Ethereum Specification

Table of Contents

Introduction

Entry point for the Ethereum specification.

Module Contents

Classes

BlockChain

History and current state of the block chain.

Functions

`apply_fork`	Transforms the state from the previous hard fork (old) into the block
`get_last_256_block_hashes`	Obtain the list of hashes of the previous 256 blocks in order of
`state_transition`	Attempts to apply a block to an existing block chain.
`calculate_base_fee_per_gas`	Calculates the base fee per gas for the block.
`validate_header`	Verifies a block header.
`check_transaction`	Check if the transaction is includable in the block.
`make_receipt`	Make the receipt for a transaction that was executed.
`apply_body`	Executes a block.
`process_transaction`	Execute a transaction against the provided environment.
`validate_transaction`	Verifies a transaction.
`calculate_intrinsic_cost`	Calculates the gas that is charged before execution is started.
`recover_sender`	Extracts the sender address from a transaction.
`signing_hash_pre155`	Compute the hash of a transaction used in a legacy (pre EIP 155) signature.
`signing_hash_155`	Compute the hash of a transaction used in a EIP 155 signature.
`signing_hash_2930`	Compute the hash of a transaction used in a EIP 2930 signature.
`signing_hash_1559`	Compute the hash of a transaction used in a EIP 1559 signature.
`compute_header_hash`	Computes the hash of a block header.
`check_gas_limit`	Validates the gas limit for a block.

Attributes

`BASE_FEE_MAX_CHANGE_DENOMINATOR`
`ELASTICITY_MULTIPLIER`
`GAS_LIMIT_ADJUSTMENT_FACTOR`
`GAS_LIMIT_MINIMUM`
`EMPTY_OMMER_HASH`

Module Details

BASE_FEE_MAX_CHANGE_DENOMINATOR

BASE_FEE_MAX_CHANGE_DENOMINATOR

BASE_FEE_MAX_CHANGE_DENOMINATOR = 8

ELASTICITY_MULTIPLIER

ELASTICITY_MULTIPLIER

ELASTICITY_MULTIPLIER = 2

GAS_LIMIT_ADJUSTMENT_FACTOR

GAS_LIMIT_ADJUSTMENT_FACTOR

GAS_LIMIT_ADJUSTMENT_FACTOR = 1024

GAS_LIMIT_MINIMUM

GAS_LIMIT_MINIMUM

GAS_LIMIT_MINIMUM = 5000

EMPTY_OMMER_HASH

EMPTY_OMMER_HASH

EMPTY_OMMER_HASH = keccak256(rlp.encode([]))

BlockChain

History and current state of the block chain.

class BlockChain

blocks :List[ethereum.shanghai.fork_types.Block]

state :ethereum.shanghai.state.State

chain_id :ethereum.base_types.U64

apply_fork

apply_fork(old: BlockChain) → BlockChain 

Transforms the state from the previous hard fork (old) into the block chain object for this hard fork and returns it.

When forks need to implement an irregular state transition, this function is used to handle the irregularity. See the DAO Fork for an example.

Parameters: old – Previous block chain object.
Returns: new – Upgraded block chain object for this hard fork.
Return type: BlockChain

def apply_fork(old: BlockChain) -> BlockChain:
    return old

get_last_256_block_hashes

get_last_256_block_hashes(chain: BlockChain) → List[ethereum.crypto.hash.Hash32]

Obtain the list of hashes of the previous 256 blocks in order of increasing block number.

This function will return less hashes for the first 256 blocks.

The BLOCKHASH opcode needs to access the latest hashes on the chain, therefore this function retrieves them.

Parameters: chain – History and current state.
Returns: recent_block_hashes – Hashes of the recent 256 blocks in order of increasing block number.
Return type: List[Hash32]

def get_last_256_block_hashes(chain: BlockChain) -> List[Hash32]:
    recent_blocks = chain.blocks[-255:]
    # TODO: This function has not been tested rigorously
    if len(recent_blocks) == 0:
        return []

    recent_block_hashes = []

    for block in recent_blocks:
        prev_block_hash = block.header.parent_hash
        recent_block_hashes.append(prev_block_hash)

    # We are computing the hash only for the most recent block and not for
    # the rest of the blocks as they have successors which have the hash of
    # the current block as parent hash.
    most_recent_block_hash = keccak256(rlp.encode(recent_blocks[-1].header))
    recent_block_hashes.append(most_recent_block_hash)

    return recent_block_hashes

state_transition

state_transition(chain: BlockChain, block: ethereum.shanghai.fork_types.Block) → None

Attempts to apply a block to an existing block chain.

All parts of the block’s contents need to be verified before being added to the chain. Blocks are verified by ensuring that the contents of the block make logical sense with the contents of the parent block. The information in the block’s header must also match the corresponding information in the block.

To implement Ethereum, in theory clients are only required to store the most recent 255 blocks of the chain since as far as execution is concerned, only those blocks are accessed. Practically, however, clients should store more blocks to handle reorgs.

Parameters

chain – History and current state.
block – Block to apply to chain.

def state_transition(chain: BlockChain, block: Block) -> None:
    parent_header = chain.blocks[-1].header
    validate_header(block.header, parent_header)
    ensure(block.ommers == (), InvalidBlock)
    (
        gas_used,
        transactions_root,
        receipt_root,
        block_logs_bloom,
        state,
        withdrawals_root,
    ) = apply_body(
        chain.state,
        get_last_256_block_hashes(chain),
        block.header.coinbase,
        block.header.number,
        block.header.base_fee_per_gas,
        block.header.gas_limit,
        block.header.timestamp,
        block.header.prev_randao,
        block.transactions,
        chain.chain_id,
        block.withdrawals,
    )
    ensure(gas_used == block.header.gas_used, InvalidBlock)
    ensure(transactions_root == block.header.transactions_root, InvalidBlock)
    ensure(state_root(state) == block.header.state_root, InvalidBlock)
    ensure(receipt_root == block.header.receipt_root, InvalidBlock)
    ensure(block_logs_bloom == block.header.bloom, InvalidBlock)
    ensure(withdrawals_root == block.header.withdrawals_root, InvalidBlock)

    chain.blocks.append(block)
    if len(chain.blocks) > 255:
        # Real clients have to store more blocks to deal with reorgs, but the
        # protocol only requires the last 255
        chain.blocks = chain.blocks[-255:]

calculate_base_fee_per_gas

calculate_base_fee_per_gas(block_gas_limit: ethereum.base_types.Uint, parent_gas_limit: ethereum.base_types.Uint, parent_gas_used: ethereum.base_types.Uint, parent_base_fee_per_gas: ethereum.base_types.Uint) → ethereum.base_types.Uint 

Calculates the base fee per gas for the block.

Parameters

block_gas_limit – Gas limit of the block for which the base fee is being calculated.
parent_gas_limit – Gas limit of the parent block.
parent_gas_used – Gas used in the parent block.
parent_base_fee_per_gas – Base fee per gas of the parent block.

Returns

base_fee_per_gas – Base fee per gas for the block.

Return type

Uint

def calculate_base_fee_per_gas(
    block_gas_limit: Uint,
    parent_gas_limit: Uint,
    parent_gas_used: Uint,
    parent_base_fee_per_gas: Uint,
) -> Uint:
    parent_gas_target = parent_gas_limit // ELASTICITY_MULTIPLIER

    ensure(
        check_gas_limit(block_gas_limit, parent_gas_limit),
        InvalidBlock,
    )

    if parent_gas_used == parent_gas_target:
        expected_base_fee_per_gas = parent_base_fee_per_gas
    elif parent_gas_used > parent_gas_target:
        gas_used_delta = parent_gas_used - parent_gas_target

        parent_fee_gas_delta = parent_base_fee_per_gas * gas_used_delta
        target_fee_gas_delta = parent_fee_gas_delta // parent_gas_target

        base_fee_per_gas_delta = max(
            target_fee_gas_delta // BASE_FEE_MAX_CHANGE_DENOMINATOR,
            1,
        )

        expected_base_fee_per_gas = (
            parent_base_fee_per_gas + base_fee_per_gas_delta
        )
    else:
        gas_used_delta = parent_gas_target - parent_gas_used

        parent_fee_gas_delta = parent_base_fee_per_gas * gas_used_delta
        target_fee_gas_delta = parent_fee_gas_delta // parent_gas_target

        base_fee_per_gas_delta = (
            target_fee_gas_delta // BASE_FEE_MAX_CHANGE_DENOMINATOR
        )

        expected_base_fee_per_gas = (
            parent_base_fee_per_gas - base_fee_per_gas_delta
        )

    return Uint(expected_base_fee_per_gas)

validate_header

validate_header(header: ethereum.shanghai.fork_types.Header, parent_header: ethereum.shanghai.fork_types.Header) → None

Verifies a block header.

In order to consider a block’s header valid, the logic for the quantities in the header should match the logic for the block itself. For example the header timestamp should be greater than the block’s parent timestamp because the block was created after the parent block. Additionally, the block’s number should be directly folowing the parent block’s number since it is the next block in the sequence.

Parameters

header – Header to check for correctness.
parent_header – Parent Header of the header to check for correctness

def validate_header(header: Header, parent_header: Header) -> None:
    ensure(header.gas_used <= header.gas_limit, InvalidBlock)

    expected_base_fee_per_gas = calculate_base_fee_per_gas(
        header.gas_limit,
        parent_header.gas_limit,
        parent_header.gas_used,
        parent_header.base_fee_per_gas,
    )

    ensure(expected_base_fee_per_gas == header.base_fee_per_gas, InvalidBlock)

    ensure(header.timestamp > parent_header.timestamp, InvalidBlock)
    ensure(header.number == parent_header.number + 1, InvalidBlock)
    ensure(len(header.extra_data) <= 32, InvalidBlock)

    ensure(header.difficulty == 0, InvalidBlock)
    ensure(header.nonce == b"\x00\x00\x00\x00\x00\x00\x00\x00", InvalidBlock)
    ensure(header.ommers_hash == EMPTY_OMMER_HASH, InvalidBlock)

    block_parent_hash = keccak256(rlp.encode(parent_header))
    ensure(header.parent_hash == block_parent_hash, InvalidBlock)

check_transaction

check_transaction(tx: ethereum.shanghai.fork_types.Transaction, base_fee_per_gas: ethereum.base_types.Uint, gas_available: ethereum.base_types.Uint, chain_id: ethereum.base_types.U64) → Tuple[ethereum.shanghai.fork_types.Address, ethereum.base_types.Uint]

Check if the transaction is includable in the block.

Parameters

tx – The transaction.
base_fee_per_gas – The block base fee.
gas_available – The gas remaining in the block.
chain_id – The ID of the current chain.

Returns

sender_address – The sender of the transaction.
effective_gas_price – The price to charge for gas when the transaction is executed.

Raises

InvalidBlock : – If the transaction is not includable.

def check_transaction(
    tx: Transaction,
    base_fee_per_gas: Uint,
    gas_available: Uint,
    chain_id: U64,
) -> Tuple[Address, Uint]:
    ensure(tx.gas <= gas_available, InvalidBlock)
    sender_address = recover_sender(chain_id, tx)

    if isinstance(tx, FeeMarketTransaction):
        ensure(tx.max_fee_per_gas >= tx.max_priority_fee_per_gas, InvalidBlock)
        ensure(tx.max_fee_per_gas >= base_fee_per_gas, InvalidBlock)

        priority_fee_per_gas = min(
            tx.max_priority_fee_per_gas,
            tx.max_fee_per_gas - base_fee_per_gas,
        )
        effective_gas_price = priority_fee_per_gas + base_fee_per_gas
    else:
        ensure(tx.gas_price >= base_fee_per_gas, InvalidBlock)
        effective_gas_price = tx.gas_price

    return sender_address, effective_gas_price

make_receipt

make_receipt(tx: ethereum.shanghai.fork_types.Transaction, has_erred: bool, cumulative_gas_used: ethereum.base_types.Uint, logs: Tuple[ethereum.shanghai.fork_types.Log, Ellipsis]) → Union[ethereum.base_types.Bytes, ethereum.shanghai.fork_types.Receipt]

Make the receipt for a transaction that was executed.

Parameters

tx – The executed transaction.
has_erred – Whether the top level frame of the transaction exited with an error.
cumulative_gas_used – The total gas used so far in the block after the transaction was executed.
logs – The logs produced by the transaction.

Returns

The receipt for the transaction.

Return type

receipt

def make_receipt(
    tx: Transaction,
    has_erred: bool,
    cumulative_gas_used: Uint,
    logs: Tuple[Log, ...],
) -> Union[Bytes, Receipt]:
    receipt = Receipt(
        succeeded=not has_erred,
        cumulative_gas_used=cumulative_gas_used,
        bloom=logs_bloom(logs),
        logs=logs,
    )

    if isinstance(tx, AccessListTransaction):
        return b"\x01" + rlp.encode(receipt)
    if isinstance(tx, FeeMarketTransaction):
        return b"\x02" + rlp.encode(receipt)
    else:
        return receipt

apply_body

apply_body(state: ethereum.shanghai.state.State, block_hashes: List[ethereum.crypto.hash.Hash32], coinbase: ethereum.shanghai.fork_types.Address, block_number: ethereum.base_types.Uint, base_fee_per_gas: ethereum.base_types.Uint, block_gas_limit: ethereum.base_types.Uint, block_time: ethereum.base_types.U256, prev_randao: ethereum.base_types.Bytes32, transactions: Tuple[Union[ethereum.shanghai.fork_types.LegacyTransaction, ethereum.base_types.Bytes], Ellipsis], chain_id: ethereum.base_types.U64, withdrawals: Tuple[ethereum.shanghai.fork_types.Withdrawal, Ellipsis]) → Tuple[ethereum.base_types.Uint, ethereum.shanghai.fork_types.Root, ethereum.shanghai.fork_types.Root, ethereum.shanghai.fork_types.Bloom, ethereum.shanghai.state.State, ethereum.shanghai.fork_types.Root]

Executes a block.

Many of the contents of a block are stored in data structures called tries. There is a transactions trie which is similar to a ledger of the transactions stored in the current block. There is also a receipts trie which stores the results of executing a transaction, like the post state and gas used. This function creates and executes the block that is to be added to the chain.

Parameters

state – Current account state.
block_hashes – List of hashes of the previous 256 blocks in the order of increasing block number.
coinbase – Address of account which receives block reward and transaction fees.
block_number – Position of the block within the chain.
base_fee_per_gas – Base fee per gas of within the block.
block_gas_limit – Initial amount of gas available for execution in this block.
block_time – Time the block was produced, measured in seconds since the epoch.
prev_randao – The previous randao from the beacon chain.
transactions – Transactions included in the block.
ommers – Headers of ancestor blocks which are not direct parents (formerly uncles.)
chain_id – ID of the executing chain.
withdrawals – Withdrawals to be processed in the current block.

Returns

gas_available (ethereum.base_types.Uint) – Remaining gas after all transactions have been executed.
transactions_root (ethereum.fork_types.Root) – Trie root of all the transactions in the block.
receipt_root (ethereum.fork_types.Root) – Trie root of all the receipts in the block.
block_logs_bloom (Bloom) – Logs bloom of all the logs included in all the transactions of the block.
state (ethereum.fork_types.State) – State after all transactions have been executed.

def apply_body(
    state: State,
    block_hashes: List[Hash32],
    coinbase: Address,
    block_number: Uint,
    base_fee_per_gas: Uint,
    block_gas_limit: Uint,
    block_time: U256,
    prev_randao: Bytes32,
    transactions: Tuple[Union[LegacyTransaction, Bytes], ...],
    chain_id: U64,
    withdrawals: Tuple[Withdrawal, ...],
) -> Tuple[Uint, Root, Root, Bloom, State, Root]:
    gas_available = block_gas_limit
    transactions_trie: Trie[
        Bytes, Optional[Union[Bytes, LegacyTransaction]]
    ] = Trie(secured=False, default=None)
    receipts_trie: Trie[Bytes, Optional[Union[Bytes, Receipt]]] = Trie(
        secured=False, default=None
    )
    withdrawals_trie: Trie[Bytes, Optional[Union[Bytes, Withdrawal]]] = Trie(
        secured=False, default=None
    )
    block_logs: Tuple[Log, ...] = ()

    for i, tx in enumerate(map(decode_transaction, transactions)):
        trie_set(
            transactions_trie, rlp.encode(Uint(i)), encode_transaction(tx)
        )

        sender_address, effective_gas_price = check_transaction(
            tx, base_fee_per_gas, gas_available, chain_id
        )

        env = vm.Environment(
            caller=sender_address,
            origin=sender_address,
            block_hashes=block_hashes,
            coinbase=coinbase,
            number=block_number,
            gas_limit=block_gas_limit,
            base_fee_per_gas=base_fee_per_gas,
            gas_price=effective_gas_price,
            time=block_time,
            prev_randao=prev_randao,
            state=state,
            chain_id=chain_id,
            traces=[],
        )

        gas_used, logs, has_erred = process_transaction(env, tx)
        gas_available -= gas_used

        receipt = make_receipt(
            tx, has_erred, (block_gas_limit - gas_available), logs
        )

        trie_set(
            receipts_trie,
            rlp.encode(Uint(i)),
            receipt,
        )

        block_logs += logs

    block_gas_used = block_gas_limit - gas_available

    block_logs_bloom = logs_bloom(block_logs)

    for i, wd in enumerate(withdrawals):
        trie_set(withdrawals_trie, rlp.encode(Uint(i)), rlp.encode(wd))

        process_withdrawal(state, wd)

        if account_exists_and_is_empty(state, wd.address):
            destroy_account(state, wd.address)

    return (
        block_gas_used,
        root(transactions_trie),
        root(receipts_trie),
        block_logs_bloom,
        state,
        root(withdrawals_trie),
    )

process_transaction

process_transaction(env: ethereum.shanghai.vm.Environment, tx: ethereum.shanghai.fork_types.Transaction) → Tuple[ethereum.base_types.Uint, Tuple[ethereum.shanghai.fork_types.Log, Ellipsis], bool]

Execute a transaction against the provided environment.

This function processes the actions needed to execute a transaction. It decrements the sender’s account after calculating the gas fee and refunds them the proper amount after execution. Calling contracts, deploying code, and incrementing nonces are all examples of actions that happen within this function or from a call made within this function.

Accounts that are marked for deletion are processed and destroyed after execution.

Parameters

env – Environment for the Ethereum Virtual Machine.
tx – Transaction to execute.

Returns

gas_left (ethereum.base_types.U256) – Remaining gas after execution.
logs (Tuple[ethereum.fork_types.Log, …]) – Logs generated during execution.

def process_transaction(
    env: vm.Environment, tx: Transaction
) -> Tuple[Uint, Tuple[Log, ...], bool]:
    ensure(validate_transaction(tx), InvalidBlock)

    sender = env.origin
    sender_account = get_account(env.state, sender)

    if isinstance(tx, FeeMarketTransaction):
        gas_fee = tx.gas * tx.max_fee_per_gas
    else:
        gas_fee = tx.gas * tx.gas_price

    ensure(sender_account.nonce == tx.nonce, InvalidBlock)
    ensure(sender_account.balance >= gas_fee + tx.value, InvalidBlock)
    ensure(sender_account.code == bytearray(), InvalidBlock)

    effective_gas_fee = tx.gas * env.gas_price

    gas = tx.gas - calculate_intrinsic_cost(tx)
    increment_nonce(env.state, sender)

    sender_balance_after_gas_fee = sender_account.balance - effective_gas_fee
    set_account_balance(env.state, sender, sender_balance_after_gas_fee)

    preaccessed_addresses = set()
    preaccessed_storage_keys = set()
    preaccessed_addresses.add(env.coinbase)
    if isinstance(tx, (AccessListTransaction, FeeMarketTransaction)):
        for (address, keys) in tx.access_list:
            preaccessed_addresses.add(address)
            for key in keys:
                preaccessed_storage_keys.add((address, key))

    message = prepare_message(
        sender,
        tx.to,
        tx.value,
        tx.data,
        gas,
        env,
        preaccessed_addresses=frozenset(preaccessed_addresses),
        preaccessed_storage_keys=frozenset(preaccessed_storage_keys),
    )

    output = process_message_call(message, env)

    gas_used = tx.gas - output.gas_left
    gas_refund = min(gas_used // 5, output.refund_counter)
    gas_refund_amount = (output.gas_left + gas_refund) * env.gas_price

    # For non-1559 transactions env.gas_price == tx.gas_price
    priority_fee_per_gas = env.gas_price - env.base_fee_per_gas
    transaction_fee = (
        tx.gas - output.gas_left - gas_refund
    ) * priority_fee_per_gas

    total_gas_used = gas_used - gas_refund

    # refund gas
    sender_balance_after_refund = (
        get_account(env.state, sender).balance + gas_refund_amount
    )
    set_account_balance(env.state, sender, sender_balance_after_refund)

    # transfer miner fees
    coinbase_balance_after_mining_fee = (
        get_account(env.state, env.coinbase).balance + transaction_fee
    )
    if coinbase_balance_after_mining_fee != 0:
        set_account_balance(
            env.state, env.coinbase, coinbase_balance_after_mining_fee
        )
    elif account_exists_and_is_empty(env.state, env.coinbase):
        destroy_account(env.state, env.coinbase)

    for address in output.accounts_to_delete:
        destroy_account(env.state, address)

    for address in output.touched_accounts:
        if account_exists_and_is_empty(env.state, address):
            destroy_account(env.state, address)

    return total_gas_used, output.logs, output.has_erred

validate_transaction

validate_transaction(tx: ethereum.shanghai.fork_types.Transaction) → bool

Verifies a transaction.

The gas in a transaction gets used to pay for the intrinsic cost of operations, therefore if there is insufficient gas then it would not be possible to execute a transaction and it will be declared invalid.

Additionally, the nonce of a transaction must not equal or exceed the limit defined in EIP-2681. In practice, defining the limit as 2**64-1 has no impact because sending 2**64-1 transactions is improbable. It’s not strictly impossible though, 2**64-1 transactions is the entire capacity of the Ethereum blockchain at 2022 gas limits for a little over 22 years.

Parameters: tx – Transaction to validate.
Returns: verified – True if the transaction can be executed, or False otherwise.
Return type: bool

def validate_transaction(tx: Transaction) -> bool:
    if calculate_intrinsic_cost(tx) > tx.gas:
        return False
    if tx.nonce >= 2**64 - 1:
        return False
    if tx.to == Bytes0(b"") and len(tx.data) > 2 * MAX_CODE_SIZE:
        return False

    return True

calculate_intrinsic_cost

calculate_intrinsic_cost(tx: ethereum.shanghai.fork_types.Transaction) → ethereum.base_types.Uint 

Calculates the gas that is charged before execution is started.

The intrinsic cost of the transaction is charged before execution has begun. Functions/operations in the EVM cost money to execute so this intrinsic cost is for the operations that need to be paid for as part of the transaction. Data transfer, for example, is part of this intrinsic cost. It costs ether to send data over the wire and that ether is accounted for in the intrinsic cost calculated in this function. This intrinsic cost must be calculated and paid for before execution in order for all operations to be implemented.

Parameters: tx – Transaction to compute the intrinsic cost of.
Returns: verified – The intrinsic cost of the transaction.
Return type: ethereum.base_types.Uint

def calculate_intrinsic_cost(tx: Transaction) -> Uint:
    data_cost = 0

    for byte in tx.data:
        if byte == 0:
            data_cost += TX_DATA_COST_PER_ZERO
        else:
            data_cost += TX_DATA_COST_PER_NON_ZERO

    if tx.to == Bytes0(b""):
        create_cost = TX_CREATE_COST + int(init_code_cost(Uint(len(tx.data))))
    else:
        create_cost = 0

    access_list_cost = 0
    if isinstance(tx, (AccessListTransaction, FeeMarketTransaction)):
        for (_address, keys) in tx.access_list:
            access_list_cost += TX_ACCESS_LIST_ADDRESS_COST
            access_list_cost += len(keys) * TX_ACCESS_LIST_STORAGE_KEY_COST

    return Uint(TX_BASE_COST + data_cost + create_cost + access_list_cost)

recover_sender

recover_sender(chain_id: ethereum.base_types.U64, tx: ethereum.shanghai.fork_types.Transaction) → ethereum.shanghai.fork_types.Address 

Extracts the sender address from a transaction.

The v, r, and s values are the three parts that make up the signature of a transaction. In order to recover the sender of a transaction the two components needed are the signature (v, r, and s) and the signing hash of the transaction. The sender’s public key can be obtained with these two values and therefore the sender address can be retrieved.

Parameters

tx – Transaction of interest.
chain_id – ID of the executing chain.

Returns

sender – The address of the account that signed the transaction.

Return type

ethereum.fork_types.Address

def recover_sender(chain_id: U64, tx: Transaction) -> Address:
    r, s = tx.r, tx.s

    ensure(0 < r and r < SECP256K1N, InvalidBlock)
    ensure(0 < s and s <= SECP256K1N // 2, InvalidBlock)

    if isinstance(tx, LegacyTransaction):
        v = tx.v
        if v == 27 or v == 28:
            public_key = secp256k1_recover(
                r, s, v - 27, signing_hash_pre155(tx)
            )
        else:
            ensure(
                v == 35 + chain_id * 2 or v == 36 + chain_id * 2, InvalidBlock
            )
            public_key = secp256k1_recover(
                r, s, v - 35 - chain_id * 2, signing_hash_155(tx, chain_id)
            )
    elif isinstance(tx, AccessListTransaction):
        public_key = secp256k1_recover(
            r, s, tx.y_parity, signing_hash_2930(tx)
        )
    elif isinstance(tx, FeeMarketTransaction):
        public_key = secp256k1_recover(
            r, s, tx.y_parity, signing_hash_1559(tx)
        )

    return Address(keccak256(public_key)[12:32])

signing_hash_pre155

signing_hash_pre155(tx: ethereum.shanghai.fork_types.LegacyTransaction) → ethereum.crypto.hash.Hash32 

Compute the hash of a transaction used in a legacy (pre EIP 155) signature.

Parameters: tx – Transaction of interest.
Returns: hash – Hash of the transaction.
Return type: ethereum.crypto.hash.Hash32

def signing_hash_pre155(tx: LegacyTransaction) -> Hash32:
    return keccak256(
        rlp.encode(
            (
                tx.nonce,
                tx.gas_price,
                tx.gas,
                tx.to,
                tx.value,
                tx.data,
            )
        )
    )

signing_hash_155

signing_hash_155(tx: ethereum.shanghai.fork_types.LegacyTransaction, chain_id: ethereum.base_types.U64) → ethereum.crypto.hash.Hash32 

Compute the hash of a transaction used in a EIP 155 signature.

Parameters

tx – Transaction of interest.
chain_id – The id of the current chain.

Returns

hash – Hash of the transaction.

Return type

ethereum.crypto.hash.Hash32

def signing_hash_155(tx: LegacyTransaction, chain_id: U64) -> Hash32:
    return keccak256(
        rlp.encode(
            (
                tx.nonce,
                tx.gas_price,
                tx.gas,
                tx.to,
                tx.value,
                tx.data,
                chain_id,
                Uint(0),
                Uint(0),
            )
        )
    )

signing_hash_2930

signing_hash_2930(tx: ethereum.shanghai.fork_types.AccessListTransaction) → ethereum.crypto.hash.Hash32 

Compute the hash of a transaction used in a EIP 2930 signature.

Parameters: tx – Transaction of interest.
Returns: hash – Hash of the transaction.
Return type: ethereum.crypto.hash.Hash32

def signing_hash_2930(tx: AccessListTransaction) -> Hash32:
    return keccak256(
        b"\x01"
        + rlp.encode(
            (
                tx.chain_id,
                tx.nonce,
                tx.gas_price,
                tx.gas,
                tx.to,
                tx.value,
                tx.data,
                tx.access_list,
            )
        )
    )

signing_hash_1559

signing_hash_1559(tx: ethereum.shanghai.fork_types.FeeMarketTransaction) → ethereum.crypto.hash.Hash32 

Compute the hash of a transaction used in a EIP 1559 signature.

Parameters: tx – Transaction of interest.
Returns: hash – Hash of the transaction.
Return type: ethereum.crypto.hash.Hash32

def signing_hash_1559(tx: FeeMarketTransaction) -> Hash32:
    return keccak256(
        b"\x02"
        + rlp.encode(
            (
                tx.chain_id,
                tx.nonce,
                tx.max_priority_fee_per_gas,
                tx.max_fee_per_gas,
                tx.gas,
                tx.to,
                tx.value,
                tx.data,
                tx.access_list,
            )
        )
    )

compute_header_hash

compute_header_hash(header: ethereum.shanghai.fork_types.Header) → ethereum.crypto.hash.Hash32 

Computes the hash of a block header.

The header hash of a block is the canonical hash that is used to refer to a specific block and completely distinguishes a block from another.

keccak256 is a function that produces a 256 bit hash of any input. It also takes in any number of bytes as an input and produces a single hash for them. A hash is a completely unique output for a single input. So an input corresponds to one unique hash that can be used to identify the input exactly.

Prior to using the keccak256 hash function, the header must be encoded using the Recursive-Length Prefix. See Recursive Length Prefix (RLP) Encoding. RLP encoding the header converts it into a space-efficient format that allows for easy transfer of data between nodes. The purpose of RLP is to encode arbitrarily nested arrays of binary data, and RLP is the primary encoding method used to serialize objects in Ethereum’s execution layer. The only purpose of RLP is to encode structure; encoding specific data types (e.g. strings, floats) is left up to higher-order protocols.

Parameters: header – Header of interest.
Returns: hash – Hash of the header.
Return type: ethereum.crypto.hash.Hash32

def compute_header_hash(header: Header) -> Hash32:
    return keccak256(rlp.encode(header))

check_gas_limit

check_gas_limit(gas_limit: ethereum.base_types.Uint, parent_gas_limit: ethereum.base_types.Uint) → bool

Validates the gas limit for a block.

The bounds of the gas limit, max_adjustment_delta, is set as the quotient of the parent block’s gas limit and the GAS_LIMIT_ADJUSTMENT_FACTOR. Therefore, if the gas limit that is passed through as a parameter is greater than or equal to the sum of the parent’s gas and the adjustment delta then the limit for gas is too high and fails this function’s check. Similarly, if the limit is less than or equal to the difference of the parent’s gas and the adjustment delta or the predefined GAS_LIMIT_MINIMUM then this function’s check fails because the gas limit doesn’t allow for a sufficient or reasonable amount of gas to be used on a block.

Parameters

gas_limit – Gas limit to validate.
parent_gas_limit – Gas limit of the parent block.

Returns

check – True if gas limit constraints are satisfied, False otherwise.

Return type

bool

def check_gas_limit(gas_limit: Uint, parent_gas_limit: Uint) -> bool:
    max_adjustment_delta = parent_gas_limit // GAS_LIMIT_ADJUSTMENT_FACTOR
    if gas_limit >= parent_gas_limit + max_adjustment_delta:
        return False
    if gas_limit <= parent_gas_limit - max_adjustment_delta:
        return False
    if gas_limit < GAS_LIMIT_MINIMUM:
        return False

    return True