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eth2.0-specs/specs/core/1_shard-data-chains.md

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Ethereum 2.0 Phase 1 -- Shard Data Chains

tags: spec, eth2.0, casper, sharding

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.

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.

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 in addition to the following:

Constant Value Unit Approximation
SHARD_CHUNK_SIZE 2**5 (= 32) bytes
SHARD_BLOCK_SIZE 2**14 (= 16,384) bytes
CROSSLINK_LOOKBACK 2**5 (= 32) slots
PERSISTENT_COMMITTEE_PERIOD 2**11 (= 2,048) epochs 9 days

Flags, domains, etc.

Constant Value
SHARD_PROPOSER_DOMAIN 129
SHARD_ATTESTER_DOMAIN 130

Helper functions

get_split_offset

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

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

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

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:

{
    # 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), SHARD_PROPOSER_DOMAIN)) 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), SHARD_ATTESTER_DOMAIN)) 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:

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

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:

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 block referenced in the most recent accepted crosslink (ie. state.crosslinks[shard].shard_block_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).