24 KiB
24 KiB
Ethereum 2.0 Phase 1 -- Custody Game
Notice: This document is a work-in-progress for researchers and implementers.
Table of contents
- Introduction
- Constants
- Configuration
- Data structures
- Helpers
- Per-block processing
- Per-epoch processing
Introduction
This document details the beacon chain additions and changes in Phase 1 of Ethereum 2.0 to support the shard data custody game, building upon the Phase 0 specification.
Constants
Misc
| Name | Value | Unit |
|---|---|---|
CUSTODY_PRIME |
2 ** 256 - 189 |
- |
CUSTODY_SECRETS |
3 |
- |
BYTES_PER_CUSTODY_ATOM |
32 |
bytes |
CUSTODY_PROBABILITY_EXPONENT |
10 |
- |
Configuration
Time parameters
| Name | Value | Unit | Duration |
|---|---|---|---|
RANDAO_PENALTY_EPOCHS |
2**1 (= 2) |
epochs | 12.8 minutes |
EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS |
2**15 (= 32,768) |
epochs | ~146 days |
EPOCHS_PER_CUSTODY_PERIOD |
2**14 (= 16,384) |
epochs | ~73 days |
CUSTODY_PERIOD_TO_RANDAO_PADDING |
2**11 (= 2,048) |
epochs | ~9 days |
MAX_CHUNK_CHALLENGE_DELAY |
2**15 (= 32,768) |
epochs | ~146 days |
CHUNK_RESPONSE_DEADLINE |
2**14 (= 16,384) |
epochs | ~73 days |
Max operations per block
| Name | Value |
|---|---|
MAX_CUSTODY_KEY_REVEALS |
2**8 (= 256) |
MAX_EARLY_DERIVED_SECRET_REVEALS |
2**0 (= 1) |
MAX_CUSTODY_CHUNK_CHALLENGES |
2**2 (= 4) |
MAX_CUSTODY_CHUNK_CHALLENGE_RESPONSES |
2**4 (= 16) |
MAX_CUSTODY_SLASHINGS |
2**0 (= 1) |
Reward and penalty quotients
| Name | Value |
|---|---|
EARLY_DERIVED_SECRET_REVEAL_SLOT_REWARD_MULTIPLE |
2**1 (= 2) |
MINOR_REWARD_QUOTIENT |
2**8 (= 256) |
Signature domain types
The following types are defined, mapping into DomainType (little endian):
| Name | Value |
|---|---|
DOMAIN_CUSTODY_BIT_SLASHING |
DomainType('0x83000000') |
Data structures
New Beacon Chain operations
CustodyChunkChallenge
class CustodyChunkChallenge(Container):
responder_index: ValidatorIndex
shard_transition: ShardTransition
attestation: Attestation
data_index: uint64
chunk_index: uint64
CustodyChunkChallengeRecord
class CustodyChunkChallengeRecord(Container):
challenge_index: uint64
challenger_index: ValidatorIndex
responder_index: ValidatorIndex
inclusion_epoch: Epoch
data_root: Root
chunk_index: uint64
CustodyChunkResponse
class CustodyChunkResponse(Container):
challenge_index: uint64
chunk_index: uint64
chunk: ByteVector[BYTES_PER_CUSTODY_CHUNK]
branch: Vector[Root, CUSTODY_RESPONSE_DEPTH]
CustodySlashing
class CustodySlashing(Container):
# (Attestation.data.shard_transition_root as ShardTransition).shard_data_roots[data_index] is the root of the data.
data_index: uint64
malefactor_index: ValidatorIndex
malefactor_secret: BLSSignature
whistleblower_index: ValidatorIndex
shard_transition: ShardTransition
attestation: Attestation
data: ByteList[MAX_SHARD_BLOCK_SIZE]
SignedCustodySlashing
class SignedCustodySlashing(Container):
message: CustodySlashing
signature: BLSSignature
CustodyKeyReveal
class CustodyKeyReveal(Container):
# Index of the validator whose key is being revealed
revealer_index: ValidatorIndex
# Reveal (masked signature)
reveal: BLSSignature
EarlyDerivedSecretReveal
Represents an early (punishable) reveal of one of the derived secrets, where derived secrets are RANDAO reveals and custody reveals (both are part of the same domain).
class EarlyDerivedSecretReveal(Container):
# Index of the validator whose key is being revealed
revealed_index: ValidatorIndex
# RANDAO epoch of the key that is being revealed
epoch: Epoch
# Reveal (masked signature)
reveal: BLSSignature
# Index of the validator who revealed (whistleblower)
masker_index: ValidatorIndex
# Mask used to hide the actual reveal signature (prevent reveal from being stolen)
mask: Bytes32
Helpers
replace_empty_or_append
def replace_empty_or_append(l: List, new_element: Any) -> int:
for i in range(len(l)):
if l[i] == type(new_element)():
l[i] = new_element
return i
l.append(new_element)
return len(l) - 1
legendre_bit
Returns the Legendre symbol (a/q) normalizes as a bit (i.e. ((a/q) + 1) // 2). In a production implementation, a well-optimized library (e.g. GMP) should be used for this.
def legendre_bit(a: int, q: int) -> int:
if a >= q:
return legendre_bit(a % q, q)
if a == 0:
return 0
assert(q > a > 0 and q % 2 == 1)
t = 1
n = q
while a != 0:
while a % 2 == 0:
a //= 2
r = n % 8
if r == 3 or r == 5:
t = -t
a, n = n, a
if a % 4 == n % 4 == 3:
t = -t
a %= n
if n == 1:
return (t + 1) // 2
else:
return 0
get_custody_atoms
Given one set of data, return the custody atoms: each atom will be combined with one legendre bit.
def get_custody_atoms(bytez: bytes) -> Sequence[bytes]:
bytez += b'\x00' * (-len(bytez) % BYTES_PER_CUSTODY_ATOM) # right-padding
return [bytez[i:i + BYTES_PER_CUSTODY_ATOM]
for i in range(0, len(bytez), BYTES_PER_CUSTODY_ATOM)]
get_custody_secrets
Extract the custody secrets from the signature
def get_custody_secrets(key: BLSSignature) -> Sequence[int]:
full_G2_element = bls.signature_to_G2(key)
signature = full_G2_element[0].coeffs
signature_bytes = b"".join(x.to_bytes(48, "little") for x in signature)
secrets = [int.from_bytes(signature_bytes[i:i + BYTES_PER_CUSTODY_ATOM], "little")
for i in range(0, len(signature_bytes), 32)]
return secrets
universal_hash_function
def universal_hash_function(data_chunks: Sequence[bytes], secrets: Sequence[int]) -> int:
n = len(data_chunks)
return (
sum(
secrets[i % CUSTODY_SECRETS]**i * int.from_bytes(atom, "little") % CUSTODY_PRIME
for i, atom in enumerate(data_chunks)
) + secrets[n % CUSTODY_SECRETS]**n
) % CUSTODY_PRIME
compute_custody_bit
def compute_custody_bit(key: BLSSignature, data: ByteList[MAX_SHARD_BLOCK_SIZE]) -> bit:
custody_atoms = get_custody_atoms(data)
secrets = get_custody_secrets(key)
uhf = universal_hash_function(custody_atoms, secrets)
legendre_bits = [legendre_bit(uhf + secrets[0] + i, CUSTODY_PRIME) for i in range(CUSTODY_PROBABILITY_EXPONENT)]
return all(legendre_bits)
get_randao_epoch_for_custody_period
def get_randao_epoch_for_custody_period(period: uint64, validator_index: ValidatorIndex) -> Epoch:
next_period_start = (period + 1) * EPOCHS_PER_CUSTODY_PERIOD - validator_index % EPOCHS_PER_CUSTODY_PERIOD
return Epoch(next_period_start + CUSTODY_PERIOD_TO_RANDAO_PADDING)
get_custody_period_for_validator
def get_custody_period_for_validator(validator_index: ValidatorIndex, epoch: Epoch) -> int:
'''
Return the reveal period for a given validator.
'''
return (epoch + validator_index % EPOCHS_PER_CUSTODY_PERIOD) // EPOCHS_PER_CUSTODY_PERIOD
Per-block processing
Custody Game Operations
def process_custody_game_operations(state: BeaconState, body: BeaconBlockBody) -> None:
def for_ops(operations: Sequence[Any], fn: Callable[[BeaconState, Any], None]) -> None:
for operation in operations:
fn(state, operation)
for_ops(body.chunk_challenges, process_chunk_challenge)
for_ops(body.chunk_challenge_responses, process_chunk_challenge)
for_ops(body.custody_key_reveals, process_custody_key_reveal)
for_ops(body.early_derived_secret_reveals, process_early_derived_secret_reveal)
for_ops(body.custody_slashings, process_custody_slashing)
Chunk challenges
def process_chunk_challenge(state: BeaconState, challenge: CustodyChunkChallenge) -> None:
# Verify the attestation
assert is_valid_indexed_attestation(state, get_indexed_attestation(state, challenge.attestation))
# Verify it is not too late to challenge the attestation
max_attestation_challenge_epoch = challenge.attestation.data.target.epoch + MAX_CHUNK_CHALLENGE_DELAY
assert get_current_epoch(state) <= max_attestation_challenge_epoch
# Verify it is not too late to challenge the responder
responder = state.validators[challenge.responder_index]
if responder.exit_epoch < FAR_FUTURE_EPOCH:
assert get_current_epoch(state) <= responder.exit_epoch + MAX_CHUNK_CHALLENGE_DELAY
# Verify responder is slashable
assert is_slashable_validator(responder, get_current_epoch(state))
# Verify the responder participated in the attestation
attesters = get_attesting_indices(state, challenge.attestation.data, challenge.attestation.aggregation_bits)
assert challenge.responder_index in attesters
# Verify shard transition is correctly given
assert hash_tree_root(challenge.shard_transition) == challenge.attestation.data.shard_transition_root
data_root = challenge.shard_transition.shard_data_roots[challenge.data_index]
# Verify the challenge is not a duplicate
for record in state.custody_chunk_challenge_records:
assert (
record.data_root != data_root or
record.chunk_index != challenge.chunk_index
)
# Verify depth
shard_block_length = challenge.shard_transition.shard_block_lengths[challenge.data_index]
transition_chunks = (shard_block_length + BYTES_PER_CUSTODY_CHUNK - 1) // BYTES_PER_CUSTODY_CHUNK
assert challenge.chunk_index < transition_chunks
# Add new chunk challenge record
new_record = CustodyChunkChallengeRecord(
challenge_index=state.custody_chunk_challenge_index,
challenger_index=get_beacon_proposer_index(state),
responder_index=challenge.responder_index,
inclusion_epoch=get_current_epoch(state),
data_root=challenge.shard_transition.shard_data_roots[challenge.data_index],
chunk_index=challenge.chunk_index,
)
replace_empty_or_append(state.custody_chunk_challenge_records, new_record)
state.custody_chunk_challenge_index += 1
# Postpone responder withdrawability
responder.withdrawable_epoch = FAR_FUTURE_EPOCH
Custody chunk response
def process_chunk_challenge_response(state: BeaconState,
response: CustodyChunkResponse) -> None:
# Get matching challenge (if any) from records
matching_challenges = [
record for record in state.custody_chunk_challenge_records
if record.challenge_index == response.challenge_index
]
assert len(matching_challenges) > 0
challenge = matching_challenges[0]
# Verify chunk index
assert response.chunk_index == challenge.chunk_index
# Verify the chunk matches the crosslink data root
assert is_valid_merkle_branch(
leaf=hash_tree_root(response.chunk),
branch=response.branch,
depth=CUSTODY_RESPONSE_DEPTH,
index=response.chunk_index,
root=challenge.data_root,
)
# Clear the challenge
index_in_records = state.custody_chunk_challenge_records.index(challenge)
state.custody_chunk_challenge_records[index_in_records] = CustodyChunkChallengeRecord()
# Reward the proposer
proposer_index = get_beacon_proposer_index(state)
increase_balance(state, proposer_index, Gwei(get_base_reward(state, proposer_index) // MINOR_REWARD_QUOTIENT))
Custody key reveals
def process_custody_key_reveal(state: BeaconState, reveal: CustodyKeyReveal) -> None:
"""
Process ``CustodyKeyReveal`` operation.
Note that this function mutates ``state``.
"""
revealer = state.validators[reveal.revealer_index]
epoch_to_sign = get_randao_epoch_for_custody_period(revealer.next_custody_secret_to_reveal, reveal.revealer_index)
custody_reveal_period = get_custody_period_for_validator(reveal.revealer_index, get_current_epoch(state))
# Only past custody periods can be revealed, except after exiting the exit period can be revealed
is_past_reveal = revealer.next_custody_secret_to_reveal < custody_reveal_period
is_exited = revealer.exit_epoch <= get_current_epoch(state)
is_exit_period_reveal = (
revealer.next_custody_secret_to_reveal
== get_custody_period_for_validator(reveal.revealer_index, revealer.exit_epoch - 1)
)
assert is_past_reveal or (is_exited and is_exit_period_reveal)
# Revealed validator is active or exited, but not withdrawn
assert is_slashable_validator(revealer, get_current_epoch(state))
# Verify signature
domain = get_domain(state, DOMAIN_RANDAO, epoch_to_sign)
signing_root = compute_signing_root(epoch_to_sign, domain)
assert bls.Verify(revealer.pubkey, signing_root, reveal.reveal)
# Process reveal
if is_exited and is_exit_period_reveal:
revealer.all_custody_secrets_revealed_epoch = get_current_epoch(state)
revealer.next_custody_secret_to_reveal += 1
# Reward Block Proposer
proposer_index = get_beacon_proposer_index(state)
increase_balance(
state,
proposer_index,
Gwei(get_base_reward(state, reveal.revealer_index) // MINOR_REWARD_QUOTIENT)
)
Early derived secret reveals
def process_early_derived_secret_reveal(state: BeaconState, reveal: EarlyDerivedSecretReveal) -> None:
"""
Process ``EarlyDerivedSecretReveal`` operation.
Note that this function mutates ``state``.
"""
revealed_validator = state.validators[reveal.revealed_index]
derived_secret_location = reveal.epoch % EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS
assert reveal.epoch >= get_current_epoch(state) + RANDAO_PENALTY_EPOCHS
assert reveal.epoch < get_current_epoch(state) + EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS
assert not revealed_validator.slashed
assert reveal.revealed_index not in state.exposed_derived_secrets[derived_secret_location]
# Verify signature correctness
masker = state.validators[reveal.masker_index]
pubkeys = [revealed_validator.pubkey, masker.pubkey]
domain = get_domain(state, DOMAIN_RANDAO, reveal.epoch)
signing_roots = [compute_signing_root(root, domain) for root in [hash_tree_root(reveal.epoch), reveal.mask]]
assert bls.AggregateVerify(pubkeys, signing_roots, reveal.reveal)
if reveal.epoch >= get_current_epoch(state) + CUSTODY_PERIOD_TO_RANDAO_PADDING:
# Full slashing when the secret was revealed so early it may be a valid custody
# round key
slash_validator(state, reveal.revealed_index, reveal.masker_index)
else:
# Only a small penalty proportional to proposer slot reward for RANDAO reveal
# that does not interfere with the custody period
# The penalty is proportional to the max proposer reward
# Calculate penalty
max_proposer_slot_reward = (
get_base_reward(state, reveal.revealed_index)
* SLOTS_PER_EPOCH
// len(get_active_validator_indices(state, get_current_epoch(state)))
// PROPOSER_REWARD_QUOTIENT
)
penalty = Gwei(
max_proposer_slot_reward
* EARLY_DERIVED_SECRET_REVEAL_SLOT_REWARD_MULTIPLE
* (len(state.exposed_derived_secrets[derived_secret_location]) + 1)
)
# Apply penalty
proposer_index = get_beacon_proposer_index(state)
whistleblower_index = reveal.masker_index
whistleblowing_reward = Gwei(penalty // WHISTLEBLOWER_REWARD_QUOTIENT)
proposer_reward = Gwei(whistleblowing_reward // PROPOSER_REWARD_QUOTIENT)
increase_balance(state, proposer_index, proposer_reward)
increase_balance(state, whistleblower_index, whistleblowing_reward - proposer_reward)
decrease_balance(state, reveal.revealed_index, penalty)
# Mark this derived secret as exposed so validator cannot be punished repeatedly
state.exposed_derived_secrets[derived_secret_location].append(reveal.revealed_index)
Custody Slashings
def process_custody_slashing(state: BeaconState, signed_custody_slashing: SignedCustodySlashing) -> None:
custody_slashing = signed_custody_slashing.message
attestation = custody_slashing.attestation
# Any signed custody-slashing should result in at least one slashing.
# If the custody bits are valid, then the claim itself is slashed.
malefactor = state.validators[custody_slashing.malefactor_index]
whistleblower = state.validators[custody_slashing.whistleblower_index]
domain = get_domain(state, DOMAIN_CUSTODY_BIT_SLASHING, get_current_epoch(state))
signing_root = compute_signing_root(custody_slashing, domain)
assert bls.Verify(whistleblower.pubkey, signing_root, signed_custody_slashing.signature)
# Verify that the whistleblower is slashable
assert is_slashable_validator(whistleblower, get_current_epoch(state))
# Verify that the claimed malefactor is slashable
assert is_slashable_validator(malefactor, get_current_epoch(state))
# Verify the attestation
assert is_valid_indexed_attestation(state, get_indexed_attestation(state, attestation))
# TODO: can do a single combined merkle proof of data being attested.
# Verify the shard transition is indeed attested by the attestation
shard_transition = custody_slashing.shard_transition
assert hash_tree_root(shard_transition) == attestation.data.shard_transition_root
# Verify that the provided data matches the shard-transition
assert (
custody_slashing.data.get_backing().get_left().merkle_root()
== shard_transition.shard_data_roots[custody_slashing.data_index]
)
assert len(custody_slashing.data) == shard_transition.shard_block_lengths[custody_slashing.data_index]
# Verify existence and participation of claimed malefactor
attesters = get_attesting_indices(state, attestation.data, attestation.aggregation_bits)
assert custody_slashing.malefactor_index in attesters
# Verify the malefactor custody key
epoch_to_sign = get_randao_epoch_for_custody_period(
get_custody_period_for_validator(custody_slashing.malefactor_index, attestation.data.target.epoch),
custody_slashing.malefactor_index,
)
domain = get_domain(state, DOMAIN_RANDAO, epoch_to_sign)
signing_root = compute_signing_root(epoch_to_sign, domain)
assert bls.Verify(malefactor.pubkey, signing_root, custody_slashing.malefactor_secret)
# Compute the custody bit
computed_custody_bit = compute_custody_bit(custody_slashing.malefactor_secret, custody_slashing.data)
# Verify the claim
if computed_custody_bit == 1:
# Slash the malefactor, reward the other committee members
slash_validator(state, custody_slashing.malefactor_index)
committee = get_beacon_committee(state, attestation.data.slot, attestation.data.index)
others_count = len(committee) - 1
whistleblower_reward = Gwei(malefactor.effective_balance // WHISTLEBLOWER_REWARD_QUOTIENT // others_count)
for attester_index in attesters:
if attester_index != custody_slashing.malefactor_index:
increase_balance(state, attester_index, whistleblower_reward)
# No special whisteblower reward: it is expected to be an attester. Others are free to slash too however.
else:
# The claim was false, the custody bit was correct. Slash the whistleblower that induced this work.
slash_validator(state, custody_slashing.whistleblower_index)
Per-epoch processing
Handling of reveal deadlines
def process_reveal_deadlines(state: BeaconState) -> None:
epoch = get_current_epoch(state)
for index, validator in enumerate(state.validators):
deadline = validator.next_custody_secret_to_reveal + 1
if get_custody_period_for_validator(ValidatorIndex(index), epoch) > deadline:
slash_validator(state, ValidatorIndex(index))
def process_challenge_deadlines(state: BeaconState) -> None:
for custody_chunk_challenge in state.custody_chunk_challenge_records:
if get_current_epoch(state) > custody_chunk_challenge.inclusion_epoch + EPOCHS_PER_CUSTODY_PERIOD:
slash_validator(state, custody_chunk_challenge.responder_index, custody_chunk_challenge.challenger_index)
index_in_records = state.custody_chunk_challenge_records.index(custody_chunk_challenge)
state.custody_chunk_challenge_records[index_in_records] = CustodyChunkChallengeRecord()
Final updates
def process_custody_final_updates(state: BeaconState) -> None:
# Clean up exposed RANDAO key reveals
state.exposed_derived_secrets[get_current_epoch(state) % EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS] = []
# Reset withdrawable epochs if challenge records are empty
records = state.custody_chunk_challenge_records
validator_indices_in_records = set([record.responder_index for record in records])
for index, validator in enumerate(state.validators):
if validator.exit_epoch != FAR_FUTURE_EPOCH:
all_secrets_are_revealed = validator.all_custody_secrets_revealed_epoch == FAR_FUTURE_EPOCH
if index in validator_indices_in_records or all_secrets_are_revealed:
# Delay withdrawable epochs if challenge records are not empty or not all
# custody secrets revealed
validator.withdrawable_epoch = FAR_FUTURE_EPOCH
else:
# Reset withdrawable epochs if challenge records are empty
if validator.withdrawable_epoch == FAR_FUTURE_EPOCH:
validator.withdrawable_epoch = Epoch(validator.all_custody_secrets_revealed_epoch
+ MIN_VALIDATOR_WITHDRAWABILITY_DELAY)