eth2.0-specs/specs/core/1_new_shards.md

Ethereum 2.0 Phase 1 -- Crosslinks and Shard Data

Notice: This document is a work-in-progress for researchers and implementers.

Table of contents

• Ethereum 2.0 Phase 1 -- Shard Data Chains
  • Table of contents
  • Introduction
  • Configuration
    • Misc
  • Containers
  • Helpers
  • Beacon Chain Changes
    • New state variables
    • New block data structures
    • Attestation processing
    • [Light client signature processing)(#light-client-signature-processing)
    • Epoch transition
    • Fraud proofs
  • Shard state transition function
  • Honest committee member behavior

Introduction

This document describes the shard transition function (data layer only) and the shard fork choice rule as part of Phase 1 of Ethereum 2.0.

Configuration

Misc

Name	Value	Unit	Duration
MAX_SHARDS	2**10 (= 1024)
ACTIVE_SHARDS	2**6 (= 64)
MAX_CATCHUP_RATIO	2**2 (= 4)
ONLINE_PERIOD	2**3 (= 8)	epochs	~51 min
LIGHT_CLIENT_COMMITTEE_SIZE	2**7 (= 128)
LIGHT_CLIENT_COMMITTEE_PERIOD	2**8 (= 256)	epochs	~29 hours

Containers

AttestationData

class AttestationData(Container):
    # Slot
    slot: Slot
    # LMD GHOST vote
    beacon_block_root: Hash
    # FFG vote
    source: Checkpoint
    target: Checkpoint
    # Shard data roots
    shard_data_roots: List[Hash, MAX_CATCHUP_RATIO * MAX_SHARDS]
    # Intermediate state roots
    shard_state_roots: List[Hash, MAX_CATCHUP_RATIO * MAX_SHARDS]
    # Index
    index: uint64

Attestation

class Attestation(Container):
    aggregation_bits: Bitlist[MAX_VALIDATORS_PER_COMMITTEE]
    data: AttestationData
    custody_bits: List[Bitlist[MAX_VALIDATORS_PER_COMMITTEE], MAX_CATCHUP_RATIO * MAX_SHARDS]
    signature: BLSSignature

CompactCommittee

class CompactCommittee(Container):
    pubkeys: List[BLSPubkey, MAX_VALIDATORS_PER_COMMITTEE]
    compact_validators: List[uint64, MAX_VALIDATORS_PER_COMMITTEE]

Helpers

get_online_validators

def get_online_indices(state: BeaconState) -> Set[ValidatorIndex]:
    active_validators = get_active_validator_indices(state, get_current_epoch(state))
    return set([i for i in active_validators if state.online_countdown[i] != 0])

pack_compact_validator

def pack_compact_validator(index: int, slashed: bool, balance_in_increments: int) -> int:
    """
    Creates a compact validator object representing index, slashed status, and compressed balance.
    Takes as input balance-in-increments (// EFFECTIVE_BALANCE_INCREMENT) to preserve symmetry with
    the unpacking function.
    """
    return (index << 16) + (slashed << 15) + balance_in_increments

unpack_compact_validator

def unpack_compact_validator(compact_validator: int) -> Tuple[int, bool, int]:
    """
    Returns validator index, slashed, balance // EFFECTIVE_BALANCE_INCREMENT
    """
    return compact_validator >> 16, bool((compact_validator >> 15) % 2), compact_validator & (2**15 - 1)

committee_to_compact_committee

def committee_to_compact_committee(state: BeaconState, committee: Sequence[ValidatorIndex]) -> CompactCommittee:
    """
    Given a state and a list of validator indices, outputs the CompactCommittee representing them.
    """
    validators = [state.validators[i] for i in committee]
    compact_validators = [
        pack_compact_validator(i, v.slashed, v.effective_balance // EFFECTIVE_BALANCE_INCREMENT)
        for i, v in zip(committee, validators)
    ]
    pubkeys = [v.pubkey for v in validators]
    return CompactCommittee(pubkeys=pubkeys, compact_validators=compact_validators)

Beacon Chain Changes

New state variables

    shard_state_roots: Vector[Hash, MAX_SHARDS]
    shard_trace_commitments: Vector[Hash, MAX_SHARDS]
    shard_next_slots: Vector[Slot, MAX_SHARDS]
    online_countdown: Bytes[VALIDATOR_REGISTRY_LIMIT]
    current_light_committee: CompactCommittee
    next_light_committee: CompactCommittee

New block data structures

    light_client_signature_bitfield: Bitlist[LIGHT_CLIENT_COMMITTEE_SIZE]
    light_client_signature: BLSSignature

Attestation processing

def process_attestation(state: BeaconState, attestation: Attestation) -> None:
    data = attestation.data
    assert data.index < ACTIVE_SHARDS
    shard = (data.index + get_start_shard(state, data.slot)) % ACTIVE_SHARDS

    # Signature check
    committee = get_crosslink_committee(state, get_current_epoch(state), shard)
    for bits in attestation.custody_bits + [attestation.aggregation_bits]:
        assert bits == len(committee)
    # Check signature
    assert is_valid_indexed_attestation(state, get_indexed_attestation(state, attestation))
    # Get attesting indices
    attesting_indices = get_attesting_indices(state, attestation.data, attestation.aggregation_bits)
    
    # Type 1: on-time attestations
    if data.custody_bits != []:
        # Correct start slot
        assert data.slot == state.shard_next_slots[shard]
        # Correct data root count
        max_catchup = ACTIVE_SHARDS * MAX_CATCHUP_RATIO // get_committee_count(state, state.slot)
        assert len(data.shard_data_roots) == len(attestation.custody_bits) == len(data.shard_state_roots) == min(state.slot - data.slot, max_catchup)
        # Correct parent block root
        assert data.beacon_block_root == get_block_root_at_slot(state, state.slot - 1)
        # Apply
        online_indices = get_online_indices(state)
        if get_total_balance(state, online_indices.intersection(attesting_indices)) * 3 >= get_total_balance(state, online_indices) * 2:
            # Save trace commitment (used for fraud proofs)
            trace = List[Hash, MAX_CATCHUP_RATIO * MAX_SHARDS * 2 + 1]([state.shard_state_roots[shard]])
            for data, state in zip(data.shard_data_roots, data.shard_state_roots):
                trace.extend([data, state])
            state.shard_trace_commitments[shard] = hash_tree_root(trace)
            # Save state root and next slot
            state.shard_state_roots[shard] = data.shard_state_roots[-1]
            state.shard_next_slots[shard] += len(data.shard_data_roots)
        
    # Type 2: delayed attestations
    else:
        assert slot_to_epoch(data.slot) in (get_current_epoch(state), get_previous_epoch(state))
        assert len(data.shard_data_roots) == len(data.intermediate_state_roots) == 0

    for index in attesting_indices:
        online_countdown[index] = ONLINE_PERIOD

    pending_attestation = PendingAttestation(
        slot=data.slot,
        shard=shard,
        aggregation_bits=attestation.aggregation_bits,
        inclusion_delay=state.slot - attestation_slot,
        proposer_index=get_beacon_proposer_index(state),
    )

    if data.target.epoch == get_current_epoch(state):
        assert data.source == state.current_justified_checkpoint
        state.current_epoch_attestations.append(pending_attestation)
    else:
        assert data.source == state.previous_justified_checkpoint
        state.previous_epoch_attestations.append(pending_attestation)

Check the length of attestations using len(block.attestations) <= 4 * get_committee_count(state, state.slot).

Light client processing

signer_validators = []
signer_keys = []
for i, bit in enumerate(block.light_client_signature_bitfield):
    if bit:
        signer_keys.append(state.current_light_committee.pubkeys[i])
        index, _, _ = unpack_compact_validator(state.current_light_committee.compact_validators[i])
        signer_validators.append(index)

assert bls_verify(
    pubkey=bls_aggregate_pubkeys(signer_keys),
    message_hash=get_block_root_at_slot(state, state.slot - 1),
    signature=block.light_client_signature,
    domain=DOMAIN_LIGHT_CLIENT
)

Epoch transition

# Slowly remove validators from the "online" set if they do not show up
for index in range(len(state.validators)):
    if state.online_countdown[index] != 0:
        state.online_countdown[index] = state.online_countdown[index] - 1

# Update light client committees
if get_current_epoch(state) % LIGHT_CLIENT_COMMITTEE_PERIOD == 0:
    state.current_light_committee = state.next_light_committee
    seed = get_seed(state, get_current_epoch(state), DOMAIN_LIGHT_CLIENT)
    active_indices = get_active_validator_indices(state, get_current_epoch(state))
    committee = [active_indices[compute_shuffled_index(ValidatorIndex(i), len(active_indices), seed)] for i in range(LIGHT_CLIENT_COMMITTEE_SIZE)]
    state.next_light_committee = committee_to_compact_committee(state, committee)

Fraud proofs

TODO. The intent is to have a single universal fraud proof type, which contains (i) an on-time attestation on shard s signing a set of data_roots, (ii) an index i of a particular data root to focus on, (iii) the full contents of the i'th data, (iii) a Merkle proof to the shard_state_roots in the parent block the attestation is referencing, and which then verifies that one of the two conditions is false:

• custody_bits[i][j] != generate_custody_bit(subkey, block_contents) for any j
• execute_state_transition(shard, slot, attestation.shard_state_roots[i-1], hash_tree_root(parent), get_shard_proposer(state, shard, slot), block_contents) != shard_state_roots[i] (if i=0 then instead use parent.shard_state_roots[s][-1])

Shard state transition function

def shard_state_transition(shard: Shard, slot: Slot, pre_state: Hash, previous_beacon_root: Hash, proposer_pubkey: BLSPubkey, block_data: Bytes) -> Hash:
    # Beginning of block data is the previous state root
    assert block_data[:32] == pre_state
    assert block_data[32:64] == int_to_bytes8(slot) + b'\x00' * 24
    # Signature check (nonempty blocks only)
    if len(block_data) == 64:
        pass
    else:
        assert len(block_data) >= 160
        assert bls_verify(
            pubkey=proposer_pubkey,
            message_hash=hash_tree_root(block_data[:-96]),
            signature=block_data[-96:],
            domain=DOMAIN_SHARD_PROPOSER
        )
    # We will add something more substantive in phase 2
    return hash(pre_state + hash_tree_root(block_data))

We also provide a method to generate an empty proposal:

def make_empty_proposal(pre_state: Hash, slot: Slot) -> Bytes[64]:
    return pre_state + int_to_bytes8(slot) + b'\x00' * 24

Honest committee member behavior

Suppose you are a committee member on shard shard at slot current_slot. Let state be the head beacon state you are building on. Three seconds into slot slot, run the following procedure:

• Initialize proposals = [], shard_states = [], shard_state = state.shard_state_roots[shard][-1].
• Let max_catchup = ACTIVE_SHARDS * MAX_CATCHUP_RATIO // get_committee_count(state, current_slot))
• For slot in (state.shard_next_slots[shard], min(state.shard_next_slot + max_catchup, current_slot)), do the following:
  • Look for all valid proposals for slot; that is, a Bytes proposal where shard_state_transition(shard, slot, shard_state, get_block_root_at_slot(state, state.slot - 1), get_shard_proposer(state, shard, slot), proposal) returns a result and does not throw an exception. Let choices be the set of non-empty valid proposals you discover.
  • If len(choices) == 0, do proposals.append(make_empty_proposal(shard_state, slot))
  • If len(choices) == 1, do proposals.append(choices[0])
  • If len(choices) > 1, let winning_proposal be the proposal with the largest number of total attestations from slots in state.shard_next_slots[shard]....slot-1 supporting it or any of its descendants, breaking ties by choosing the first proposal locally seen. Do proposals.append(winning_proposal).
  • Set shard_state = shard_state_transition(shard, slot, shard_state, get_block_root_at_slot(state, state.slot - 1), get_shard_proposer(state, shard, slot), proposals[-1]) and do shard_states.append(shard_state).

Make an attestation using shard_data_roots = [hash_tree_root(proposal) for proposal in proposals] and shard_state_roots = shard_states.