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# Ethereum 2.0 Phase 1 -- Custody Game
**Notice**: This document is a work-in-progress for researchers and implementers.
## Table of contents
<!-- TOC -->
<!-- START doctoc generated TOC please keep comment here to allow auto update -->
<!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->
- [Introduction](#introduction)
- [Terminology](#terminology)
- [Constants](#constants)
- [Misc](#misc)
- [Custody game parameters](#custody-game-parameters)
- [Time parameters](#time-parameters)
- [Max operations per block](#max-operations-per-block)
- [Reward and penalty quotients](#reward-and-penalty-quotients)
- [Signature domain types](#signature-domain-types)
- [TODO PLACEHOLDER](#todo-placeholder)
- [Data structures](#data-structures)
- [Custody objects](#custody-objects)
- [`CustodyChunkChallenge`](#custodychunkchallenge)
- [`CustodyBitChallenge`](#custodybitchallenge)
- [`CustodyChunkChallengeRecord`](#custodychunkchallengerecord)
- [`CustodyBitChallengeRecord`](#custodybitchallengerecord)
- [`CustodyResponse`](#custodyresponse)
- [New beacon operations](#new-beacon-operations)
- [`CustodyKeyReveal`](#custodykeyreveal)
- [`EarlyDerivedSecretReveal`](#earlyderivedsecretreveal)
- [Phase 0 container updates](#phase-0-container-updates)
- [`Validator`](#validator)
- [`BeaconState`](#beaconstate)
- [`BeaconBlockBody`](#beaconblockbody)
- [Helpers](#helpers)
- [`ceillog2`](#ceillog2)
- [`is_valid_merkle_branch_with_mixin`](#is_valid_merkle_branch_with_mixin)
- [`get_crosslink_chunk_count`](#get_crosslink_chunk_count)
- [`legendre_bit`](#legendre_bit)
- [`custody_subchunkify`](#custody_subchunkify)
- [`get_custody_chunk_bit`](#get_custody_chunk_bit)
- [`get_chunk_bits_root`](#get_chunk_bits_root)
- [`get_randao_epoch_for_custody_period`](#get_randao_epoch_for_custody_period)
- [`get_custody_period_for_validator`](#get_custody_period_for_validator)
- [`replace_empty_or_append`](#replace_empty_or_append)
- [Per-block processing](#per-block-processing)
- [Operations](#operations)
- [Custody key reveals](#custody-key-reveals)
- [Early derived secret reveals](#early-derived-secret-reveals)
- [Chunk challenges](#chunk-challenges)
- [Bit challenges](#bit-challenges)
- [Custody responses](#custody-responses)
- [Per-epoch processing](#per-epoch-processing)
- [Handling of custody-related deadlines](#handling-of-custody-related-deadlines)
<!-- END doctoc generated TOC please keep comment here to allow auto update -->
<!-- /TOC -->
## 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](0_beacon-chain.md) specification.
## Terminology
- **Custody game**—
- **Custody period**—
- **Custody chunk**—
- **Custody chunk bit**—
- **Custody chunk challenge**—
- **Custody bit**—
- **Custody bit challenge**—
- **Custody key**—
- **Custody key reveal**—
- **Custody key mask**—
- **Custody response**—
- **Custody response deadline**—
## Constants
### Misc
| Name | Value |
| - | - |
| `BLS12_381_Q` | `4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787` |
| `MINOR_REWARD_QUOTIENT` | `2**8` (= 256) |
| `MAX_EPOCHS_PER_CROSSLINK` | `2**6` (= 64) | epochs | ~7 hours |
### Custody game parameters
| Name | Value |
| - | - |
| `BYTES_PER_SHARD_BLOCK` | `2**14` (= 16,384) |
| `BYTES_PER_CUSTODY_CHUNK` | `2**9` (= 512) |
| `BYTES_PER_CUSTODY_SUBCHUNK` | `48` |
| `CHUNKS_PER_EPOCH` | `2 * BYTES_PER_SHARD_BLOCK * SLOTS_PER_EPOCH // BYTES_PER_CUSTODY_CHUNK` |
| `MAX_CUSTODY_CHUNKS` | `MAX_EPOCHS_PER_CROSSLINK * CHUNKS_PER_EPOCH` |
| `CUSTODY_DATA_DEPTH` | `ceillog2(MAX_CUSTODY_CHUNKS) + 1` |
| `CUSTODY_CHUNK_BIT_DEPTH` | `ceillog2(MAX_EPOCHS_PER_CROSSLINK * CHUNKS_PER_EPOCH // 256) + 2` |
### Time parameters
| Name | Value | Unit | Duration |
| - | - | :-: | :-: |
| `MAX_CHUNK_CHALLENGE_DELAY` | `2**11` (= 2,048) | epochs | ~9 days |
| `CUSTODY_RESPONSE_DEADLINE` | `2**14` (= 16,384) | epochs | ~73 days |
| `RANDAO_PENALTY_EPOCHS` | `2**1` (= 2) | epochs | 12.8 minutes |
| `EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS` | `2**14` | epochs | ~73 days |
| `EPOCHS_PER_CUSTODY_PERIOD` | `2**11` (= 2,048) | epochs | ~9 days |
| `CUSTODY_PERIOD_TO_RANDAO_PADDING` | `2**11` (= 2,048) | epochs | ~9 days |
| `MAX_REVEAL_LATENESS_DECREMENT` | `2**7` (= 128) | epochs | ~14 hours |
### Max operations per block
| Name | Value |
| - | - |
| `MAX_CUSTODY_KEY_REVEALS` | `2**4` (= 16) |
| `MAX_EARLY_DERIVED_SECRET_REVEALS` | `1` |
| `MAX_CUSTODY_CHUNK_CHALLENGES` | `2**2` (= 4) |
| `MAX_CUSTODY_BIT_CHALLENGES` | `2**2` (= 4) |
| `MAX_CUSTODY_RESPONSES` | `2**5` (= 32) |
### Reward and penalty quotients
| Name | Value |
| - | - |
| `EARLY_DERIVED_SECRET_REVEAL_SLOT_REWARD_MULTIPLE` | `2**1` (= 2) |
### Signature domain types
The following types are defined, mapping into `DomainType` (little endian):
| Name | Value |
| - | - |
| `DOMAIN_CUSTODY_BIT_CHALLENGE` | `DomainType('0x06000000')` |
### TODO PLACEHOLDER
| Name | Value |
| - | - |
| `PLACEHOLDER` | `2**32` |
## Data structures
### Custody objects
#### `CustodyChunkChallenge`
```python
class CustodyChunkChallenge(Container):
responder_index: ValidatorIndex
attestation: Attestation
chunk_index: uint64
```
#### `CustodyBitChallenge`
```python
class CustodyBitChallenge(Container):
responder_index: ValidatorIndex
attestation: Attestation
challenger_index: ValidatorIndex
responder_key: BLSSignature
chunk_bits: Bitlist[MAX_CUSTODY_CHUNKS]
signature: BLSSignature
```
#### `CustodyChunkChallengeRecord`
```python
class CustodyChunkChallengeRecord(Container):
challenge_index: uint64
challenger_index: ValidatorIndex
responder_index: ValidatorIndex
inclusion_epoch: Epoch
data_root: Root
depth: uint64
chunk_index: uint64
```
#### `CustodyBitChallengeRecord`
```python
class CustodyBitChallengeRecord(Container):
challenge_index: uint64
challenger_index: ValidatorIndex
responder_index: ValidatorIndex
inclusion_epoch: Epoch
data_root: Root
chunk_count: uint64
chunk_bits_merkle_root: Root
responder_key: BLSSignature
```
#### `CustodyResponse`
```python
class CustodyResponse(Container):
challenge_index: uint64
chunk_index: uint64
chunk: ByteVector[BYTES_PER_CUSTODY_CHUNK]
data_branch: List[Bytes32, CUSTODY_DATA_DEPTH]
chunk_bits_branch: List[Bytes32, CUSTODY_CHUNK_BIT_DEPTH]
chunk_bits_leaf: Bitvector[256]
```
### New beacon operations
#### `CustodyKeyReveal`
```python
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).
```python
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
```
### Phase 0 container updates
Add the following fields to the end of the specified container objects. Fields with underlying type `uint64` are initialized to `0` and list fields are initialized to `[]`.
#### `Validator`
```python
class Validator(Container):
# next_custody_secret_to_reveal is initialised to the custody period
# (of the particular validator) in which the validator is activated
# = get_custody_period_for_validator(...)
next_custody_secret_to_reveal: uint64
max_reveal_lateness: Epoch
```
#### `BeaconState`
```python
class BeaconState(Container):
custody_chunk_challenge_records: List[CustodyChunkChallengeRecord, PLACEHOLDER]
custody_bit_challenge_records: List[CustodyBitChallengeRecord, PLACEHOLDER]
custody_challenge_index: uint64
# Future derived secrets already exposed; contains the indices of the exposed validator
# at RANDAO reveal period % EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS
exposed_derived_secrets: Vector[List[ValidatorIndex, PLACEHOLDER],
EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS]
```
#### `BeaconBlockBody`
```python
class BeaconBlockBody(Container):
custody_chunk_challenges: List[CustodyChunkChallenge, PLACEHOLDER]
custody_bit_challenges: List[CustodyBitChallenge, PLACEHOLDER]
custody_responses: List[CustodyResponse, PLACEHOLDER]
custody_key_reveals: List[CustodyKeyReveal, PLACEHOLDER]
early_derived_secret_reveals: List[EarlyDerivedSecretReveal, PLACEHOLDER]
```
## Helpers
### `ceillog2`
```python
def ceillog2(x: uint64) -> int:
return (x - 1).bit_length()
```
### `is_valid_merkle_branch_with_mixin`
```python
def is_valid_merkle_branch_with_mixin(leaf: Bytes32,
branch: Sequence[Bytes32],
depth: uint64,
index: uint64,
root: Root,
mixin: uint64) -> bool:
value = leaf
for i in range(depth):
if index // (2**i) % 2:
value = hash(branch[i] + value)
else:
value = hash(value + branch[i])
value = hash(value + mixin.to_bytes(32, "little"))
return value == root
```
### `get_crosslink_chunk_count`
```python
def get_custody_chunk_count(crosslink: Crosslink) -> int:
crosslink_length = min(MAX_EPOCHS_PER_CROSSLINK, crosslink.end_epoch - crosslink.start_epoch)
return crosslink_length * CHUNKS_PER_EPOCH
```
### `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.
```python
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
```
### `custody_subchunkify`
Given one proof of custody chunk, returns the proof of custody subchunks of the correct sizes.
```python
def custody_subchunkify(bytez: bytes) -> Sequence[bytes]:
bytez += b'\x00' * (-len(bytez) % BYTES_PER_CUSTODY_SUBCHUNK)
return [bytez[i:i + BYTES_PER_CUSTODY_SUBCHUNK]
for i in range(0, len(bytez), BYTES_PER_CUSTODY_SUBCHUNK)]
```
### `get_custody_chunk_bit`
```python
def get_custody_chunk_bit(key: BLSSignature, chunk: bytes) -> bool:
full_G2_element = bls.signature_to_G2(key)
s = full_G2_element[0].coeffs
bits = [legendre_bit((i + 1) * s[i % 2] + int.from_bytes(subchunk, "little"), BLS12_381_Q)
for i, subchunk in enumerate(custody_subchunkify(chunk))]
return bool(sum(bits) % 2)
```
### `get_chunk_bits_root`
```python
def get_chunk_bits_root(chunk_bits: Bitlist[MAX_CUSTODY_CHUNKS]) -> bit:
aggregated_bits = 0
for i, b in enumerate(chunk_bits):
aggregated_bits += 2**i * b
return legendre_bit(aggregated_bits, BLS12_381_Q)
```
### `get_randao_epoch_for_custody_period`
```python
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`
```python
def get_custody_period_for_validator(state: BeaconState, validator_index: ValidatorIndex, epoch: Epoch=None) -> int:
'''
Return the reveal period for a given validator.
'''
epoch = get_current_epoch(state) if epoch is None else epoch
return (epoch + validator_index % EPOCHS_PER_CUSTODY_PERIOD) // EPOCHS_PER_CUSTODY_PERIOD
```
### `replace_empty_or_append`
```python
def replace_empty_or_append(list: MutableSequence[Any], new_element: Any) -> int:
for i in range(len(list)):
if is_zero(list[i]):
list[i] = new_element
return i
list.append(new_element)
return len(list) - 1
```
## Per-block processing
### Operations
Add the following operations to the per-block processing, in the order given below and after all other operations in Phase 0.
#### Custody key reveals
Verify that `len(block.body.custody_key_reveals) <= MAX_CUSTODY_KEY_REVEALS`.
For each `reveal` in `block.body.custody_key_reveals`, run the following function:
```python
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)
assert revealer.next_custody_secret_to_reveal < get_custody_period_for_validator(state, reveal.revealer_index)
# 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)
# Decrement max reveal lateness if response is timely
if epoch_to_sign + EPOCHS_PER_CUSTODY_PERIOD >= get_current_epoch(state):
if revealer.max_reveal_lateness >= MAX_REVEAL_LATENESS_DECREMENT:
revealer.max_reveal_lateness -= MAX_REVEAL_LATENESS_DECREMENT
else:
revealer.max_reveal_lateness = 0
else:
revealer.max_reveal_lateness = max(
revealer.max_reveal_lateness,
get_current_epoch(state) - epoch_to_sign - EPOCHS_PER_CUSTODY_PERIOD
)
# Process reveal
revealer.next_custody_secret_to_reveal += 1
# Reward Block Preposer
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
Verify that `len(block.body.early_derived_secret_reveals) <= MAX_EARLY_DERIVED_SECRET_REVEALS`.
For each `reveal` in `block.body.early_derived_secret_reveals`, run the following function:
```python
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(zip(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)
```
#### Chunk challenges
Verify that `len(block.body.custody_chunk_challenges) <= MAX_CUSTODY_CHUNK_CHALLENGES`.
For each `challenge` in `block.body.custody_chunk_challenges`, run the following function:
```python
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
assert (compute_epoch_at_slot(challenge.attestation.data.slot)
>= get_current_epoch(state) - MAX_CHUNK_CHALLENGE_DELAY)
responder = state.validators[challenge.responder_index]
assert responder.exit_epoch >= get_current_epoch(state) - MAX_CHUNK_CHALLENGE_DELAY
# 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 the challenge is not a duplicate
for record in state.custody_chunk_challenge_records:
assert (
record.data_root != challenge.attestation.data.crosslink.data_root or
record.chunk_index != challenge.chunk_index
)
# Verify depth
depth = ceillog2(get_custody_chunk_count(challenge.attestation.data.crosslink))
assert challenge.chunk_index < 2**depth
# Add new chunk challenge record
new_record = CustodyChunkChallengeRecord(
challenge_index=state.custody_challenge_index,
challenger_index=get_beacon_proposer_index(state),
responder_index=challenge.responder_index,
inclusion_epoch=get_current_epoch(state),
data_root=challenge.attestation.data.crosslink.data_root,
depth=depth,
chunk_index=challenge.chunk_index,
)
replace_empty_or_append(state.custody_chunk_challenge_records, new_record)
state.custody_challenge_index += 1
# Postpone responder withdrawability
responder.withdrawable_epoch = FAR_FUTURE_EPOCH
```
#### Bit challenges
Verify that `len(block.body.custody_bit_challenges) <= MAX_CUSTODY_BIT_CHALLENGES`.
For each `challenge` in `block.body.custody_bit_challenges`, run the following function:
```python
def process_bit_challenge(state: BeaconState, challenge: CustodyBitChallenge) -> None:
attestation = challenge.attestation
epoch = attestation.data.target.epoch
shard = attestation.data.crosslink.shard
# Verify challenge signature
challenger = state.validators[challenge.challenger_index]
domain = get_domain(state, DOMAIN_CUSTODY_BIT_CHALLENGE, get_current_epoch(state))
# TODO incorrect hash-tree-root, but this changes with phase 1 PR #1483
assert bls.Verify(challenger.pubkey, compute_signing_root(challenge, domain), challenge.signature)
# Verify challenger is slashable
assert is_slashable_validator(challenger, get_current_epoch(state))
# Verify attestation
assert is_valid_indexed_attestation(state, get_indexed_attestation(state, attestation))
# Verify attestation is eligible for challenging
responder = state.validators[challenge.responder_index]
assert get_current_epoch(state) <= get_randao_epoch_for_custody_period(
get_custody_period_for_validator(state, challenge.responder_index, epoch),
challenge.responder_index
) + 2 * EPOCHS_PER_CUSTODY_PERIOD + responder.max_reveal_lateness
# Verify the responder participated in the attestation
attesters = get_attesting_indices(state, attestation.data, attestation.aggregation_bits)
assert challenge.responder_index in attesters
# Verifier challenger is not already challenging
for record in state.custody_bit_challenge_records:
assert record.challenger_index != challenge.challenger_index
# Verify the responder custody key
epoch_to_sign = get_randao_epoch_for_custody_period(
get_custody_period_for_validator(state, challenge.responder_index, epoch),
challenge.responder_index,
)
domain = get_domain(state, DOMAIN_RANDAO, epoch_to_sign)
assert bls.Verify(responder.pubkey, compute_signing_root(epoch_to_sign, domain), challenge.responder_key)
# Verify the chunk count
chunk_count = get_custody_chunk_count(attestation.data.crosslink)
assert chunk_count == len(challenge.chunk_bits)
# Verify custody bit is incorrect
committee = get_beacon_committee(state, epoch, shard)
custody_bit = attestation.custody_bits[committee.index(challenge.responder_index)]
assert custody_bit != get_chunk_bits_root(challenge.chunk_bits)
# Add new bit challenge record
new_record = CustodyBitChallengeRecord(
challenge_index=state.custody_challenge_index,
challenger_index=challenge.challenger_index,
responder_index=challenge.responder_index,
inclusion_epoch=get_current_epoch(state),
data_root=attestation.data.crosslink.data_root,
chunk_count=chunk_count,
chunk_bits_merkle_root=hash_tree_root(challenge.chunk_bits),
responder_key=challenge.responder_key,
)
replace_empty_or_append(state.custody_bit_challenge_records, new_record)
state.custody_challenge_index += 1
# Postpone responder withdrawability
responder.withdrawable_epoch = FAR_FUTURE_EPOCH
```
#### Custody responses
Verify that `len(block.body.custody_responses) <= MAX_CUSTODY_RESPONSES`.
For each `response` in `block.body.custody_responses`, run the following function:
```python
def process_custody_response(state: BeaconState, response: CustodyResponse) -> None:
chunk_challenge = next((record for record in state.custody_chunk_challenge_records
if record.challenge_index == response.challenge_index), None)
if chunk_challenge is not None:
return process_chunk_challenge_response(state, response, chunk_challenge)
bit_challenge = next((record for record in state.custody_bit_challenge_records
if record.challenge_index == response.challenge_index), None)
if bit_challenge is not None:
return process_bit_challenge_response(state, response, bit_challenge)
assert False
```
```python
def process_chunk_challenge_response(state: BeaconState,
response: CustodyResponse,
challenge: CustodyChunkChallengeRecord) -> None:
# Verify chunk index
assert response.chunk_index == challenge.chunk_index
# Verify bit challenge data is null
assert response.chunk_bits_branch == [] and response.chunk_bits_leaf == Bytes32()
# Verify minimum delay
assert get_current_epoch(state) >= challenge.inclusion_epoch + MAX_SEED_LOOKAHEAD
# Verify the chunk matches the crosslink data root
assert is_valid_merkle_branch(
leaf=hash_tree_root(response.chunk),
branch=response.data_branch,
depth=challenge.depth,
index=response.chunk_index,
root=challenge.data_root,
)
# Clear the challenge
records = state.custody_chunk_challenge_records
records[records.index(challenge)] = 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))
```
```python
def process_bit_challenge_response(state: BeaconState,
response: CustodyResponse,
challenge: CustodyBitChallengeRecord) -> None:
# Verify chunk index
assert response.chunk_index < challenge.chunk_count
# Verify responder has not been slashed
responder = state.validators[challenge.responder_index]
assert not responder.slashed
# Verify the chunk matches the crosslink data root
assert is_valid_merkle_branch(
leaf=hash_tree_root(response.chunk),
branch=response.data_branch,
depth=ceillog2(challenge.chunk_count),
index=response.chunk_index,
root=challenge.data_root,
)
# Verify the chunk bit leaf matches the challenge data
assert is_valid_merkle_branch_with_mixin(
leaf=hash_tree_root(response.chunk_bits_leaf),
branch=response.chunk_bits_branch,
depth=ceillog2(MAX_CUSTODY_CHUNKS // 256),
index=response.chunk_index // 256,
root=challenge.chunk_bits_merkle_root,
mixin=challenge.chunk_count,
)
# Verify the chunk bit does not match the challenge chunk bit
assert (get_custody_chunk_bit(challenge.responder_key, response.chunk)
!= response.chunk_bits_leaf[response.chunk_index % 256])
# Clear the challenge
records = state.custody_bit_challenge_records
records[records.index(challenge)] = CustodyBitChallengeRecord()
# Slash challenger
slash_validator(state, challenge.challenger_index, challenge.responder_index)
```
## Per-epoch processing
### Handling of custody-related deadlines
Run `process_reveal_deadlines(state)` immediately after `process_registry_updates(state)`:
```python
# begin insert @process_reveal_deadlines
process_reveal_deadlines(state)
# end insert @process_reveal_deadlines
def process_reveal_deadlines(state: BeaconState) -> None:
for index, validator in enumerate(state.validators):
deadline = validator.next_custody_secret_to_reveal + (CUSTODY_RESPONSE_DEADLINE // EPOCHS_PER_CUSTODY_PERIOD)
if get_custody_period_for_validator(state, ValidatorIndex(index)) > deadline:
slash_validator(state, ValidatorIndex(index))
```
Run `process_challenge_deadlines(state)` immediately after `process_reveal_deadlines(state)`:
```python
# begin insert @process_challenge_deadlines
process_challenge_deadlines(state)
# end insert @process_challenge_deadlines
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 + CUSTODY_RESPONSE_DEADLINE:
slash_validator(state, custody_chunk_challenge.responder_index, custody_chunk_challenge.challenger_index)
records = state.custody_chunk_challenge
records[records.index(custody_chunk_challenge)] = CustodyChunkChallengeRecord()
for custody_bit_challenge in state.custody_bit_challenge_records:
if get_current_epoch(state) > custody_bit_challenge.inclusion_epoch + CUSTODY_RESPONSE_DEADLINE:
slash_validator(state, custody_bit_challenge.responder_index, custody_bit_challenge.challenger_index)
records = state.custody_bit_challenge_records
records[records.index(custody_bit_challenge)] = CustodyBitChallengeRecord()
```
Append this to `process_final_updates(state)`:
```python
# begin insert @after_process_final_updates
after_process_final_updates(state)
# end insert @after_process_final_updates
def after_process_final_updates(state: BeaconState) -> None:
current_epoch = get_current_epoch(state)
# Clean up exposed RANDAO key reveals
state.exposed_derived_secrets[current_epoch % EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS] = []
# Reset withdrawable epochs if challenge records are empty
records = state.custody_chunk_challenge_records + state.custody_bit_challenge_records
validator_indices_in_records = set(
[record.challenger_index for record in records] + [record.responder_index for record in records]
)
for index, validator in enumerate(state.validators):
if index not in validator_indices_in_records:
if validator.exit_epoch != FAR_FUTURE_EPOCH and validator.withdrawable_epoch == FAR_FUTURE_EPOCH:
validator.withdrawable_epoch = Epoch(validator.exit_epoch + MIN_VALIDATOR_WITHDRAWABILITY_DELAY)
```
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