11 KiB
11 KiB
Ethereum 2.0 Phase 1 -- Shard Transition and Fraud Proofs
Notice: This document is a work-in-progress for researchers and implementers.
Table of contents
Table of Contents generated with DocToc
Introduction
This document describes the shard transition function and fraud proofs as part of Phase 1 of Ethereum 2.0.
Helper functions
Misc
def compute_shard_transition_digest(beacon_state: BeaconState,
shard_state: ShardState,
beacon_parent_root: Root,
shard_body_root: Root) -> Bytes32:
# TODO: use SSZ hash tree root
return hash(
hash_tree_root(shard_state) + beacon_parent_root + shard_body_root
)
Shard block verification functions
def verify_shard_block_message(beacon_state: BeaconState,
shard_state: ShardState,
block: ShardBlock,
slot: Slot,
shard: Shard) -> bool:
assert block.shard_parent_root == shard_state.latest_block_root
assert block.slot == slot
assert block.proposer_index == get_shard_proposer_index(beacon_state, slot, shard)
assert 0 < len(block.body) <= MAX_SHARD_BLOCK_SIZE
return True
def verify_shard_block_signature(beacon_state: BeaconState,
signed_block: SignedShardBlock) -> bool:
proposer = beacon_state.validators[signed_block.message.proposer_index]
domain = get_domain(beacon_state, DOMAIN_SHARD_PROPOSAL, compute_epoch_at_slot(signed_block.message.slot))
signing_root = compute_signing_root(signed_block.message, domain)
return bls.Verify(proposer.pubkey, signing_root, signed_block.signature)
Shard state transition
def shard_state_transition(beacon_state: BeaconState,
shard_state: ShardState,
block: ShardBlock) -> None:
# Update shard state
prev_gasprice = shard_state.gasprice
if len(block.body) == 0:
latest_block_root = shard_state.latest_block_root
else:
latest_block_root = hash_tree_root(block)
shard_state.transition_digest = compute_shard_transition_digest(
beacon_state,
shard_state,
block.beacon_parent_root,
block.body,
)
shard_state.gasprice = compute_updated_gasprice(prev_gasprice, len(block.body))
shard_state.slot = block.slot
shard_state.latest_block_root = latest_block_root
We have a pure function get_post_shard_state for describing the fraud proof verification and honest validator behavior.
def get_post_shard_state(beacon_state: BeaconState,
shard_state: ShardState,
block: ShardBlock) -> ShardState:
"""
A pure function that returns a new post ShardState instead of modifying the given `shard_state`.
"""
post_state = shard_state.copy()
shard_state_transition(beacon_state, post_state, block)
return post_state
Fraud proofs
Verifying the proof
TODO. The intent is to have a single universal fraud proof type, which contains the following parts:
- An on-time attestation
attestationon some shardshardsigning atransition: ShardTransition - An index
offset_indexof a particular position to focus on - The
transition: ShardTransitionitself - The full body of the shard block
shard_block - A Merkle proof to the
shard_statesin the parent block the attestation is referencing - The
subkeyto generate the custody bit
Call the following function to verify the proof:
def is_valid_fraud_proof(beacon_state: BeaconState,
attestation: Attestation,
offset_index: uint64,
transition: ShardTransition,
block: ShardBlock,
subkey: BLSPubkey,
beacon_parent_block: BeaconBlock) -> bool:
# 1. Check if `custody_bits[offset_index][j] != generate_custody_bit(subkey, block_contents)` for any `j`.
custody_bits = attestation.custody_bits_blocks
for j in range(custody_bits[offset_index]):
if custody_bits[offset_index][j] != generate_custody_bit(subkey, block):
return True
# 2. Check if the shard state transition result is wrong between
# `transition.shard_states[offset_index - 1]` to `transition.shard_states[offset_index]`.
if offset_index == 0:
shard = get_shard(beacon_state, attestation)
shard_state = beacon_parent_block.shard_transitions[shard].shard_states[-1]
else:
shard_state = transition.shard_states[offset_index - 1] # Not doing the actual state updates here.
shard_state = get_post_shard_state(beacon_state, shard_state, block)
if shard_state.transition_digest != transition.shard_states[offset_index].transition_digest:
return True
return False
def generate_custody_bit(subkey: BLSPubkey, block: ShardBlock) -> bool:
# TODO
...
Honest committee member behavior
Helper functions
def get_winning_proposal(beacon_state: BeaconState, proposals: Sequence[SignedShardBlock]) -> SignedShardBlock:
# TODO: 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)`.
return proposals[-1] # stub
def compute_shard_body_roots(proposals: Sequence[SignedShardBlock]) -> Sequence[Root]:
return [hash_tree_root(proposal.message.body) for proposal in proposals]
def get_proposal_choices_at_slot(beacon_state: BeaconState,
shard_state: ShardState,
slot: Slot,
shard: Shard,
shard_blocks: Sequence[SignedShardBlock],
validate_signature: bool=True) -> Sequence[SignedShardBlock]:
"""
Return the valid shard blocks at the given ``slot``.
Note that this function doesn't change the state.
"""
choices = []
shard_blocks_at_slot = [block for block in shard_blocks if block.message.slot == slot]
for block in shard_blocks_at_slot:
try:
# Verify block message and signature
# TODO these validations should have been checked upon receiving shard blocks.
assert verify_shard_block_message(beacon_state, shard_state, block.message, slot, shard)
if validate_signature:
assert verify_shard_block_signature(beacon_state, block)
shard_state = get_post_shard_state(beacon_state, shard_state, block.message)
except Exception:
pass # TODO: throw error in the test helper
else:
choices.append(block)
return choices
def get_proposal_at_slot(beacon_state: BeaconState,
shard_state: ShardState,
slot: Shard,
shard: Shard,
shard_blocks: Sequence[SignedShardBlock],
validate_signature: bool=True) -> Tuple[SignedShardBlock, ShardState]:
"""
Return ``proposal``, ``shard_state`` of the given ``slot``.
Note that this function doesn't change the state.
"""
choices = get_proposal_choices_at_slot(
beacon_state=beacon_state,
shard_state=shard_state,
slot=slot,
shard=shard,
shard_blocks=shard_blocks,
validate_signature=validate_signature,
)
if len(choices) == 0:
block = ShardBlock(slot=slot)
proposal = SignedShardBlock(message=block)
elif len(choices) == 1:
proposal = choices[0]
else:
proposal = get_winning_proposal(beacon_state, choices)
# Apply state transition
shard_state = get_post_shard_state(beacon_state, shard_state, proposal.message)
return proposal, shard_state
def get_shard_state_transition_result(
beacon_state: BeaconState,
shard: Shard,
shard_blocks: Sequence[SignedShardBlock],
validate_signature: bool=True,
) -> Tuple[Sequence[SignedShardBlock], Sequence[ShardState], Sequence[Root]]:
proposals = []
shard_states = []
shard_state = beacon_state.shard_states[shard]
for slot in get_offset_slots(beacon_state, shard):
proposal, shard_state = get_proposal_at_slot(
beacon_state=beacon_state,
shard_state=shard_state,
slot=slot,
shard=shard,
shard_blocks=shard_blocks,
validate_signature=validate_signature,
)
shard_states.append(shard_state)
proposals.append(proposal)
shard_data_roots = compute_shard_body_roots(proposals)
return proposals, shard_states, shard_data_roots
Make attestations
Suppose you are a committee member on shard shard at slot current_slot and you have received shard blocks shard_blocks since the latest successful crosslink for shard into the beacon chain. Let beacon_state be the head beacon state you are building on, and let QUARTER_PERIOD = SECONDS_PER_SLOT // 4. 2 * QUARTER_PERIOD seconds into slot current_slot, run get_shard_transition(beacon_state, shard, shard_blocks) to get shard_transition.
def get_shard_transition(beacon_state: BeaconState,
shard: Shard,
shard_blocks: Sequence[SignedShardBlock]) -> ShardTransition:
offset_slots = get_offset_slots(beacon_state, shard)
start_slot = offset_slots[0]
proposals, shard_states, shard_data_roots = get_shard_state_transition_result(beacon_state, shard, shard_blocks)
assert len(proposals) > 0
assert len(shard_data_roots) > 0
shard_block_lengths = []
proposer_signatures = []
for proposal in proposals:
shard_block_lengths.append(len(proposal.message.body))
if proposal.signature != NO_SIGNATURE:
proposer_signatures.append(proposal.signature)
if len(proposer_signatures) > 0:
proposer_signature_aggregate = bls.Aggregate(proposer_signatures)
else:
proposer_signature_aggregate = NO_SIGNATURE
return ShardTransition(
start_slot=start_slot,
shard_block_lengths=shard_block_lengths,
shard_data_roots=shard_data_roots,
shard_states=shard_states,
proposer_signature_aggregate=proposer_signature_aggregate,
)