits': [Deposit], 'voluntary_exits': [VoluntaryExit], 'transfers': [Transfer], } ``` #### `BeaconBlock` ```python { # Header 'slot': 'uint64', 'previous_block_root': 'bytes32', 'state_root': 'bytes32', 'body': BeaconBlockBody, 'signature': 'bytes96', } ``` ### Beacon state #### `BeaconState` ```python { # Misc 'slot': 'uint64', 'genesis_time': 'uint64', 'fork': Fork, # For versioning hard forks # Validator registry 'validator_registry': [Validator], 'validator_balances': ['uint64'], 'validator_registry_update_epoch': 'uint64', # Randomness and committees 'latest_randao_mixes': ['bytes32', LATEST_RANDAO_MIXES_LENGTH], 'previous_shuffling_start_shard': 'uint64', 'current_shuffling_start_shard': 'uint64', 'previous_shuffling_epoch': 'uint64', 'current_shuffling_epoch': 'uint64', 'previous_shuffling_seed': 'bytes32', 'current_shuffling_seed': 'bytes32', # Finality 'previous_epoch_attestations': [PendingAttestation], 'current_epoch_attestations': [PendingAttestation], 'previous_justified_epoch': 'uint64', 'current_justified_epoch': 'uint64', 'previous_justified_root': 'bytes32', 'current_justified_root': 'bytes32', 'justification_bitfield': 'uint64', 'finalized_epoch': 'uint64', 'finalized_root': 'bytes32', # Recent state 'latest_crosslinks': [Crosslink, SHARD_COUNT], 'latest_block_roots': ['bytes32', SLOTS_PER_HISTORICAL_ROOT], 'latest_state_roots': ['bytes32', SLOTS_PER_HISTORICAL_ROOT], 'latest_active_index_roots': ['bytes32', LATEST_ACTIVE_INDEX_ROOTS_LENGTH], 'latest_slashed_balances': ['uint64', LATEST_SLASHED_EXIT_LENGTH], # Balances slashed at every withdrawal period 'latest_block_header': BeaconBlockHeader, # `latest_block_header.state_root == ZERO_HASH` temporarily 'historical_roots': ['bytes32'], # Ethereum 1.0 chain data 'latest_eth1_data': Eth1Data, 'eth1_data_votes': [Eth1DataVote], 'deposit_index': 'uint64', } ``` ## Custom Types We define the following Python custom types for type hinting and readability: | Name | SSZ equivalent | Description | | - | - | - | | `Slot` | `uint64` | a slot number | | `Epoch` | `uint64` | an epoch number | | `Shard` | `uint64` | a shard number | | `ValidatorIndex` | `uint64` | a validator registry index | | `Gwei` | `uint64` | an amount in Gwei | | `Bytes32` | `bytes32` | 32 bytes of binary data | | `BLSPubkey` | `bytes48` | a BLS12-381 public key | | `BLSSignature` | `bytes96` | a BLS12-381 signature | ## Helper functions Note: The definitions below are for specification purposes and are not necessarily optimal implementations. ### `xor` ```python def xor(bytes1: Bytes32, bytes2: Bytes32) -> Bytes32: return bytes(a ^ b for a, b in zip(bytes1, bytes2)) ``` ### `hash` The hash function is denoted by `hash`. In Phase 0 the beacon chain is deployed with the same hash function as Ethereum 1.0, i.e. Keccak-256 (also incorrectly known as SHA3). Note: We aim to migrate to a S[T/N]ARK-friendly hash function in a future Ethereum 2.0 deployment phase. ### `hash_tree_root` `def hash_tree_root(object: SSZSerializable) -> Bytes32` is a function for hashing objects into a single root utilizing a hash tree structure. `hash_tree_root` is defined in the [SimpleSerialize spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/simple-serialize.md#tree-hash). ### `signed_root` `def signed_root(object: SSZContainer) -> Bytes32` is a function defined in the [SimpleSerialize spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/simple-serialize.md#signed-roots) to compute signed messages. ### `get_temporary_block_header` ```python def get_temporary_block_header(block: BeaconBlock) -> BeaconBlockHeader: """ Return the block header corresponding to a block with ``state_root`` set to ``ZERO_HASH``. """ return BeaconBlockHeader( slot=block.slot, previous_block_root=block.previous_block_root, state_root=ZERO_HASH, block_body_root=hash_tree_root(block.body), signature=block.signature, ) ``` ### `slot_to_epoch` ```python def slot_to_epoch(slot: Slot) -> Epoch: """ Return the epoch number of the given ``slot``. """ return slot // SLOTS_PER_EPOCH ``` ### `get_previous_epoch` ```python def get_previous_epoch(state: BeaconState) -> Epoch: """` Return the previous epoch of the given ``state``. """ return get_current_epoch(state) - 1 ``` ### `get_current_epoch` ```python def get_current_epoch(state: BeaconState) -> Epoch: """ Return the current epoch of the given ``state``. """ return slot_to_epoch(state.slot) ``` ### `get_epoch_start_slot` ```python def get_epoch_start_slot(epoch: Epoch) -> Slot: """ Return the starting slot of the given ``epoch``. """ return epoch * SLOTS_PER_EPOCH ``` ### `is_active_validator` ```python def is_active_validator(validator: Validator, epoch: Epoch) -> bool: """ Check if ``validator`` is active. """ return validator.activation_epoch <= epoch < validator.exit_epoch ``` ### `get_active_validator_indices` ```python def get_active_validator_indices(validators: List[Validator], epoch: Epoch) -> List[ValidatorIndex]: """ Get indices of active validators from ``validators``. """ return [i for i, v in enumerate(validators) if is_active_validator(v, epoch)] ``` ### `get_permuted_index` ```python def get_permuted_index(index: int, list_size: int, seed: Bytes32) -> int: """ Return `p(index)` in a pseudorandom permutation `p` of `0...list_size-1` with ``seed`` as entropy. Utilizes 'swap or not' shuffling found in https://link.springer.com/content/pdf/10.1007%2F978-3-642-32009-5_1.pdf See the 'generalized domain' algorithm on page 3. """ assert index < list_size assert list_size <= 2**40 for round in range(SHUFFLE_ROUND_COUNT): pivot = bytes_to_int(hash(seed + int_to_bytes1(round))[0:8]) % list_size flip = (pivot - index) % list_size position = max(index, flip) source = hash(seed + int_to_bytes1(round) + int_to_bytes4(position // 256)) byte = source[(position % 256) // 8] bit = (byte >> (position % 8)) % 2 index = flip if bit else index return index ``` ### `get_split_offset` ```python def get_split_offset(list_length: int, split_count: int, index: int) -> int: return (list_length * index) // split_count ``` ### `get_epoch_committee_count` ```python def get_epoch_committee_count(active_validator_count: int) -> int: """ Return the number of committees in one epoch. """ return max( 1, min( SHARD_COUNT // SLOTS_PER_EPOCH, active_validator_count // SLOTS_PER_EPOCH // TARGET_COMMITTEE_SIZE, ) ) * SLOTS_PER_EPOCH ``` ### `compute_committee` ```python def compute_committee(validator_indices: List[ValidatorIndex], seed: Bytes32, index: int, total_committees: int) -> List[ValidatorIndex]: """ Return the ``index``'th shuffled committee out of a total ``total_committees`` using ``validator_indices`` and ``seed``. """ start_offset = get_split_offset(len(validator_indices), total_committees, index) end_offset = get_split_offset(len(validator_indices), total_committees, index + 1) return [ validator_indices[get_permuted_index(i, len(validator_indices), seed)] for i in range(start_offset, end_offset) ] ``` **Note**: this definition and the next few definitions are highly inefficient as algorithms as they re-calculate many sub-expressions. Production implementations are expected to appropriately use caching/memoization to avoid redoing work. ### `get_previous_epoch_committee_count` ```python def get_previous_epoch_committee_count(state: BeaconState) -> int: """ Return the number of committees in the previous epoch of the given ``state``. """ previous_active_validators = get_active_validator_indices( state.validator_registry, state.previous_shuffling_epoch, ) return get_epoch_committee_count(len(previous_active_validators)) ``` ### `get_current_epoch_committee_count` ```python def get_current_epoch_committee_count(state: BeaconState) -> int: """ Return the number of committees in the current epoch of the given ``state``. """ current_active_validators = get_active_validator_indices( state.validator_registry, state.current_shuffling_epoch, ) return get_epoch_committee_count(len(current_active_validators)) ``` ### `get_next_epoch_committee_count` ```python def get_next_epoch_committee_count(state: BeaconState) -> int: """ Return the number of committees in the next epoch of the given ``state``. """ next_active_validators = get_active_validator_indices( state.validator_registry, get_current_epoch(state) + 1, ) return get_epoch_committee_count(len(next_active_validators)) ``` ### `get_crosslink_committees_at_slot` ```python def get_crosslink_committees_at_slot(state: BeaconState, slot: Slot, registry_change: bool=False) -> List[Tuple[List[ValidatorIndex], Shard]]: """ Return the list of ``(committee, shard)`` tuples for the ``slot``. Note: There are two possible shufflings for crosslink committees for a ``slot`` in the next epoch -- with and without a `registry_change` """ epoch = slot_to_epoch(slot) current_epoch = get_current_epoch(state) previous_epoch = get_previous_epoch(state) next_epoch = current_epoch + 1 assert previous_epoch <= epoch <= next_epoch if epoch == current_epoch: committees_per_epoch = get_current_epoch_committee_count(state) seed = state.current_shuffling_seed shuffling_epoch = state.current_shuffling_epoch shuffling_start_shard = state.current_shuffling_start_shard elif epoch == previous_epoch: committees_per_epoch = get_previous_epoch_committee_count(state) seed = state.previous_shuffling_seed shuffling_epoch = state.previous_shuffling_epoch shuffling_start_shard = state.previous_shuffling_start_shard elif epoch == next_epoch: epochs_since_last_registry_update = current_epoch - state.validator_registry_update_epoch if registry_change: committees_per_epoch = get_next_epoch_committee_count(state) seed = generate_seed(state, next_epoch) shuffling_epoch = next_epoch current_committees_per_epoch = get_current_epoch_committee_count(state) shuffling_start_shard = (state.current_shuffling_start_shard + current_committees_per_epoch) % SHARD_COUNT elif epochs_since_last_registry_update > 1 and is_power_of_two(epochs_since_last_registry_update): committees_per_epoch = get_next_epoch_committee_count(state) seed = generate_seed(state, next_epoch) shuffling_epoch = next_epoch shuffling_start_shard = state.current_shuffling_start_shard else: committees_per_epoch = get_current_epoch_committee_count(state) seed = state.current_shuffling_seed shuffling_epoch = state.current_shuffling_epoch shuffling_start_shard = state.current_shuffling_start_shard indices = get_active_validator_indices(state.validator_registry, shuffling_epoch) committees_per_slot = committees_per_epoch // SLOTS_PER_EPOCH offset = slot % SLOTS_PER_EPOCH slot_start_shard = (shuffling_start_shard + committees_per_slot * offset) % SHARD_COUNT return [ ( compute_committee(indices, seed, committees_per_slot * offset + i, committees_per_epoch), (slot_start_shard + i) % SHARD_COUNT, ) for i in range(committees_per_slot) ] ``` ### `get_block_root` ```python def get_block_root(state: BeaconState, slot: Slot) -> Bytes32: """ Return the block root at a recent ``slot``. """ assert slot < state.slot <= slot + SLOTS_PER_HISTORICAL_ROOT return state.latest_block_roots[slot % SLOTS_PER_HISTORICAL_ROOT] ``` `get_block_root(_, s)` should always return `hash_tree_root` of the block in the beacon chain at slot `s`, and `get_crosslink_committees_at_slot(_, s)` should not change unless the [validator](#dfn-validator) registry changes. ### `get_state_root` ```python def get_state_root(state: BeaconState, slot: Slot) -> Bytes32: """ Return the state root at a recent ``slot``. """ assert slot < state.slot <= slot + SLOTS_PER_HISTORICAL_ROOT return state.latest_state_roots[slot % SLOTS_PER_HISTORICAL_ROOT] ``` ### `get_randao_mix` ```python def get_randao_mix(state: BeaconState, epoch: Epoch) -> Bytes32: """ Return the randao mix at a recent ``epoch``. """ assert get_current_epoch(state) - LATEST_RANDAO_MIXES_LENGTH < epoch <= get_current_epoch(state) return state.latest_randao_mixes[epoch % LATEST_RANDAO_MIXES_LENGTH] ``` ### `get_active_index_root` ```python def get_active_index_root(state: BeaconState, epoch: Epoch) -> Bytes32: """ Return the index root at a recent ``epoch``. """ assert get_current_epoch(state) - LATEST_ACTIVE_INDEX_ROOTS_LENGTH + ACTIVATION_EXIT_DELAY < epoch <= get_current_epoch(state) + ACTIVATION_EXIT_DELAY return state.latest_active_index_roots[epoch % LATEST_ACTIVE_INDEX_ROOTS_LENGTH] ``` ### `generate_seed` ```python def generate_seed(state: BeaconState, epoch: Epoch) -> Bytes32: """ Generate a seed for the given ``epoch``. """ return hash( get_randao_mix(state, epoch - MIN_SEED_LOOKAHEAD) + get_active_index_root(state, epoch) + int_to_bytes32(epoch) ) ``` ### `get_beacon_proposer_index` ```python def get_beacon_proposer_index(state: BeaconState, slot: Slot, registry_change: bool=False) -> ValidatorIndex: """ Return the beacon proposer index for the ``slot``. """ epoch = slot_to_epoch(slot) current_epoch = get_current_epoch(state) previous_epoch = get_previous_epoch(state) next_epoch = current_epoch + 1 assert previous_epoch <= epoch <= next_epoch first_committee, _ = get_crosslink_committees_at_slot(state, slot, registry_change)[0] return first_committee[epoch % len(first_committee)] ``` ### `verify_merkle_branch` ```python def verify_merkle_branch(leaf: Bytes32, proof: List[Bytes32], depth: int, index: int, root: Bytes32) -> bool: """ Verify that the given ``leaf`` is on the merkle branch ``proof`` starting with the given ``root``. """ value = leaf for i in range(depth): if index // (2**i) % 2: value = hash(proof[i] + value) else: value = hash(value + proof[i]) return value == root ``` ### `get_attestation_participants` ```python def get_attestation_participants(state: BeaconState, attestation_data: AttestationData, bitfield: bytes) -> List[ValidatorIndex]: """ Return the participant indices corresponding to ``attestation_data`` and ``bitfield``. """ # Find the committee in the list with the desired shard crosslink_committees = get_crosslink_committees_at_slot(state, attestation_data.slot) assert attestation_data.shard in [shard for _, shard in crosslink_committees] crosslink_committee = [committee for committee, shard in crosslink_committees if shard == attestation_data.shard][0] assert verify_bitfield(bitfield, len(crosslink_committee)) # Find the participating attesters in the committee participants = [] for i, validator_index in enumerate(crosslink_committee): aggregation_bit = get_bitfield_bit(bitfield, i) if aggregation_bit == 0b1: participants.append(validator_index) return participants ``` ### `is_power_of_two` ```python def is_power_of_two(value: int) -> bool: """ Check if ``value`` is a power of two integer. """ return (value > 0) and (value & (value - 1) == 0) ``` ### `int_to_bytes1`, `int_to_bytes2`, ... `int_to_bytes1(x): return x.to_bytes(1, 'little')`, `int_to_bytes2(x): return x.to_bytes(2, 'little')`, and so on for all integers, particularly 1, 2, 3, 4, 8, 32, 48, 96. ### `bytes_to_int` ```python def bytes_to_int(data: bytes) -> int: return int.from_bytes(data, 'little') ``` ### `get_effective_balance` ```python def get_effective_balance(state: BeaconState, index: ValidatorIndex) -> Gwei: """ Return the effective balance (also known as "balance at stake") for a validator with the given ``index``. """ return min(state.validator_balances[index], MAX_DEPOSIT_AMOUNT) ``` ### `get_total_balance` ```python def get_total_balance(state: BeaconState, validators: List[ValidatorIndex]) -> Gwei: """ Return the combined effective balance of an array of ``validators``. """ return sum([get_effective_balance(state, i) for i in validators]) ``` ### `get_fork_version` ```python def get_fork_version(fork: Fork, epoch: Epoch) -> bytes: """ Return the fork version of the given ``epoch``. """ if epoch < fork.epoch: return fork.previous_version else: return fork.current_version ``` ### `get_domain` ```python def get_domain(fork: Fork, epoch: Epoch, domain_type: int) -> int: """ Get the domain number that represents the fork meta and signature domain. """ return bytes_to_int(get_fork_version(fork, epoch) + int_to_bytes4(domain_type)) ``` ### `get_bitfield_bit` ```python def get_bitfield_bit(bitfield: bytes, i: int) -> int: """ Extract the bit in ``bitfield`` at position ``i``. """ return (bitfield[i // 8] >> (i % 8)) % 2 ``` ### `verify_bitfield` ```python def verify_bitfield(bitfield: bytes, committee_size: int) -> bool: """ Verify ``bitfield`` against the ``committee_size``. """ if len(bitfield) != (committee_size + 7) // 8: return False # Check `bitfield` is padded with zero bits only for i in range(committee_size, len(bitfield) * 8): if get_bitfield_bit(bitfield, i) == 0b1: return False return True ``` ### `verify_slashable_attestation` ```python def verify_slashable_attestation(state: BeaconState, slashable_attestation: SlashableAttestation) -> bool: """ Verify validity of ``slashable_attestation`` fields. """ if slashable_attestation.custody_bitfield != b'\x00' * len(slashable_attestation.custody_bitfield): # [TO BE REMOVED IN PHASE 1] return False if len(slashable_attestation.validator_indices) == 0: return False for i in range(len(slashable_attestation.validator_indices) - 1): if slashable_attestation.validator_indices[i] >= slashable_attestation.validator_indices[i + 1]: return False if not verify_bitfield(slashable_attestation.custody_bitfield, len(slashable_attestation.validator_indices)): return False if len(slashable_attestation.validator_indices) > MAX_INDICES_PER_SLASHABLE_VOTE: return False custody_bit_0_indices = [] custody_bit_1_indices = [] for i, validator_index in enumerate(slashable_attestation.validator_indices): if get_bitfield_bit(slashable_attestation.custody_bitfield, i) == 0b0: custody_bit_0_indices.append(validator_index) else: custody_bit_1_indices.append(validator_index) return bls_verify_multiple( pubkeys=[ bls_aggregate_pubkeys([state.validator_registry[i].pubkey for i in custody_bit_0_indices]), bls_aggregate_pubkeys([state.validator_registry[i].pubkey for i in custody_bit_1_indices]), ], message_hashes=[ hash_tree_root(AttestationDataAndCustodyBit(data=slashable_attestation.data, custody_bit=0b0)), hash_tree_root(AttestationDataAndCustodyBit(data=slashable_attestation.data, custody_bit=0b1)), ], signature=slashable_attestation.aggregate_signature, domain=get_domain(state.fork, slot_to_epoch(slashable_attestation.data.slot), DOMAIN_ATTESTATION), ) ``` ### `is_double_vote` ```python def is_double_vote(attestation_data_1: AttestationData, attestation_data_2: AttestationData) -> bool: """ Check if ``attestation_data_1`` and ``attestation_data_2`` have the same target. """ target_epoch_1 = slot_to_epoch(attestation_data_1.slot) target_epoch_2 = slot_to_epoch(attestation_data_2.slot) return target_epoch_1 == target_epoch_2 ``` ### `is_surround_vote` ```python def is_surround_vote(attestation_data_1: AttestationData, attestation_data_2: AttestationData) -> bool: """ Check if ``attestation_data_1`` surrounds ``attestation_data_2``. """ source_epoch_1 = attestation_data_1.source_epoch source_epoch_2 = attestation_data_2.source_epoch target_epoch_1 = slot_to_epoch(attestation_data_1.slot) target_epoch_2 = slot_to_epoch(attestation_data_2.slot) return source_epoch_1 < source_epoch_2 and target_epoch_2 < target_epoch_1 ``` ### `integer_squareroot` ```python def integer_squareroot(n: int) -> int: """ The largest integer ``x`` such that ``x**2`` is less than or equal to ``n``. """ assert n >= 0 x = n y = (x + 1) // 2 while y < x: x = y y = (x + n // x) // 2 return x ``` ### `get_delayed_activation_exit_epoch` ```python def get_delayed_activation_exit_epoch(epoch: Epoch) -> Epoch: """ Return the epoch at which an activation or exit triggered in ``epoch`` takes effect. """ return epoch + 1 + ACTIVATION_EXIT_DELAY ``` ### `bls_verify` `bls_verify` is a function for verifying a BLS signature, defined in the [BLS Signature spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/bls_signature.md#bls_verify). ### `bls_verify_multiple` `bls_verify_multiple` is a function for verifying a BLS signature constructed from multiple messages, defined in the [BLS Signature spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/bls_signature.md#bls_verify_multiple). ### `bls_aggregate_pubkeys` `bls_aggregate_pubkeys` is a function for aggregating multiple BLS public keys into a single aggregate key, defined in the [BLS Signature spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/bls_signature.md#bls_aggregate_pubkeys). ### `process_deposit` Used to add a [validator](#dfn-validator) or top up an existing [validator](#dfn-validator)'s balance by some `deposit` amount: ```python def process_deposit(state: BeaconState, deposit: Deposit) -> None: """ Process a deposit from Ethereum 1.0. Note that this function mutates ``state``. """ deposit_input = deposit.deposit_data.deposit_input # Should equal 8 bytes for deposit_data.amount + # 8 bytes for deposit_data.timestamp + # 176 bytes for deposit_data.deposit_input # It should match the deposit_data in the eth1.0 deposit contract serialized_deposit_data = serialize(deposit.deposit_data) # Deposits must be processed in order assert deposit.index == state.deposit_index # Verify the Merkle branch merkle_branch_is_valid = verify_merkle_branch( leaf=hash(serialized_deposit_data), proof=deposit.proof, depth=DEPOSIT_CONTRACT_TREE_DEPTH, index=deposit.index, root=state.latest_eth1_data.deposit_root, ) assert merkle_branch_is_valid # Increment the next deposit index we are expecting. Note that this # needs to be done here because while the deposit contract will never # create an invalid Merkle branch, it may admit an invalid deposit # object, and we need to be able to skip over it state.deposit_index += 1 validator_pubkeys = [v.pubkey for v in state.validator_registry] pubkey = deposit_input.pubkey amount = deposit.deposit_data.amount withdrawal_credentials = deposit_input.withdrawal_credentials if pubkey not in validator_pubkeys: # Verify the proof of possession proof_is_valid = bls_verify( pubkey=deposit_input.pubkey, message_hash=signed_root(deposit_input), signature=deposit_input.proof_of_possession, domain=get_domain( state.fork, get_current_epoch(state), DOMAIN_DEPOSIT, ) ) if not proof_is_valid: return # Add new validator validator = Validator( pubkey=pubkey, withdrawal_credentials=withdrawal_credentials, activation_epoch=FAR_FUTURE_EPOCH, exit_epoch=FAR_FUTURE_EPOCH, withdrawable_epoch=FAR_FUTURE_EPOCH, initiated_exit=False, slashed=False, ) # Note: In phase 2 registry indices that have been withdrawn for a long time will be recycled. state.validator_registry.append(validator) state.validator_balances.append(amount) else: # Increase balance by deposit amount state.validator_balances[validator_pubkeys.index(pubkey)] += amount ``` ### Routines for updating validator status Note: All functions in this section mutate `state`. #### `activate_validator` ```python def activate_validator(state: BeaconState, index: ValidatorIndex, is_genesis: bool) -> None: """ Activate the validator of the given ``index``. Note that this function mutates ``state``. """ validator = state.validator_registry[index] validator.activation_epoch = GENESIS_EPOCH if is_genesis else get_delayed_activation_exit_epoch(get_current_epoch(state)) ``` #### `initiate_validator_exit` ```python def initiate_validator_exit(state: BeaconState, index: ValidatorIndex) -> None: """ Initiate the validator of the given ``index``. Note that this function mutates ``state``. """ validator = state.validator_registry[index] validator.initiated_exit = True ``` #### `exit_validator` ```python def exit_validator(state: BeaconState, index: ValidatorIndex) -> None: """ Exit the validator of the given ``index``. Note that this function mutates ``state``. """ validator = state.validator_registry[index] delayed_activation_exit_epoch = get_delayed_activation_exit_epoch(get_current_epoch(state)) # The following updates only occur if not previous exited if validator.exit_epoch <= delayed_activation_exit_epoch: return else: validator.exit_epoch = delayed_activation_exit_epoch ``` #### `slash_validator` ```python def slash_validator(state: BeaconState, index: ValidatorIndex) -> None: """ Slash the validator with index ``index``. Note that this function mutates ``state``. """ validator = state.validator_registry[index] assert state.slot < get_epoch_start_slot(validator.withdrawable_epoch) # [TO BE REMOVED IN PHASE 2] exit_validator(state, index) state.latest_slashed_balances[get_current_epoch(state) % LATEST_SLASHED_EXIT_LENGTH] += get_effective_balance(state, index) whistleblower_index = get_beacon_proposer_index(state, state.slot) whistleblower_reward = get_effective_balance(state, index) // WHISTLEBLOWER_REWARD_QUOTIENT state.validator_balances[whistleblower_index] += whistleblower_reward state.validator_balances[index] -= whistleblower_reward validator.slashed = True validator.withdrawable_epoch = get_current_epoch(state) + LATEST_SLASHED_EXIT_LENGTH ``` #### `prepare_validator_for_withdrawal` ```python def prepare_validator_for_withdrawal(state: BeaconState, index: ValidatorIndex) -> None: """ Set the validator with the given ``index`` as withdrawable ``MIN_VALIDATOR_WITHDRAWABILITY_DELAY`` after the current epoch. Note that this function mutates ``state``. """ validator = state.validator_registry[index] validator.withdrawable_epoch = get_current_epoch(state) + MIN_VALIDATOR_WITHDRAWABILITY_DELAY ``` ## Ethereum 1.0 deposit contract The initial deployment phases of Ethereum 2.0 are implemented without consensus changes to Ethereum 1.0. A deposit contract at address `DEPOSIT_CONTRACT_ADDRESS` is added to Ethereum 1.0 for deposits of ETH to the beacon chain. Validator balances will be withdrawable to the shards in phase 2, i.e. when the EVM2.0 is deployed and the shards have state. ### Deposit arguments The deposit contract has a single `deposit` function which takes as argument a SimpleSerialize'd `DepositInput`. ### Withdrawal credentials One of the `DepositInput` fields is `withdrawal_credentials`. It is a commitment to credentials for withdrawals to shards. The first byte of `withdrawal_credentials` is a version number. As of now the only expected format is as follows: * `withdrawal_credentials[:1] == BLS_WITHDRAWAL_PREFIX_BYTE` * `withdrawal_credentials[1:] == hash(withdrawal_pubkey)[1:]` where `withdrawal_pubkey` is a BLS pubkey The private key corresponding to `withdrawal_pubkey` will be required to initiate a withdrawal. It can be stored separately until a withdrawal is required, e.g. in cold storage. ### `Deposit` logs Every Ethereum 1.0 deposit, of size between `MIN_DEPOSIT_AMOUNT` and `MAX_DEPOSIT_AMOUNT`, emits a `Deposit` log for consumption by the beacon chain. The deposit contract does little validation, pushing most of the validator onboarding logic to the beacon chain. In particular, the proof of possession (a BLS12 signature) is not verified by the deposit contract. ### `Eth2Genesis` log When sufficiently many full deposits have been made the deposit contract emits the `Eth2Genesis` log. The beacon chain state may then be initialized by calling the `get_genesis_beacon_state` function (defined below) where: * `genesis_time` equals `time` in the `Eth2Genesis` log * `latest_eth1_data.deposit_root` equals `deposit_root` in the `Eth2Genesis` log * `latest_eth1_data.block_hash` equals the hash of the block that included the log * `genesis_validator_deposits` is a list of `Deposit` objects built according to the `Deposit` logs up to the deposit that triggered the `Eth2Genesis` log, processed in the order in which they were emitted (oldest to newest) ### Vyper code The source for the Vyper contract lives in a [separate repository](https://github.com/ethereum/deposit_contract) at [https://github.com/ethereum/deposit_contract/blob/master/deposit_contract/contracts/validator_registration.v.py](https://github.com/ethereum/deposit_contract/blob/master/deposit_contract/contracts/validator_registration.v.py). Note: to save ~10x on gas this contract uses a somewhat unintuitive progressive Merkle root calculation algo that requires only O(log(n)) storage. See https://github.com/ethereum/research/blob/master/beacon_chain_impl/progressive_merkle_tree.py for an implementation of the same algo in python tested for correctness. For convenience, we provide the interface to the contract here: * `__init__()`: initializes the contract * `get_deposit_root() -> bytes32`: returns the current root of the deposit tree * `deposit(bytes[512])`: adds a deposit instance to the deposit tree, incorporating the input argument and the value transferred in the given call. Note: the amount of value transferred *must* be within `MIN_DEPOSIT_AMOUNT` and `MAX_DEPOSIT_AMOUNT`, inclusive. Each of these constants are specified in units of Gwei. ## On genesis When enough full deposits have been made to the deposit contract, an `Eth2Genesis` log is emitted. Construct a corresponding `genesis_state` and `genesis_block` as follows: * Let `genesis_validator_deposits` be the list of deposits, ordered chronologically, up to and including the deposit that triggered the `Eth2Genesis` log. * Let `genesis_time` be the timestamp specified in the `Eth2Genesis` log. * Let `genesis_eth1_data` be the `Eth1Data` object where: * `genesis_eth1_data.deposit_root` is the `deposit_root` contained in the `Eth2Genesis` log. * `genesis_eth1_data.block_hash` is the hash of the Ethereum 1.0 block that emitted the `Eth2Genesis` log. * Let `genesis_state = get_genesis_beacon_state(genesis_validator_deposits, genesis_time, genesis_eth1_data)`. * Let `genesis_block = get_empty_block()`. * Set `genesis_block.state_root = hash_tree_root(genesis_state)`. ```python def get_empty_block() -> BeaconBlock: """ Get an empty ``BeaconBlock``. """ return BeaconBlock( slot=GENESIS_SLOT, previous_block_root=ZERO_HASH, state_root=ZERO_HASH, body=BeaconBlockBody( randao_reveal=EMPTY_SIGNATURE, eth1_data=Eth1Data( deposit_root=ZERO_HASH, block_hash=ZERO_HASH, ), proposer_slashings=[], attester_slashings=[], attestations=[], deposits=[], voluntary_exits=[], transfers=[], ), signature=EMPTY_SIGNATURE, ) ``` ```python def get_genesis_beacon_state(genesis_validator_deposits: List[Deposit], genesis_time: int, genesis_eth1_data: Eth1Data) -> BeaconState: """ Get the genesis ``BeaconState``. """ state = BeaconState( # Misc slot=GENESIS_SLOT, genesis_time=genesis_time, fork=Fork( previous_version=GENESIS_FORK_VERSION, current_version=GENESIS_FORK_VERSION, epoch=GENESIS_EPOCH, ), # Validator registry validator_registry=[], validator_balances=[], validator_registry_update_epoch=GENESIS_EPOCH, # Randomness and committees latest_randao_mixes=Vector([ZERO_HASH for _ in range(LATEST_RANDAO_MIXES_LENGTH)]), previous_shuffling_start_shard=GENESIS_START_SHARD, current_shuffling_start_shard=GENESIS_START_SHARD, previous_shuffling_epoch=GENESIS_EPOCH, current_shuffling_epoch=GENESIS_EPOCH, previous_shuffling_seed=ZERO_HASH, current_shuffling_seed=ZERO_HASH, # Finality previous_epoch_attestations=[], current_epoch_attestations=[], previous_justified_epoch=GENESIS_EPOCH, current_justified_epoch=GENESIS_EPOCH, previous_justified_root=ZERO_HASH, current_justified_root=ZERO_HASH, justification_bitfield=0, finalized_epoch=GENESIS_EPOCH, finalized_root=ZERO_HASH, # Recent state latest_crosslinks=Vector([Crosslink(epoch=GENESIS_EPOCH, crosslink_data_root=ZERO_HASH) for _ in range(SHARD_COUNT)]), latest_block_roots=Vector([ZERO_HASH for _ in range(SLOTS_PER_HISTORICAL_ROOT)]), latest_state_roots=Vector([ZERO_HASH for _ in range(SLOTS_PER_HISTORICAL_ROOT)]), latest_active_index_roots=Vector([ZERO_HASH for _ in range(LATEST_ACTIVE_INDEX_ROOTS_LENGTH)]), latest_slashed_balances=Vector([0 for _ in range(LATEST_SLASHED_EXIT_LENGTH)]), latest_block_header=get_temporary_block_header(get_empty_block()), historical_roots=[], # Ethereum 1.0 chain data latest_eth1_data=genesis_eth1_data, eth1_data_votes=[], deposit_index=0, ) # Process genesis deposits for deposit in genesis_validator_deposits: process_deposit(state, deposit) # Process genesis activations for validator_index, _ in enumerate(state.validator_registry): if get_effective_balance(state, validator_index) >= MAX_DEPOSIT_AMOUNT: activate_validator(state, validator_index, is_genesis=True) genesis_active_index_root = hash_tree_root(get_active_validator_indices(state.validator_registry, GENESIS_EPOCH)) for index in range(LATEST_ACTIVE_INDEX_ROOTS_LENGTH): state.latest_active_index_roots[index] = genesis_active_index_root state.current_shuffling_seed = generate_seed(state, GENESIS_EPOCH) return state ``` ## Beacon chain processing The beacon chain is the system chain for Ethereum 2.0. The main responsibilities of the beacon chain are: * Store and maintain the registry of [validators](#dfn-validator) * Process crosslinks (see above) * Process its per-block consensus, as well as the finality gadget Processing the beacon chain is similar to processing the Ethereum 1.0 chain. Clients download and process blocks, and maintain a view of what is the current "canonical chain", terminating at the current "head". However, because of the beacon chain's relationship with Ethereum 1.0, and because it is a proof-of-stake chain, there are differences. For a beacon chain block, `block`, to be processed by a node, the following conditions must be met: * The parent block with root `block.previous_block_root` has been processed and accepted. * An Ethereum 1.0 block pointed to by the `state.latest_eth1_data.block_hash` has been processed and accepted. * The node's Unix time is greater than or equal to `state.genesis_time + (block.slot - GENESIS_SLOT) * SECONDS_PER_SLOT`. (Note that leap seconds mean that slots will occasionally last `SECONDS_PER_SLOT + 1` or `SECONDS_PER_SLOT - 1` seconds, possibly several times a year.) If these conditions are not met, the client should delay processing the beacon block until the conditions are all satisfied. Beacon block production is significantly different because of the proof of stake mechanism. A client simply checks what it thinks is the canonical chain when it should create a block, and looks up what its slot number is; when the slot arrives, it either proposes or attests to a block as required. Note that this requires each node to have a clock that is roughly (i.e. within `SECONDS_PER_SLOT` seconds) synchronized with the other nodes. ### Beacon chain fork choice rule The beacon chain fork choice rule is a hybrid that combines justification and finality with Latest Message Driven (LMD) Greediest Heaviest Observed SubTree (GHOST). At any point in time a [validator](#dfn-validator) `v` subjectively calculates the beacon chain head as follows. * Abstractly define `Store` as the type of storage object for the chain data and `store` be the set of attestations and blocks that the [validator](#dfn-validator) `v` has observed and verified (in particular, block ancestors must be recursively verified). Attestations not yet included in any chain are still included in `store`. * Let `finalized_head` be the finalized block with the highest epoch. (A block `B` is finalized if there is a descendant of `B` in `store` the processing of which sets `B` as finalized.) * Let `justified_head` be the descendant of `finalized_head` with the highest epoch that has been justified for at least 1 epoch. (A block `B` is justified if there is a descendant of `B` in `store` the processing of which sets `B` as justified.) If no such descendant exists set `justified_head` to `finalized_head`. * Let `get_ancestor(store: Store, block: BeaconBlock, slot: Slot) -> BeaconBlock` be the ancestor of `block` with slot number `slot`. The `get_ancestor` function can be defined recursively as: ```python def get_ancestor(store: Store, block: BeaconBlock, slot: Slot) -> BeaconBlock: """ Get the ancestor of ``block`` with slot number ``slot``; return ``None`` if not found. """ if block.slot == slot: return block elif block.slot < slot: return None else: return get_ancestor(store, store.get_parent(block), slot) ``` * Let `get_latest_attestation(store: Store, validator_index: ValidatorIndex) -> Attestation` be the attestation with the highest slot number in `store` from the validator with the given `validator_index`. If several such attestations exist, use the one the [validator](#dfn-validator) `v` observed first. * Let `get_latest_attestation_target(store: Store, validator_index: ValidatorIndex) -> BeaconBlock` be the target block in the attestation `get_latest_attestation(store, validator_index)`. * Let `get_children(store: Store, block: BeaconBlock) -> List[BeaconBlock]` returns the child blocks of the given `block`. * Let `justified_head_state` be the resulting `BeaconState` object from processing the chain up to the `justified_head`. * The `head` is `lmd_ghost(store, justified_head_state, justified_head)` where the function `lmd_ghost` is defined below. Note that the implementation below is suboptimal; there are implementations that compute the head in time logarithmic in slot count. ```python def lmd_ghost(store: Store, start_state: BeaconState, start_block: BeaconBlock) -> BeaconBlock: """ Execute the LMD-GHOST algorithm to find the head ``BeaconBlock``. """ validators = start_state.validator_registry active_validator_indices = get_active_validator_indices(validators, slot_to_epoch(start_state.slot)) attestation_targets = [ (validator_index, get_latest_attestation_target(store, validator_index)) for validator_index in active_validator_indices ] def get_vote_count(block: BeaconBlock) -> int: return sum( get_effective_balance(start_state.validator_balances[validator_index]) // FORK_CHOICE_BALANCE_INCREMENT for validator_index, target in attestation_targets if get_ancestor(store, target, block.slot) == block ) head = start_block while 1: children = get_children(store, head) if len(children) == 0: return head head = max(children, key=lambda x: (get_vote_count(x), hash_tree_root(x))) ``` ## Beacon chain state transition function We now define the state transition function. At a high level the state transition is made up of four parts: 1. State caching, which happens at the start of every slot. 2. The per-epoch transitions, which happens at the start of the first slot of every epoch. 3. The per-slot transitions, which happens at every slot. 4. The per-block transitions, which happens at every block. Transition section notes: * The state caching, caches the state root of the previous slot. * The per-epoch transitions focus on the [validator](#dfn-validator) registry, including adjusting balances and activating and exiting [validators](#dfn-validator), as well as processing crosslinks and managing block justification/finalization. * The per-slot transitions focus on the slot counter and block roots records updates. * The per-block transitions generally focus on verifying aggregate signatures and saving temporary records relating to the per-block activity in the `BeaconState`. Beacon blocks that trigger unhandled Python exceptions (e.g. out-of-range list accesses) and failed `assert`s during the state transition are considered invalid. _Note_: If there are skipped slots between a block and its parent block, run the steps in the [state-root](#state-caching), [per-epoch](#per-epoch-processing), and [per-slot](#per-slot-processing) sections once for each skipped slot and then once for the slot containing the new block. ### State caching At every `slot > GENESIS_SLOT` run the following function: ```python def cache_state(state: BeaconState) -> None: previous_slot_state_root = hash_tree_root(state) # store the previous slot's post state transition root state.latest_state_roots[state.slot % SLOTS_PER_HISTORICAL_ROOT] = previous_slot_state_root # cache state root in stored latest_block_header if empty if state.latest_block_header.state_root == ZERO_HASH: state.latest_block_header.state_root = previous_slot_state_root # store latest known block for previous slot state.latest_block_roots[state.slot % SLOTS_PER_HISTORICAL_ROOT] = hash_tree_root(state.latest_block_header) ``` ### Per-epoch processing The steps below happen when `state.slot > GENESIS_SLOT and (state.slot + 1) % SLOTS_PER_EPOCH == 0`. #### Helper functions We define some helper functions utilized when processing an epoch transition: ```python def get_current_total_balance(state: BeaconState) -> Gwei: return get_total_balance(state, get_active_validator_indices(state.validator_registry, get_current_epoch(state))) ``` ```python def get_previous_total_balance(state: BeaconState) -> Gwei: return get_total_balance(state, get_active_validator_indices(state.validator_registry, get_previous_epoch(state))) ``` ```python def get_attesting_indices(state: BeaconState, attestations: List[PendingAttestation]) -> List[ValidatorIndex]: output = set() for a in attestations: output = output.union(get_attestation_participants(state, a.data, a.aggregation_bitfield)) return sorted(list(output)) ``` ```python def get_attesting_balance(state: BeaconState, attestations: List[PendingAttestation]) -> Gwei: return get_total_balance(state, get_attesting_indices(state, attestations)) ``` ```python def get_current_epoch_boundary_attestations(state: BeaconState) -> List[PendingAttestation]: return [ a for a in state.current_epoch_attestations if a.data.target_root == get_block_root(state, get_epoch_start_slot(get_current_epoch(state))) ] ``` ```python def get_previous_epoch_boundary_attestations(state: BeaconState) -> List[PendingAttestation]: return [ a for a in state.previous_epoch_attestations if a.data.target_root == get_block_root(state, get_epoch_start_slot(get_previous_epoch(state))) ] ``` ```python def get_previous_epoch_matching_head_attestations(state: BeaconState) -> List[PendingAttestation]: return [ a for a in state.previous_epoch_attestations if a.data.beacon_block_root == get_block_root(state, a.data.slot) ] ``` **Note**: Total balances computed for the previous epoch might be marginally different than the actual total balances during the previous epoch transition. Due to the tight bound on validator churn each epoch and small per-epoch rewards/penalties, the potential balance difference is very low and only marginally affects consensus safety. ```python def get_winning_root_and_participants(state: BeaconState, shard: Shard) -> Tuple[Bytes32, List[ValidatorIndex]]: all_attestations = state.current_epoch_attestations + state.previous_epoch_attestations valid_attestations = [ a for a in all_attestations if a.data.previous_crosslink == state.latest_crosslinks[shard] ] all_roots = [a.data.crosslink_data_root for a in valid_attestations] # handle when no attestations for shard available if len(all_roots) == 0: return ZERO_HASH, [] def get_attestations_for(root) -> List[PendingAttestation]: return [a for a in valid_attestations if a.data.crosslink_data_root == root] # Winning crosslink root is the root with the most votes for it, ties broken in favor of # lexicographically higher hash winning_root = max(all_roots, key=lambda r: (get_attesting_balance(state, get_attestations_for(r)), r)) return winning_root, get_attesting_indices(state, get_attestations_for(winning_root)) ``` ```python def earliest_attestation(state: BeaconState, validator_index: ValidatorIndex) -> PendingAttestation: return min([ a for a in state.previous_epoch_attestations if validator_index in get_attestation_participants(state, a.data, a.aggregation_bitfield) ], key=lambda a: a.inclusion_slot) ``` ```python def inclusion_slot(state: BeaconState, validator_index: ValidatorIndex) -> Slot: return earliest_attestation(state, validator_index).inclusion_slot ``` ```python def inclusion_distance(state: BeaconState, validator_index: ValidatorIndex) -> int: attestation = earliest_attestation(state, validator_index) return attestation.inclusion_slot - attestation.data.slot ``` #### Justification Run the following function: ```python def update_justification_and_finalization(state: BeaconState) -> None: new_justified_epoch = state.current_justified_epoch new_finalized_epoch = state.finalized_epoch # Rotate the justification bitfield up one epoch to make room for the current epoch state.justification_bitfield <<= 1 # If the previous epoch gets justified, fill the second last bit previous_boundary_attesting_balance = get_attesting_balance(state, get_previous_epoch_boundary_attestations(state)) if previous_boundary_attesting_balance * 3 >= get_previous_total_balance(state) * 2: new_justified_epoch = get_current_epoch(state) - 1 state.justification_bitfield |= 2 # If the current epoch gets justified, fill the last bit current_boundary_attesting_balance = get_attesting_balance(state, get_current_epoch_boundary_attestations(state)) if current_boundary_attesting_balance * 3 >= get_current_total_balance(state) * 2: new_justified_epoch = get_current_epoch(state) state.justification_bitfield |= 1 # Process finalizations bitfield = state.justification_bitfield current_epoch = get_current_epoch(state) # The 2nd/3rd/4th most recent epochs are all justified, the 2nd using the 4th as source if (bitfield >> 1) % 8 == 0b111 and state.previous_justified_epoch == current_epoch - 3: new_finalized_epoch = state.previous_justified_epoch # The 2nd/3rd most recent epochs are both justified, the 2nd using the 3rd as source if (bitfield >> 1) % 4 == 0b11 and state.previous_justified_epoch == current_epoch - 2: new_finalized_epoch = state.previous_justified_epoch # The 1st/2nd/3rd most recent epochs are all justified, the 1st using the 3rd as source if (bitfield >> 0) % 8 == 0b111 and state.current_justified_epoch == current_epoch - 2: new_finalized_epoch = state.current_justified_epoch # The 1st/2nd most recent epochs are both justified, the 1st using the 2nd as source if (bitfield >> 0) % 4 == 0b11 and state.current_justified_epoch == current_epoch - 1: new_finalized_epoch = state.current_justified_epoch # Update state jusification/finality fields state.previous_justified_epoch = state.current_justified_epoch state.previous_justified_root = state.current_justified_root if new_justified_epoch != state.current_justified_epoch: state.current_justified_epoch = new_justified_epoch state.current_justified_root = get_block_root(state, get_epoch_start_slot(new_justified_epoch)) if new_finalized_epoch != state.finalized_epoch: state.finalized_epoch = new_finalized_epoch state.finalized_root = get_block_root(state, get_epoch_start_slot(new_finalized_epoch)) ``` #### Crosslinks Run the following function: ```python def process_crosslinks(state: BeaconState) -> None: current_epoch = get_current_epoch(state) previous_epoch = current_epoch - 1 next_epoch = current_epoch + 1 for slot in range(get_epoch_start_slot(previous_epoch), get_epoch_start_slot(next_epoch)): for crosslink_committee, shard in get_crosslink_committees_at_slot(state, slot): winning_root, participants = get_winning_root_and_participants(state, shard) participating_balance = get_total_balance(state, participants) total_balance = get_total_balance(state, crosslink_committee) if 3 * participating_balance >= 2 * total_balance: state.latest_crosslinks[shard] = Crosslink( epoch=slot_to_epoch(slot), crosslink_data_root=winning_root ) ``` #### Eth1 data Run the following function: ```python def maybe_reset_eth1_period(state: BeaconState) -> None: if (get_current_epoch(state) + 1) % EPOCHS_PER_ETH1_VOTING_PERIOD == 0: for eth1_data_vote in state.eth1_data_votes: # If a majority of all votes were for a particular eth1_data value, # then set that as the new canonical value if eth1_data_vote.vote_count * 2 > EPOCHS_PER_ETH1_VOTING_PERIOD * SLOTS_PER_EPOCH: state.latest_eth1_data = eth1_data_vote.eth1_data state.eth1_data_votes = [] ``` #### Rewards and penalties First, we define some additional helpers: ```python def get_base_reward(state: BeaconState, index: ValidatorIndex) -> Gwei: if get_previous_total_balance(state) == 0: return 0 adjusted_quotient = integer_squareroot(get_previous_total_balance(state)) // BASE_REWARD_QUOTIENT return get_effective_balance(state, index) // adjusted_quotient // 5 ``` ```python def get_inactivity_penalty(state: BeaconState, index: ValidatorIndex, epochs_since_finality: int) -> Gwei: return ( get_base_reward(state, index) + get_effective_balance(state, index) * epochs_since_finality // INACTIVITY_PENALTY_QUOTIENT // 2 ) ``` Note: When applying penalties in the following balance recalculations implementers should make sure the `uint64` does not underflow. ##### Justification and finalization ```python def get_justification_and_finalization_deltas(state: BeaconState) -> Tuple[List[Gwei], List[Gwei]]: epochs_since_finality = get_current_epoch(state) + 1 - state.finalized_epoch if epochs_since_finality <= 4: return compute_normal_justification_and_finalization_deltas(state) else: return compute_inactivity_leak_deltas(state) ``` When blocks are finalizing normally... ```python def compute_normal_justification_and_finalization_deltas(state: BeaconState) -> Tuple[List[Gwei], List[Gwei]]: # deltas[0] for rewards # deltas[1] for penalties deltas = [ [0 for index in range(len(state.validator_registry))], [0 for index in range(len(state.validator_registry))] ] # Some helper variables boundary_attestations = get_previous_epoch_boundary_attestations(state) boundary_attesting_balance = get_attesting_balance(state, boundary_attestations) total_balance = get_previous_total_balance(state) total_attesting_balance = get_attesting_balance(state, state.previous_epoch_attestations) matching_head_attestations = get_previous_epoch_matching_head_attestations(state) matching_head_balance = get_attesting_balance(state, matching_head_attestations) # Process rewards or penalties for all validators for index in get_active_validator_indices(state.validator_registry, get_previous_epoch(state)): # Expected FFG source if index in get_attesting_indices(state, state.previous_epoch_attestations): deltas[0][index] += get_base_reward(state, index) * total_attesting_balance // total_balance # Inclusion speed bonus deltas[0][index] += ( get_base_reward(state, index) * MIN_ATTESTATION_INCLUSION_DELAY // inclusion_distance(state, index) ) else: deltas[1][index] += get_base_reward(state, index) # Expected FFG target if index in get_attesting_indices(state, boundary_attestations): deltas[0][index] += get_base_reward(state, index) * boundary_attesting_balance // total_balance else: deltas[1][index] += get_base_reward(state, index) # Expected head if index in get_attesting_indices(state, matching_head_attestations): deltas[0][index] += get_base_reward(state, index) * matching_head_balance // total_balance else: deltas[1][index] += get_base_reward(state, index) # Proposer bonus if index in get_attesting_indices(state, state.previous_epoch_attestations): proposer_index = get_beacon_proposer_index(state, inclusion_slot(state, index)) deltas[0][proposer_index] += get_base_reward(state, index) // ATTESTATION_INCLUSION_REWARD_QUOTIENT return deltas ``` When blocks are not finalizing normally... ```python def compute_inactivity_leak_deltas(state: BeaconState) -> Tuple[List[Gwei], List[Gwei]]: # deltas[0] for rewards # deltas[1] for penalties deltas = [ [0 for index in range(len(state.validator_registry))], [0 for index in range(len(state.validator_registry))] ] boundary_attestations = get_previous_epoch_boundary_attestations(state) matching_head_attestations = get_previous_epoch_matching_head_attestations(state) active_validator_indices = get_active_validator_indices(state.validator_registry, get_previous_epoch(state)) epochs_since_finality = get_current_epoch(state) + 1 - state.finalized_epoch for index in active_validator_indices: if index not in get_attesting_indices(state, state.previous_epoch_attestations): deltas[1][index] += get_inactivity_penalty(state, index, epochs_since_finality) else: # If a validator did attest, apply a small penalty for getting attestations included late deltas[0][index] += ( get_base_reward(state, index) * MIN_ATTESTATION_INCLUSION_DELAY // inclusion_distance(state, index) ) deltas[1][index] += get_base_reward(state, index) if index not in get_attesting_indices(state, boundary_attestations): deltas[1][index] += get_inactivity_penalty(state, index, epochs_since_finality) if index not in get_attesting_indices(state, matching_head_attestations): deltas[1][index] += get_base_reward(state, index) # Penalize slashed-but-inactive validators as though they were active but offline for index in range(len(state.validator_registry)): eligible = ( index not in active_validator_indices and state.validator_registry[index].slashed and get_current_epoch(state) < state.validator_registry[index].withdrawable_epoch ) if eligible: deltas[1][index] += ( 2 * get_inactivity_penalty(state, index, epochs_since_finality) + get_base_reward(state, index) ) return deltas ``` ##### Crosslinks ```python def get_crosslink_deltas(state: BeaconState) -> Tuple[List[Gwei], List[Gwei]]: # deltas[0] for rewards # deltas[1] for penalties deltas = [ [0 for index in range(len(state.validator_registry))], [0 for index in range(len(state.validator_registry))] ] previous_epoch_start_slot = get_epoch_start_slot(get_previous_epoch(state)) current_epoch_start_slot = get_epoch_start_slot(get_current_epoch(state)) for slot in range(previous_epoch_start_slot, current_epoch_start_slot): for crosslink_committee, shard in get_crosslink_committees_at_slot(state, slot): winning_root, participants = get_winning_root_and_participants(state, shard) participating_balance = get_total_balance(state, participants) total_balance = get_total_balance(state, crosslink_committee) for index in crosslink_committee: if index in participants: deltas[0][index] += get_base_reward(state, index) * participating_balance // total_balance else: deltas[1][index] += get_base_reward(state, index) return deltas ``` #### Apply rewards Run the following: ```python def apply_rewards(state: BeaconState) -> None: deltas1 = get_justification_and_finalization_deltas(state) deltas2 = get_crosslink_deltas(state) for i in range(len(state.validator_registry)): state.validator_balances[i] = max( 0, state.validator_balances[i] + deltas1[0][i] + deltas2[0][i] - deltas1[1][i] - deltas2[1][i] ) ``` #### Ejections Run `process_ejections(state)`. ```python def process_ejections(state: BeaconState) -> None: """ Iterate through the validator registry and eject active validators with balance below ``EJECTION_BALANCE``. """ for index in get_active_validator_indices(state.validator_registry, get_current_epoch(state)): if state.validator_balances[index] < EJECTION_BALANCE: exit_validator(state, index) ``` #### Validator registry and shuffling seed data ```python def should_update_validator_registry(state: BeaconState) -> bool: # Must have finalized a new block if state.finalized_epoch <= state.validator_registry_update_epoch: return False # Must have processed new crosslinks on all shards of the current epoch shards_to_check = [ (state.current_shuffling_start_shard + i) % SHARD_COUNT for i in range(get_current_epoch_committee_count(state)) ] for shard in shards_to_check: if state.latest_crosslinks[shard].epoch <= state.validator_registry_update_epoch: return False return True ``` ```python def update_validator_registry(state: BeaconState) -> None: """ Update validator registry. Note that this function mutates ``state``. """ current_epoch = get_current_epoch(state) # The active validators active_validator_indices = get_active_validator_indices(state.validator_registry, current_epoch) # The total effective balance of active validators total_balance = get_total_balance(state, active_validator_indices) # The maximum balance churn in Gwei (for deposits and exits separately) max_balance_churn = max( MAX_DEPOSIT_AMOUNT, total_balance // (2 * MAX_BALANCE_CHURN_QUOTIENT) ) # Activate validators within the allowable balance churn balance_churn = 0 for index, validator in enumerate(state.validator_registry): if validator.activation_epoch == FAR_FUTURE_EPOCH and state.validator_balances[index] >= MAX_DEPOSIT_AMOUNT: # Check the balance churn would be within the allowance balance_churn += get_effective_balance(state, index) if balance_churn > max_balance_churn: break # Activate validator activate_validator(state, index, is_genesis=False) # Exit validators within the allowable balance churn balance_churn = 0 for index, validator in enumerate(state.validator_registry): if validator.exit_epoch == FAR_FUTURE_EPOCH and validator.initiated_exit: # Check the balance churn would be within the allowance balance_churn += get_effective_balance(state, index) if balance_churn > max_balance_churn: break # Exit validator exit_validator(state, index) state.validator_registry_update_epoch = current_epoch ``` Run the following function: ```python def update_registry_and_shuffling_data(state: BeaconState) -> None: # First set previous shuffling data to current shuffling data state.previous_shuffling_epoch = state.current_shuffling_epoch state.previous_shuffling_start_shard = state.current_shuffling_start_shard state.previous_shuffling_seed = state.current_shuffling_seed current_epoch = get_current_epoch(state) next_epoch = current_epoch + 1 # Check if we should update, and if so, update if should_update_validator_registry(state): update_validator_registry(state) # If we update the registry, update the shuffling data and shards as well state.current_shuffling_epoch = next_epoch state.current_shuffling_start_shard = ( state.current_shuffling_start_shard + get_current_epoch_committee_count(state) % SHARD_COUNT ) state.current_shuffling_seed = generate_seed(state, state.current_shuffling_epoch) else: # If processing at least one crosslink keeps failing, then reshuffle every power of two, # but don't update the current_shuffling_start_shard epochs_since_last_registry_update = current_epoch - state.validator_registry_update_epoch if epochs_since_last_registry_update > 1 and is_power_of_two(epochs_since_last_registry_update): state.current_shuffling_epoch = next_epoch state.current_shuffling_seed = generate_seed(state, state.current_shuffling_epoch) ``` **Invariant**: the active index root that is hashed into the shuffling seed actually is the `hash_tree_root` of the validator set that is used for that epoch. #### Slashings and exit queue Run `process_slashings(state)` and `process_exit_queue(state)`: ```python def process_slashings(state: BeaconState) -> None: """ Process the slashings. Note that this function mutates ``state``. """ current_epoch = get_current_epoch(state) active_validator_indices = get_active_validator_indices(state.validator_registry, current_epoch) total_balance = get_total_balance(state, active_validator_indices) # Compute `total_penalties` total_at_start = state.latest_slashed_balances[(current_epoch + 1) % LATEST_SLASHED_EXIT_LENGTH] total_at_end = state.latest_slashed_balances[current_epoch % LATEST_SLASHED_EXIT_LENGTH] total_penalties = total_at_end - total_at_start for index, validator in enumerate(state.validator_registry): if validator.slashed and current_epoch == validator.withdrawable_epoch - LATEST_SLASHED_EXIT_LENGTH // 2: penalty = max( get_effective_balance(state, index) * min(total_penalties * 3, total_balance) // total_balance, get_effective_balance(state, index) // MIN_PENALTY_QUOTIENT ) state.validator_balances[index] -= penalty ``` ```python def process_exit_queue(state: BeaconState) -> None: """ Process the exit queue. Note that this function mutates ``state``. """ def eligible(index): validator = state.validator_registry[index] # Filter out dequeued validators if validator.withdrawable_epoch != FAR_FUTURE_EPOCH: return False # Dequeue if the minimum amount of time has passed else: return get_current_epoch(state) >= validator.exit_epoch + MIN_VALIDATOR_WITHDRAWABILITY_DELAY eligible_indices = filter(eligible, list(range(len(state.validator_registry)))) # Sort in order of exit epoch, and validators that exit within the same epoch exit in order of validator index sorted_indices = sorted(eligible_indices, key=lambda index: state.validator_registry[index].exit_epoch) for dequeues, index in enumerate(sorted_indices): if dequeues >= MAX_EXIT_DEQUEUES_PER_EPOCH: break prepare_validator_for_withdrawal(state, index) ``` #### Final updates Run the following function: ```python def finish_epoch_update(state: BeaconState) -> None: current_epoch = get_current_epoch(state) next_epoch = current_epoch + 1 # Set active index root index_root_position = (next_epoch + ACTIVATION_EXIT_DELAY) % LATEST_ACTIVE_INDEX_ROOTS_LENGTH state.latest_active_index_roots[index_root_position] = hash_tree_root( get_active_validator_indices(state.validator_registry, next_epoch + ACTIVATION_EXIT_DELAY) ) # Set total slashed balances state.latest_slashed_balances[next_epoch % LATEST_SLASHED_EXIT_LENGTH] = ( state.latest_slashed_balances[current_epoch % LATEST_SLASHED_EXIT_LENGTH] ) # Set randao mix state.latest_randao_mixes[next_epoch % LATEST_RANDAO_MIXES_LENGTH] = get_randao_mix(state, current_epoch) # Set historical root accumulator if next_epoch % (SLOTS_PER_HISTORICAL_ROOT // SLOTS_PER_EPOCH) == 0: historical_batch = HistoricalBatch( block_roots=state.latest_block_roots, state_roots=state.latest_state_roots, ) state.historical_roots.append(hash_tree_root(historical_batch)) # Rotate current/previous epoch attestations state.previous_epoch_attestations = state.current_epoch_attestations state.current_epoch_attestations = [] ``` ### Per-slot processing At every `slot > GENESIS_SLOT` run the following function: ```python def advance_slot(state: BeaconState) -> None: state.slot += 1 ``` ### Per-block processing For every `block` except the genesis block, run `process_block_header(state, block)`, `process_randao(state, block)` and `process_eth1_data(state, block)`. #### Block header ```python def process_block_header(state: BeaconState, block: BeaconBlock) -> None: # Verify that the slots match assert block.slot == state.slot # Verify that the parent matches assert block.previous_block_root == hash_tree_root(state.latest_block_header) # Save current block as the new latest block state.latest_block_header = get_temporary_block_header(block) # Verify proposer signature proposer = state.validator_registry[get_beacon_proposer_index(state, state.slot)] assert bls_verify( pubkey=proposer.pubkey, message_hash=signed_root(block), signature=block.signature, domain=get_domain(state.fork, get_current_epoch(state), DOMAIN_BEACON_BLOCK) ) ``` #### RANDAO ```python def process_randao(state: BeaconState, block: BeaconBlock) -> None: proposer = state.validator_registry[get_beacon_proposer_index(state, state.slot)] # Verify that the provided randao value is valid assert bls_verify( pubkey=proposer.pubkey, message_hash=hash_tree_root(get_current_epoch(state)), signature=block.body.randao_reveal, domain=get_domain(state.fork, get_current_epoch(state), DOMAIN_RANDAO) ) # Mix it in state.latest_randao_mixes[get_current_epoch(state) % LATEST_RANDAO_MIXES_LENGTH] = ( xor(get_randao_mix(state, get_current_epoch(state)), hash(block.body.randao_reveal)) ) ``` #### Eth1 data ```python def process_eth1_data(state: BeaconState, block: BeaconBlock) -> None: for eth1_data_vote in state.eth1_data_votes: # If someone else has already voted for the same hash, add to its counter if eth1_data_vote.eth1_data == block.body.eth1_data: eth1_data_vote.vote_count += 1 return # If we're seeing this hash for the first time, make a new counter state.eth1_data_votes.append(Eth1DataVote(eth1_data=block.body.eth1_data, vote_count=1)) ``` #### Transactions ##### Proposer slashings Verify that `len(block.body.proposer_slashings) <= MAX_PROPOSER_SLASHINGS`. For each `proposer_slashing` in `block.body.proposer_slashings`, run the following function: ```python def process_proposer_slashing(state: BeaconState, proposer_slashing: ProposerSlashing) -> None: """ Process ``ProposerSlashing`` transaction. Note that this function mutates ``state``. """ proposer = state.validator_registry[proposer_slashing.proposer_index] # Verify that the epoch is the same assert slot_to_epoch(proposer_slashing.header_1.slot) == slot_to_epoch(proposer_slashing.header_2.slot) # But the headers are different assert proposer_slashing.header_1 != proposer_slashing.header_2 # Proposer is not yet slashed assert proposer.slashed is False # Signatures are valid for header in (proposer_slashing.header_1, proposer_slashing.header_2): assert bls_verify( pubkey=proposer.pubkey, message_hash=signed_root(header), signature=header.signature, domain=get_domain(state.fork, slot_to_epoch(header.slot), DOMAIN_BEACON_BLOCK) ) slash_validator(state, proposer_slashing.proposer_index) ``` ##### Attester slashings Verify that `len(block.body.attester_slashings) <= MAX_ATTESTER_SLASHINGS`. For each `attester_slashing` in `block.body.attester_slashings`, run the following function: ```python def process_attester_slashing(state: BeaconState, attester_slashing: AttesterSlashing) -> None: """ Process ``AttesterSlashing`` transaction. Note that this function mutates ``state``. """ attestation1 = attester_slashing.slashable_attestation_1 attestation2 = attester_slashing.slashable_attestation_2 # Check that the attestations are conflicting assert attestation1.data != attestation2.data assert ( is_double_vote(attestation1.data, attestation2.data) or is_surround_vote(attestation1.data, attestation2.data) ) assert verify_slashable_attestation(state, attestation1) assert verify_slashable_attestation(state, attestation2) slashable_indices = [ index for index in attestation1.validator_indices if ( index in attestation2.validator_indices and state.validator_registry[index].slashed is False ) ] assert len(slashable_indices) >= 1 for index in slashable_indices: slash_validator(state, index) ``` ##### Attestations Verify that `len(block.body.attestations) <= MAX_ATTESTATIONS`. For each `attestation` in `block.body.attestations`, run the following function: ```python def process_attestation(state: BeaconState, attestation: Attestation) -> None: """ Process ``Attestation`` transaction. Note that this function mutates ``state``. """ # Can't submit attestations that are too far in history (or in prehistory) assert attestation.data.slot >= GENESIS_SLOT assert state.slot <= attestation.data.slot + SLOTS_PER_EPOCH # Can't submit attestations too quickly assert attestation.data.slot + MIN_ATTESTATION_INCLUSION_DELAY <= state.slot # Verify that the justified epoch and root is correct if slot_to_epoch(attestation.data.slot) >= get_current_epoch(state): # Case 1: current epoch attestations assert attestation.data.source_epoch == state.current_justified_epoch assert attestation.data.source_root == state.current_justified_root else: # Case 2: previous epoch attestations assert attestation.data.source_epoch == state.previous_justified_epoch assert attestation.data.source_root == state.previous_justified_root # Check that the crosslink data is valid acceptable_crosslink_data = { # Case 1: Latest crosslink matches the one in the state attestation.data.previous_crosslink, # Case 2: State has already been updated, state's latest crosslink matches the crosslink # the attestation is trying to create Crosslink( crosslink_data_root=attestation.data.crosslink_data_root, epoch=slot_to_epoch(attestation.data.slot) ) } assert state.latest_crosslinks[attestation.data.shard] in acceptable_crosslink_data # Attestation must be nonempty! assert attestation.aggregation_bitfield != b'\x00' * len(attestation.aggregation_bitfield) # Custody must be empty (to be removed in phase 1) assert attestation.custody_bitfield == b'\x00' * len(attestation.custody_bitfield) # Get the committee for the specific shard that this attestation is for crosslink_committee = [ committee for committee, shard in get_crosslink_committees_at_slot(state, attestation.data.slot) if shard == attestation.data.shard ][0] # Custody bitfield must be a subset of the attestation bitfield for i in range(len(crosslink_committee)): if get_bitfield_bit(attestation.aggregation_bitfield, i) == 0b0: assert get_bitfield_bit(attestation.custody_bitfield, i) == 0b0 # Verify aggregate signature participants = get_attestation_participants(state, attestation.data, attestation.aggregation_bitfield) custody_bit_1_participants = get_attestation_participants(state, attestation.data, attestation.custody_bitfield) custody_bit_0_participants = [i for i in participants if i not in custody_bit_1_participants] assert bls_verify_multiple( pubkeys=[ bls_aggregate_pubkeys([state.validator_registry[i].pubkey for i in custody_bit_0_participants]), bls_aggregate_pubkeys([state.validator_registry[i].pubkey for i in custody_bit_1_participants]), ], message_hashes=[ hash_tree_root(AttestationDataAndCustodyBit(data=attestation.data, custody_bit=0b0)), hash_tree_root(AttestationDataAndCustodyBit(data=attestation.data, custody_bit=0b1)), ], signature=attestation.aggregate_signature, domain=get_domain(state.fork, slot_to_epoch(attestation.data.slot), DOMAIN_ATTESTATION), ) # Crosslink data root is zero (to be removed in phase 1) assert attestation.data.crosslink_data_root == ZERO_HASH # Apply the attestation pending_attestation = PendingAttestation( data=attestation.data, aggregation_bitfield=attestation.aggregation_bitfield, custody_bitfield=attestation.custody_bitfield, inclusion_slot=state.slot ) if slot_to_epoch(attestation.data.slot) == get_current_epoch(state): state.current_epoch_attestations.append(pending_attestation) elif slot_to_epoch(attestation.data.slot) == get_previous_epoch(state): state.previous_epoch_attestations.append(pending_attestation) ``` ##### Deposits Verify that `len(block.body.deposits) <= MAX_DEPOSITS`. For each `deposit` in `block.body.deposits`, run `process_deposit(state, deposit)`. ##### Voluntary exits Verify that `len(block.body.voluntary_exits) <= MAX_VOLUNTARY_EXITS`. For each `exit` in `block.body.voluntary_exits`, run the following function: ```python def process_voluntary_exit(state: BeaconState, exit: VoluntaryExit) -> None: """ Process ``VoluntaryExit`` transaction. Note that this function mutates ``state``. """ validator = state.validator_registry[exit.validator_index] # Verify the validator has not yet exited assert validator.exit_epoch == FAR_FUTURE_EPOCH # Verify the validator has not initiated an exit assert validator.initiated_exit is False # Exits must specify an epoch when they become valid; they are not valid before then assert get_current_epoch(state) >= exit.epoch # Must have been in the validator set long enough assert get_current_epoch(state) - validator.activation_epoch >= PERSISTENT_COMMITTEE_PERIOD # Verify signature assert bls_verify( pubkey=validator.pubkey, message_hash=signed_root(exit), signature=exit.signature, domain=get_domain(state.fork, exit.epoch, DOMAIN_VOLUNTARY_EXIT) ) # Run the exit initiate_validator_exit(state, exit.validator_index) ``` ##### Transfers Note: Transfers are a temporary functionality for phases 0 and 1, to be removed in phase 2. Verify that `len(block.body.transfers) <= MAX_TRANSFERS` and that all transfers are distinct. For each `transfer` in `block.body.transfers`, run the following function: ```python def process_transfer(state: BeaconState, transfer: Transfer) -> None: """ Process ``Transfer`` transaction. Note that this function mutates ``state``. """ # Verify the amount and fee aren't individually too big (for anti-overflow purposes) assert state.validator_balances[transfer.sender] >= max(transfer.amount, transfer.fee) # Verify that we have enough ETH to send, and that after the transfer the balance will be either # exactly zero or at least MIN_DEPOSIT_AMOUNT assert ( state.validator_balances[transfer.sender] == transfer.amount + transfer.fee or state.validator_balances[transfer.sender] >= transfer.amount + transfer.fee + MIN_DEPOSIT_AMOUNT ) # A transfer is valid in only one slot assert state.slot == transfer.slot # Only withdrawn or not-yet-deposited accounts can transfer assert ( get_current_epoch(state) >= state.validator_registry[transfer.sender].withdrawable_epoch or state.validator_registry[transfer.sender].activation_epoch == FAR_FUTURE_EPOCH ) # Verify that the pubkey is valid assert ( state.validator_registry[transfer.sender].withdrawal_credentials == BLS_WITHDRAWAL_PREFIX_BYTE + hash(transfer.pubkey)[1:] ) # Verify that the signature is valid assert bls_verify( pubkey=transfer.pubkey, message_hash=signed_root(transfer), signature=transfer.signature, domain=get_domain(state.fork, slot_to_epoch(transfer.slot), DOMAIN_TRANSFER) ) # Process the transfer state.validator_balances[transfer.sender] -= transfer.amount + transfer.fee state.validator_balances[transfer.recipient] += transfer.amount state.validator_balances[get_beacon_proposer_index(state, state.slot)] += transfer.fee ``` #### State root verification Verify the block's `state_root` by running the following function: ```python def verify_block_state_root(state: BeaconState, block: BeaconBlock) -> None: assert block.state_root == hash_tree_root(state) ``` # References This section is divided into Normative and Informative references. Normative references are those that must be read in order to implement this specification, while Informative references are merely that, information. An example of the former might be the details of a required consensus algorithm, and an example of the latter might be a pointer to research that demonstrates why a particular consensus algorithm might be better suited for inclusion in the standard than another. ## Normative ## Informative _**casper-ffg**_
  _Casper the Friendly Finality Gadget_. V. Buterin and V. Griffith. URL: https://arxiv.org/abs/1710.09437 _**python-poc**_
  _Python proof-of-concept implementation_. Ethereum Foundation. URL: https://github.com/ethereum/beacon_chain # Copyright Copyright and related rights waived via [CC0](https://creativecommons.org/publicdomain/zero/1.0/).