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# Ethereum 2.0 Phase 1 -- Shard Data Chains
**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](https://github.com/ethereum/beacon_chain).
## Table of contents
<!-- TOC -->
- [Ethereum 2.0 Phase 1 -- Shard Data Chains](#ethereum-20-phase-1----shard-data-chains)
- [Table of contents](#table-of-contents)
- [Introduction](#introduction)
- [Terminology](#terminology)
- [Constants](#constants)
- [Misc](#misc)
- [Time parameters](#time-parameters)
- [Max operations per block](#max-operations-per-block)
- [Signature domains](#signature-domains)
- [Helper functions](#helper-functions)
- [`get_split_offset`](#get_split_offset)
- [`get_shuffled_committee`](#get_shuffled_committee)
- [`get_persistent_committee`](#get_persistent_committee)
- [`get_shard_proposer_index`](#get_shard_proposer_index)
- [Data Structures](#data-structures)
- [Shard chain blocks](#shard-chain-blocks)
- [Shard block processing](#shard-block-processing)
- [Verifying shard block data](#verifying-shard-block-data)
- [Verifying a crosslink](#verifying-a-crosslink)
- [Shard block fork choice rule](#shard-block-fork-choice-rule)
- [Updates to the beacon chain](#updates-to-the-beacon-chain)
- [Data structures](#data-structures)
- [`Validator`](#validator)
- [`BeaconBlockBody`](#beaconblockbody)
- [`BranchChallenge`](#branchchallenge)
- [`BranchResponse`](#branchresponse)
- [`BranchChallengeRecord`](#branchchallengerecord)
- [`SubkeyReveal`](#subkeyreveal)
- [Helpers](#helpers)
- [`get_attestation_merkle_depth`](#get_attestation_merkle_depth)
- [`epoch_to_custody_period`](#epoch_to_custody_period)
- [`slot_to_custody_period`](#slot_to_custody_period)
- [`get_current_custody_period`](#get_current_custody_period)
- [`verify_custody_subkey_reveal`](#verify_custody_subkey_reveal)
- [`prepare_validator_for_withdrawal`](#prepare_validator_for_withdrawal)
- [`penalize_validator`](#penalize_validator)
- [Per-slot processing](#per-slot-processing)
- [Operations](#operations)
- [Branch challenges](#branch-challenges)
- [Branch responses](#branch-responses)
- [Subkey reveals](#subkey-reveals)
- [Per-epoch processing](#per-epoch-processing)
- [One-time phase 1 initiation transition](#one-time-phase-1-initiation-transition)
<!-- /TOC -->
### Introduction
This document represents the specification for Phase 1 of Ethereum 2.0 -- Shard Data Chains. Phase 1 depends on the implementation of [Phase 0 -- The Beacon Chain](0_beacon-chain.md).
Ethereum 2.0 consists of a central beacon chain along with `SHARD_COUNT` shard chains. Phase 1 is primarily concerned with the construction, validity, and consensus on the _data_ of these shard chains. Phase 1 does not specify shard chain state execution or account balances. This is left for future phases.
### Terminology
### Constants
Phase 1 depends upon all of the constants defined in [Phase 0](0_beacon-chain.md#constants) in addition to the following:
#### Misc
| Name | Value | Unit |
|-------------------------------|------------------|--------|
| `SHARD_CHUNK_SIZE` | 2**5 (= 32) | bytes |
| `SHARD_BLOCK_SIZE` | 2**14 (= 16,384) | bytes |
| `MINOR_REWARD_QUOTIENT` | 2**8 (= 256) | |
#### Time parameters
| Name | Value | Unit | Duration |
| - | - | :-: | :-: |
| `CROSSLINK_LOOKBACK` | 2**5 (= 32) | slots | 3.2 minutes |
| `MAX_BRANCH_CHALLENGE_DELAY` | 2**11 (= 2,048) | epochs | 9 days |
| `CUSTODY_PERIOD_LENGTH` | 2**11 (= 2,048) | epochs | 9 days |
| `PERSISTENT_COMMITTEE_PERIOD` | 2**11 (= 2,048) | epochs | 9 days |
| `CHALLENGE_RESPONSE_DEADLINE` | 2**14 (= 16,384) | epochs | 73 days |
#### Max operations per block
| Name | Value |
|-------------------------------|---------------|
| `MAX_BRANCH_CHALLENGES` | 2**2 (= 4) |
| `MAX_BRANCH_RESPONSES` | 2**4 (= 16) |
| `MAX_EARLY_SUBKEY_REVEALS` | 2**4 (= 16) |
#### Signature domains
| Name | Value |
|------------------------|-----------------|
| `DOMAIN_SHARD_PROPOSER`| 129 |
| `DOMAIN_SHARD_ATTESTER`| 130 |
| `DOMAIN_CUSTODY_SUBKEY`| 131 |
## Helper functions
#### `get_split_offset`
````python
def get_split_offset(list_size: int, chunks: int, index: int) -> int:
"""
Returns a value such that for a list L, chunk count k and index i,
split(L, k)[i] == L[get_split_offset(len(L), k, i): get_split_offset(len(L), k+1, i)]
"""
return (len(list_size) * index) // chunks
````
#### `get_shuffled_committee`
```python
def get_shuffled_committee(state: BeaconState,
shard: Shard,
committee_start_epoch: Epoch) -> List[ValidatorIndex]:
"""
Return shuffled committee.
"""
validator_indices = get_active_validator_indices(state.validators, committee_start_epoch)
seed = generate_seed(state, committee_start_epoch)
start_offset = get_split_offset(len(validator_indices), SHARD_COUNT, shard)
end_offset = get_split_offset(len(validator_indices), SHARD_COUNT, shard + 1)
return [
validator_indices[get_permuted_index(i, len(validator_indices), seed)]
for i in range(start_offset, end_offset)
]
```
#### `get_persistent_committee`
```python
def get_persistent_committee(state: BeaconState,
shard: Shard,
epoch: Epoch) -> List[ValidatorIndex]:
"""
Return the persistent committee for the given ``shard`` at the given ``epoch``.
"""
earlier_committee_start_epoch = epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD * 2
earlier_committee = get_shuffled_committee(state, shard, earlier_committee_start_epoch)
later_committee_start_epoch = epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD
later_committee = get_shuffled_committee(state, shard, later_committee_start_epoch)
def get_switchover_epoch(index):
return (
bytes_to_int(hash(earlier_seed + bytes3(index))[0:8]) %
PERSISTENT_COMMITTEE_PERIOD
)
# Take not-yet-cycled-out validators from earlier committee and already-cycled-in validators from
# later committee; return a sorted list of the union of the two, deduplicated
return sorted(list(set(
[i for i in earlier_committee if epoch % PERSISTENT_COMMITTEE_PERIOD < get_switchover_epoch(i)] +
[i for i in later_committee if epoch % PERSISTENT_COMMITTEE_PERIOD >= get_switchover_epoch(i)]
)))
```
#### `get_shard_proposer_index`
```python
def get_shard_proposer_index(state: BeaconState,
shard: Shard,
slot: Slot) -> ValidatorIndex:
seed = hash(
state.current_shuffling_seed +
int_to_bytes8(shard) +
int_to_bytes8(slot)
)
persistent_committee = get_persistent_committee(state, shard, slot_to_epoch(slot))
# Default proposer
index = bytes_to_int(seed[0:8]) % len(persistent_committee)
# If default proposer exits, try the other proposers in order; if all are exited
# return None (ie. no block can be proposed)
validators_to_try = persistent_committee[index:] + persistent_committee[:index]
for index in validators_to_try:
if is_active_validator(state.validators[index], get_current_epoch(state)):
return index
return None
```
## Data Structures
### Shard chain blocks
A `ShardBlock` object has the following fields:
```python
{
# Slot number
'slot': 'uint64',
# What shard is it on
'shard_id': 'uint64',
# Parent block's root
'parent_root': 'bytes32',
# Beacon chain block
'beacon_chain_ref': 'bytes32',
# Merkle root of data
'data_root': 'bytes32'
# State root (placeholder for now)
'state_root': 'bytes32',
# Block signature
'signature': 'bytes96',
# Attestation
'participation_bitfield': 'bytes',
'aggregate_signature': 'bytes96',
}
```
## Shard block processing
For a `shard_block` on a shard to be processed by a node, the following conditions must be met:
* The `ShardBlock` pointed to by `shard_block.parent_root` has already been processed and accepted
* The signature for the block from the _proposer_ (see below for definition) of that block is included along with the block in the network message object
To validate a block header on shard `shard_block.shard_id`, compute as follows:
* Verify that `shard_block.beacon_chain_ref` is the hash of a block in the (canonical) beacon chain with slot less than or equal to `slot`.
* Verify that `shard_block.beacon_chain_ref` is equal to or a descendant of the `shard_block.beacon_chain_ref` specified in the `ShardBlock` pointed to by `shard_block.parent_root`.
* Let `state` be the state of the beacon chain block referred to by `shard_block.beacon_chain_ref`.
* Let `persistent_committee = get_persistent_committee(state, shard_block.shard_id, slot_to_epoch(shard_block.slot))`.
* Assert `verify_bitfield(shard_block.participation_bitfield, len(persistent_committee))`
* For every `i in range(len(persistent_committee))` where `is_active_validator(state.validators[persistent_committee[i]], get_current_epoch(state))` returns `False`, verify that `get_bitfield_bit(shard_block.participation_bitfield, i) == 0`
* Let `proposer_index = get_shard_proposer_index(state, shard_block.shard_id, shard_block.slot)`.
* Verify that `proposer_index` is not `None`.
* Let `msg` be the `shard_block` but with `shard_block.signature` set to `[0, 0]`.
* Verify that `bls_verify(pubkey=validators[proposer_index].pubkey, message_hash=hash(msg), signature=shard_block.signature, domain=get_domain(state, slot_to_epoch(shard_block.slot), DOMAIN_SHARD_PROPOSER))` passes.
* Let `group_public_key = bls_aggregate_pubkeys([state.validators[index].pubkey for i, index in enumerate(persistent_committee) if get_bitfield_bit(shard_block.participation_bitfield, i) is True])`.
* Verify that `bls_verify(pubkey=group_public_key, message_hash=shard_block.parent_root, sig=shard_block.aggregate_signature, domain=get_domain(state, slot_to_epoch(shard_block.slot), DOMAIN_SHARD_ATTESTER))` passes.
### Verifying shard block data
At network layer, we expect a shard block header to be broadcast along with its `block_body`.
* Verify that `len(block_body) == SHARD_BLOCK_SIZE`
* Verify that `merkle_root(block_body)` equals the `data_root` in the header.
### Verifying a crosslink
A node should sign a crosslink only if the following conditions hold. **If a node has the capability to perform the required level of verification, it should NOT follow chains on which a crosslink for which these conditions do NOT hold has been included, or a sufficient number of signatures have been included that during the next state recalculation, a crosslink will be registered.**
First, the conditions must recursively apply to the crosslink referenced in `last_crosslink_root` for the same shard (unless `last_crosslink_root` equals zero, in which case we are at the genesis).
Second, we verify the `shard_chain_commitment`.
* Let `start_slot = state.latest_crosslinks[shard].epoch * SLOTS_PER_EPOCH + SLOTS_PER_EPOCH - CROSSLINK_LOOKBACK`.
* Let `end_slot = attestation.data.slot - attestation.data.slot % SLOTS_PER_EPOCH - CROSSLINK_LOOKBACK`.
* Let `length = end_slot - start_slot`, `headers[0] .... headers[length-1]` be the serialized block headers in the canonical shard chain from the verifer's point of view (note that this implies that `headers` and `bodies` have been checked for validity).
* Let `bodies[0] ... bodies[length-1]` be the bodies of the blocks.
* Note: If there is a missing slot, then the header and body are the same as that of the block at the most recent slot that has a block.
We define two helpers:
```python
def pad_to_power_of_2(values: List[bytes]) -> List[bytes]:
zero_shard_block = b'\x00' * SHARD_BLOCK_SIZE
while not is_power_of_two(len(values)):
values = values + [zero_shard_block]
return values
```
```python
def merkle_root_of_bytes(data: bytes) -> bytes:
return merkle_root([data[i:i + 32] for i in range(0, len(data), 32)])
```
We define the function for computing the commitment as follows:
```python
def compute_commitment(headers: List[ShardBlock], bodies: List[bytes]) -> Bytes32:
return hash(
merkle_root(
pad_to_power_of_2([
merkle_root_of_bytes(zpad(serialize(h), SHARD_BLOCK_SIZE)) for h in headers
])
) +
merkle_root(
pad_to_power_of_2([
merkle_root_of_bytes(h) for h in bodies
])
)
)
```
The `shard_chain_commitment` is only valid if it equals `compute_commitment(headers, bodies)`.
### Shard block fork choice rule
The fork choice rule for any shard is LMD GHOST using the shard chain attestations of the persistent committee and the beacon chain attestations of the crosslink committee currently assigned to that shard, but instead of being rooted in the genesis it is rooted in the latest block referenced in the most recent accepted crosslink (ie. `state.crosslinks[shard].crosslink_data_root`). Only blocks whose `beacon_chain_ref` is the block in the main beacon chain at the specified `slot` should be considered (if the beacon chain skips a slot, then the block at that slot is considered to be the block in the beacon chain at the highest slot lower than a slot).
# Updates to the beacon chain
## Data structures
### `Validator`
Add member values to the end of the `Validator` object:
```python
'open_branch_challenges': [BranchChallengeRecord],
'next_subkey_to_reveal': 'uint64',
'reveal_max_periods_late': 'uint64',
```
And the initializers:
```python
'open_branch_challenges': [],
'next_subkey_to_reveal': get_current_custody_period(state),
'reveal_max_periods_late': 0,
```
### `BeaconBlockBody`
Add member values to the `BeaconBlockBody` structure:
```python
'branch_challenges': [BranchChallenge],
'branch_responses': [BranchResponse],
'subkey_reveals': [SubkeyReveal],
```
And initialize to the following:
```python
'branch_challenges': [],
'branch_responses': [],
'subkey_reveals': [],
```
### `BranchChallenge`
Define a `BranchChallenge` as follows:
```python
{
'responder_index': 'uint64',
'data_index': 'uint64',
'attestation': SlashableAttestation,
}
```
### `BranchResponse`
Define a `BranchResponse` as follows:
```python
{
'responder_index': 'uint64',
'data': 'bytes32',
'branch': ['bytes32'],
'data_index': 'uint64',
'root': 'bytes32',
}
```
### `BranchChallengeRecord`
Define a `BranchChallengeRecord` as follows:
```python
{
'challenger_index': 'uint64',
'root': 'bytes32',
'depth': 'uint64',
'inclusion_epoch': 'uint64',
'data_index': 'uint64',
}
```
### `SubkeyReveal`
Define a `SubkeyReveal` as follows:
```python
{
'validator_index': 'uint64',
'period': 'uint64',
'subkey': 'bytes96',
'mask': 'bytes32',
'revealer_index': 'uint64'
}
```
## Helpers
### `get_attestation_merkle_depth`
```python
def get_attestation_merkle_depth(attestation: Attestation) -> int:
start_epoch = attestation.data.latest_crosslink.epoch
end_epoch = slot_to_epoch(attestation.data.slot)
chunks_per_slot = SHARD_BLOCK_SIZE // 32
chunks = (end_epoch - start_epoch) * EPOCH_LENGTH * chunks_per_slot
return log2(next_power_of_two(chunks))
```
### `epoch_to_custody_period`
```python
def epoch_to_custody_period(epoch: Epoch) -> int:
return epoch // CUSTODY_PERIOD_LENGTH
```
### `slot_to_custody_period`
```python
def slot_to_custody_period(slot: Slot) -> int:
return epoch_to_custody_period(slot_to_epoch(slot))
```
### `get_current_custody_period`
```python
def get_current_custody_period(state: BeaconState) -> int:
return epoch_to_custody_period(get_current_epoch(state))
```
### `verify_custody_subkey_reveal`
```python
def verify_custody_subkey_reveal(pubkey: bytes48,
subkey: bytes96,
mask: bytes32,
mask_pubkey: bytes48,
period: int) -> bool:
# Legitimate reveal: checking that the provided value actually is the subkey
if mask == ZERO_HASH:
pubkeys=[pubkey]
message_hashes=[hash(int_to_bytes8(period))]
# Punitive early reveal: checking that the provided value is a valid masked subkey
# (masking done to prevent "stealing the reward" from a whistleblower by block proposers)
# Secure under the aggregate extraction infeasibility assumption described on page 11-12
# of https://crypto.stanford.edu/~dabo/pubs/papers/aggreg.pdf
else:
pubkeys=[pubkey, mask_pubkey]
message_hashes=[hash(int_to_bytes8(period)), mask]
return bls_multi_verify(
pubkeys=pubkeys,
message_hashes=message_hashes,
signature=subkey,
domain=get_domain(
fork=state.fork,
epoch=period * CUSTODY_PERIOD_LENGTH,
domain_type=DOMAIN_CUSTODY_SUBKEY,
)
)
```
### `penalize_validator`
Change the definition of `penalize_validator` as follows:
```python
def penalize_validator(state: BeaconState, index: ValidatorIndex, whistleblower_index=None:ValidatorIndex) -> None:
"""
Penalize the validator of the given ``index``.
Note that this function mutates ``state``.
"""
exit_validator(state, index)
validator = state.validator_registry[index]
state.latest_penalized_balances[get_current_epoch(state) % LATEST_PENALIZED_EXIT_LENGTH] += get_effective_balance(state, index)
block_proposer_index = get_beacon_proposer_index(state, state.slot)
whistleblower_reward = get_effective_balance(state, index) // WHISTLEBLOWER_REWARD_QUOTIENT
if whistleblower_index is None:
state.validator_balances[block_proposer_index] += whistleblower_reward
else:
state.validator_balances[whistleblower_index] += (
whistleblower_reward * INCLUDER_REWARD_QUOTIENT / (INCLUDER_REWARD_QUOTIENT + 1)
)
state.validator_balances[block_proposer_index] += whistleblower_reward / (INCLUDER_REWARD_QUOTIENT + 1)
state.validator_balances[index] -= whistleblower_reward
validator.penalized_epoch = get_current_epoch(state)
validator.withdrawable_epoch = get_current_epoch(state) + LATEST_PENALIZED_EXIT_LENGTH
```
The only change is that this introduces the possibility of a penalization where the "whistleblower" that takes credit is NOT the block proposer.
## Per-slot processing
### Operations
Add the following operations to the per-slot processing, in order the given below and _after_ all other operations (specifically, right after exits).
#### Branch challenges
Verify that `len(block.body.branch_challenges) <= MAX_BRANCH_CHALLENGES`.
For each `challenge` in `block.body.branch_challenges`:
* Verify that `slot_to_epoch(challenge.attestation.data.slot) >= get_current_epoch(state) - MAX_BRANCH_CHALLENGE_DELAY`.
* Verify that `state.validator_registry[responder_index].exit_epoch >= get_current_epoch(state) - MAX_BRANCH_CHALLENGE_DELAY`.
* Verify that `verify_slashable_attestation(state, challenge.attestation)` returns `True`.
* Verify that `challenge.responder_index` is in `challenge.attestation.validator_indices`.
* Let `depth = get_attestation_merkle_depth(challenge.attestation)`. Verify that `challenge.data_index < 2**depth`.
* Verify that there does not exist a `BranchChallengeRecord` in `state.validator_registry[challenge.responder_index].open_branch_challenges` with `root == challenge.attestation.data.shard_chain_commitment` and `data_index == data_index`.
* Append to `state.validator_registry[challenge.responder_index].open_branch_challenges` the object `BranchChallengeRecord(challenger_index=get_beacon_proposer_index(state, state.slot), root=challenge.attestation.data.shard_chain_commitment, depth=depth, inclusion_epoch=get_current_epoch(state), data_index=data_index)`.
**Invariant**: the `open_branch_challenges` array will always stay sorted in order of `inclusion_epoch`.
#### Branch responses
Verify that `len(block.body.branch_responses) <= MAX_BRANCH_RESPONSES`.
For each `response` in `block.body.branch_responses`:
* Find the `BranchChallengeRecord` in `state.validator_registry[response.responder_index].open_branch_challenges` whose (`root`, `data_index`) match the (`root`, `data_index`) of the `response`. Verify that one such record exists (it is not possible for there to be more than one), call it `record`.
* Verify that `verify_merkle_branch(leaf=response.data, branch=response.branch, depth=record.depth, index=record.data_index, root=record.root)` is True.
* Verify that `get_current_epoch(state) >= record.inclusion_epoch + ENTRY_EXIT_DELAY`.
* Remove the `record` from `state.validator_registry[response.responder_index].open_branch_challenges`
* Determine the proposer `proposer_index = get_beacon_proposer_index(state, state.slot)` and set `state.validator_balances[proposer_index] += base_reward(state, index) // MINOR_REWARD_QUOTIENT`.
#### Subkey reveals
Verify that `len(block.body.early_subkey_reveals) <= MAX_EARLY_SUBKEY_REVEALS`.
For each `reveal` in `block.body.early_subkey_reveals`:
* Verify that `verify_custody_subkey_reveal(state.validator_registry[reveal.validator_index].pubkey, reveal.subkey, reveal.period, reveal.mask, state.validator_registry[reveal.revealer_index].pubkey)` returns `True`.
* Let `is_early_reveal = reveal.period > get_current_custody_period(state) or (reveal.period == get_current_custody_period(state) and state.validator_registry[reveal.validator_index].exit_epoch > get_current_epoch(state))` (ie. either the reveal is of a future period, or it's of the current period and the validator is still active)
* Verify that one of the following is true:
* (i) `is_early_reveal` is `True`
* (ii) `is_early_reveal` is `False` and `reveal.period == state.validator_registry[reveal.validator_index].next_subkey_to_reveal` (revealing a past subkey, or a current subkey for a validator that has exited) and `reveal.mask == ZERO_HASH`
In case (i):
* Verify that `state.validator_registry[reveal.validator_index].penalized_epoch > get_current_epoch(state).
* Run `penalize_validator(state, reveal.validator_index, reveal.revealer_index)`.
* Set `state.validator_balances[reveal.revealer_index] += base_reward(state, index) // MINOR_REWARD_QUOTIENT`
In case (ii):
* Determine the proposer `proposer_index = get_beacon_proposer_index(state, state.slot)` and set `state.validator_balances[proposer_index] += base_reward(state, index) // MINOR_REWARD_QUOTIENT`.
* Set `state.validator_registry[reveal.validator_index].next_subkey_to_reveal += 1`
* Set `state.validator_registry[reveal.validator_index].reveal_max_periods_late = max(state.validator_registry[reveal.validator_index].reveal_max_periods_late, get_current_period(state) - reveal.period)`.
## Per-epoch processing
Add the following loop immediately below the `process_ejections` loop:
```python
def process_challenge_absences(state: BeaconState) -> None:
"""
Iterate through the validator registry
and penalize validators with balance that did not answer challenges.
"""
for index, validator in enumerate(state.validator_registry):
if len(validator.open_branch_challenges) > 0 and get_current_epoch(state) > validator.open_branch_challenges[0].inclusion_epoch + CHALLENGE_RESPONSE_DEADLINE:
penalize_validator(state, index, validator.open_branch_challenges[0].challenger_index)
```
In `process_penalties_and_exits`, change the definition of `eligible` to the following (note that it is not a pure function because `state` is declared in the surrounding scope):
```python
def eligible(index):
validator = state.validator_registry[index]
# Cannot exit if there are still open branch challenges
if len(validator.open_branch_challenges) > 0:
return False
# Cannot exit if you have not revealed all of your subkeys
elif validator.next_subkey_to_reveal <= epoch_to_custody_period(validator.exit_epoch):
return False
# Cannot exit if you already have
elif validator.withdrawable_epoch < FAR_FUTURE_EPOCH:
return False
# Return minimum time
else:
return current_epoch >= validator.exit_epoch + MIN_VALIDATOR_WITHDRAWAL_EPOCHS
```
## One-time phase 1 initiation transition
Run the following on the fork block after per-slot processing and before per-block and per-epoch processing.
For all `validator` in `ValidatorRegistry`, update it to the new format and fill the new member values with:
```python
'open_branch_challenges': [],
'next_subkey_to_reveal': get_current_custody_period(state),
'reveal_max_periods_late': 0,
```
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