From f5c5c166af0caa7d451e5e74d8c565dca3ea4cee Mon Sep 17 00:00:00 2001 From: vbuterin Date: Thu, 28 Mar 2019 17:56:43 -0500 Subject: [PATCH] Replace custody challenge game with JABS (#812) See also #818. === * Replace custody challenge game with JABS Replace the existing proof of custody game with a new game ("Justin's Awesome Bit Sum" or JABS) that works as follows: * The data `D` is split up into 512-byte chunks `D[0] .... D[n-1]`, and use a mix function `mix(subkey, data) -> {0,1}` (currently the first bit of the hash of `subkey+data`). We calculate `M[i] = (mix(D[0]) + ... + mix(D[i-1])) % 2`, and set the custody bit to `M[n-1]` * Anyone can challenge by providing the full `M` where `M[n-1]` is not equal to the custody bit * Anyone can respond to a challenge by providing a specific position in `M` along with a branch of the data where `M[i-1] ^ mix(D[i]) != M[i]` The maximum size of data is now `2**6` epochs * `2**6` blocks * `2**14` bytes = `2**26` bytes, so assuming 512-byte mix chunks the maximum mix size is `2**17` bits or `2**14` bytes. The average mix size is `2**8` bytes. --- specs/core/1_shard-data-chains.md | 1073 ++++++++--------------------- 1 file changed, 282 insertions(+), 791 deletions(-) diff --git a/specs/core/1_shard-data-chains.md b/specs/core/1_shard-data-chains.md index 92cee4d191..8f2d12a913 100644 --- a/specs/core/1_shard-data-chains.md +++ b/specs/core/1_shard-data-chains.md @@ -1,157 +1,143 @@ # Ethereum 2.0 Phase 1 -- Shard Data Chains -**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](https://github.com/ethereum/beacon_chain). +**NOTICE**: This document is a work-in-progress for researchers and implementers. -At the current stage, Phase 1, while fundamentally feature-complete, is still subject to change. Development teams with spare resources may consider starting on the "Shard chains and crosslink data" section; at least basic properties, such as the fact that a shard block can get created every slot and is dependent on both a parent block in the same shard and a beacon chain block at or before that same slot, are unlikely to change, though details are likely to undergo similar kinds of changes to what Phase 0 has undergone since the start of the year. - -## Table of contents +## Table of Contents -- [Ethereum 2.0 Phase 1 -- Shard Data Chains](#ethereum-20-phase-1----shard-data-chains) - - [Table of contents](#table-of-contents) - - [Introduction](#introduction) - - [Terminology](#terminology) - - [Constants](#constants) - - [Misc](#misc) - - [Time parameters](#time-parameters) - - [Max operations per block](#max-operations-per-block) - - [Signature domains](#signature-domains) -- [Shard chains and crosslink data](#shard-chains-and-crosslink-data) - - [Helper functions](#helper-functions) - - [`get_shuffled_committee`](#get_shuffled_committee) - - [`get_persistent_committee`](#get_persistent_committee) - - [`get_shard_proposer_index`](#get_shard_proposer_index) - - [Data Structures](#data-structures) - - [Shard chain blocks](#shard-chain-blocks) - - [Shard block processing](#shard-block-processing) - - [Verifying shard block data](#verifying-shard-block-data) - - [Verifying a crosslink](#verifying-a-crosslink) - - [Shard block fork choice rule](#shard-block-fork-choice-rule) -- [Updates to the beacon chain](#updates-to-the-beacon-chain) +- [Ethereum 2.0 Phase 1 -- Shards Data Chains](#ethereum-20-phase-1----shard-data-chains) + - [Table of Contents](#table-of-contents) + - [Introduction](#introduction) + - [Constants](#constants) + - [Misc](#misc) + - [Time parameters](#time-parameters) + - [Signature domains](#signature-domains) - [Data structures](#data-structures) - - [`Validator`](#validator) - - [`BeaconBlockBody`](#beaconblockbody) - - [`BeaconState`](#beaconstate) - - [`BranchChallenge`](#branchchallenge) - - [`BranchResponse`](#branchresponse) - - [`BranchChallengeRecord`](#branchchallengerecord) - - [`InteractiveCustodyChallengeRecord`](#interactivecustodychallengerecord) - - [`InteractiveCustodyChallengeInitiation`](#interactivecustodychallengeinitiation) - - [`InteractiveCustodyChallengeResponse`](#interactivecustodychallengeresponse) - - [`InteractiveCustodyChallengeContinuation`](#interactivecustodychallengecontinuation) - - [`SubkeyReveal`](#subkeyreveal) - - [Helpers](#helpers) - - [`get_branch_challenge_record_by_id`](#get_branch_challenge_record_by_id) - - [`get_custody_challenge_record_by_id`](#get_custody_challenge_record_by_id) - - [`get_attestation_merkle_depth`](#get_attestation_merkle_depth) - - [`epoch_to_custody_period`](#epoch_to_custody_period) - - [`slot_to_custody_period`](#slot_to_custody_period) - - [`get_current_custody_period`](#get_current_custody_period) - - [`verify_custody_subkey_reveal`](#verify_custody_subkey_reveal) - - [`verify_signed_challenge_message`](#verify_signed_challenge_message) - - [`penalize_validator`](#penalize_validator) - - [Per-slot processing](#per-slot-processing) - - [Operations](#operations) - - [Branch challenges](#branch-challenges) - - [Branch responses](#branch-responses) - - [Subkey reveals](#subkey-reveals) - - [Interactive custody challenge initiations](#interactive-custody-challenge-initiations) - - [Interactive custody challenge responses](#interactive-custody-challenge-responses) - - [Interactive custody challenge continuations](#interactive-custody-challenge-continuations) - - [Per-epoch processing](#per-epoch-processing) - - [One-time phase 1 initiation transition](#one-time-phase-1-initiation-transition) + - [`ShardBlockBody`](#shardblockbody) + - [`ShardBlock`](#shardblock) + - [`ShardBlockHeader`](#shardblockheader) + - [`ShardAttestation`](#shardattestation) + - [Helper functions](#helper-functions) + - [`get_period_committee`](#get_period_committee) + - [`get_persistent_committee`](#get_persistent_committee) + - [`get_shard_proposer_index`](#get_shard_proposer_index) + - [`get_shard_header`](#get_shard_header) + - [`verify_shard_attestation_signature`](#verify_shard_attestation_signature) + - [`compute_crosslink_data_root`](#compute_crosslink_data_root) + - [Object validity](#object-validity) + - [Shard blocks](#shard-blocks) + - [Shard attestations](#shard-attestations) + - [Beacon attestations](#beacon-attestations) + - [Shard fork choice rule](#shard-fork-choice-rule) -### Introduction +## 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](0_beacon-chain.md). +This document describes the shard data layer and the shard fork choice rule in Phase 1 of Ethereum 2.0. -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. +## Constants -### Terminology +### Misc -### Constants +| Name | Value | +| - | - | +| `BYTES_PER_SHARD_BLOCK_BODY` | `2**14` (= 16,384) | +| `MAX_SHARD_ATTESTIONS` | `2**4` (= 16) | +| `PHASE_1_GENESIS_EPOCH` | **TBD** | +| `PHASE_1_GENESIS_SLOT` | get_epoch_start_slot(PHASE_1_GENESIS_EPOCH) | -Phase 1 depends upon all of the constants defined in [Phase 0](0_beacon-chain.md#constants) in addition to the following: +### Time parameters -#### Misc +| Name | Value | Unit | Duration | +| - | - | :-: | :-: | +| `CROSSLINK_LOOKBACK` | 2**0 (= 1) | epochs | 6.2 minutes | +| `PERSISTENT_COMMITTEE_PERIOD` | 2**11 (= 2,048) | epochs | ~9 days | -| Name | Value | Unit | -|-------------------------------|------------------|--------| -| `SHARD_CHUNK_SIZE` | 2**5 (= 32) | bytes | -| `SHARD_BLOCK_SIZE` | 2**14 (= 16,384) | bytes | -| `MINOR_REWARD_QUOTIENT` | 2**8 (= 256) | | -| `MAX_POC_RESPONSE_DEPTH` | 5 | | -| `ZERO_PUBKEY` | int_to_bytes48(0)| | -| `VALIDATOR_NULL` | 2**64 - 1 | | +### Signature domains -#### Time parameters +| Name | Value | +| - | - | +| `DOMAIN_SHARD_PROPOSER` | `128` | +| `DOMAIN_SHARD_ATTESTER` | `129` | -| Name | Value | Unit | Duration | -| - | - | :-: | :-: | -| `CROSSLINK_LOOKBACK` | 2**5 (= 32) | slots | 3.2 minutes | -| `MAX_BRANCH_CHALLENGE_DELAY` | 2**11 (= 2,048) | epochs | 9 days | -| `CUSTODY_PERIOD_LENGTH` | 2**11 (= 2,048) | epochs | 9 days | -| `PERSISTENT_COMMITTEE_PERIOD` | 2**11 (= 2,048) | epochs | 9 days | -| `CHALLENGE_RESPONSE_DEADLINE` | 2**14 (= 16,384) | epochs | 73 days | - -#### Max operations per block - -| Name | Value | -|----------------------------------------------------|---------------| -| `MAX_BRANCH_CHALLENGES` | 2**2 (= 4) | -| `MAX_BRANCH_RESPONSES` | 2**4 (= 16) | -| `MAX_EARLY_SUBKEY_REVEALS` | 2**4 (= 16) | -| `MAX_INTERACTIVE_CUSTODY_CHALLENGE_INITIATIONS` | 2 | -| `MAX_INTERACTIVE_CUSTODY_CHALLENGE_RESPONSES` | 16 | -| `MAX_INTERACTIVE_CUSTODY_CHALLENGE_CONTINUTATIONS` | 16 | - -#### Signature domains - -| Name | Value | -|------------------------------|-----------------| -| `DOMAIN_SHARD_PROPOSER` | 129 | -| `DOMAIN_SHARD_ATTESTER` | 130 | -| `DOMAIN_CUSTODY_SUBKEY` | 131 | -| `DOMAIN_CUSTODY_INTERACTIVE` | 132 | - -# Shard chains and crosslink data +## Data structures + +### `ShardBlockBody` + +```python +['byte', BYTES_PER_SHARD_BLOCK_BODY] +``` + +### `ShardBlock` + +```python +{ + 'slot': Slot, + 'shard': Shard, + 'beacon_chain_root': Hash, + 'previous_block_root': Hash, + 'data': ShardBlockBody, + 'state_root': Hash, + 'attestations': [ShardAttestation], + 'signature': BLSSignature, +} +``` + +### `ShardBlockHeader` + +```python +{ + 'slot': Slot, + 'shard': Shard, + 'beacon_chain_root': Hash, + 'previous_block_root': Hash, + 'body_root': Hash, + 'state_root': Hash, + 'attestations': [ShardAttestation], + 'signature': BLSSignature, +} +``` + +### `ShardAttestation` + +```python +{ + 'data': { + 'slot': Slot, + 'shard': Shard, + 'shard_block_root': Hash, + }, + 'aggregation_bitfield': Bitfield, + 'aggregate_signature': BLSSignature, +} +``` ## Helper functions -#### `get_shuffled_committee` +### `get_period_committee` ```python -def get_shuffled_committee(state: BeaconState, - shard: Shard, - committee_start_epoch: Epoch, - index: int, - committee_count: int) -> List[ValidatorIndex]: +def get_period_committee(state: BeaconState, + shard: Shard, + committee_start_epoch: Epoch, + index: int, + committee_count: int) -> List[ValidatorIndex]: """ - Return shuffled committee. + Return committee for a period. Used to construct persistent committees. """ active_validator_indices = get_active_validator_indices(state.validator_registry, committee_start_epoch) - length = len(active_validator_indices) seed = generate_seed(state, committee_start_epoch) - start_offset = get_split_offset( - length, - SHARD_COUNT * committee_count, - shard * committee_count + index, - ) - end_offset = get_split_offset( - length, - SHARD_COUNT * committee_count, - shard * committee_count + index + 1, + return compute_committee( + validator_indices=active_validator_indices, + seed=seed, + index=shard * committee_count + index, + total_committees=SHARD_COUNT * committee_count, ) - return [ - active_validator_indices[get_permuted_index(i, length, seed)] - for i in range(start_offset, end_offset) - ] ``` -#### `get_persistent_committee` +### `get_persistent_committee` ```python def get_persistent_committee(state: BeaconState, @@ -160,7 +146,6 @@ def get_persistent_committee(state: BeaconState, """ Return the persistent committee for the given ``shard`` at the given ``slot``. """ - earlier_start_epoch = epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD * 2 later_start_epoch = epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD @@ -172,14 +157,11 @@ def get_persistent_committee(state: BeaconState, ) + 1 index = slot % committee_count - earlier_committee = get_shuffled_committee(state, shard, earlier_start_epoch, index, committee_count) - later_committee = get_shuffled_committee(state, shard, later_start_epoch, index, committee_count) + earlier_committee = get_period_committee(state, shard, earlier_start_epoch, index, committee_count) + later_committee = get_period_committee(state, shard, later_start_epoch, index, committee_count) def get_switchover_epoch(index): - return ( - bytes_to_int(hash(earlier_seed + bytes3(index))[0:8]) % - PERSISTENT_COMMITTEE_PERIOD - ) + 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 @@ -189,723 +171,232 @@ def get_persistent_committee(state: BeaconState, ))) ``` -#### `get_shard_proposer_index` +### `get_shard_proposer_index` ```python 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) - ) + # Randomly shift persistent committee persistent_committee = get_persistent_committee(state, shard, 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: + seed = hash(state.current_shuffling_seed + int_to_bytes8(shard) + int_to_bytes8(slot)) + random_index = bytes_to_int(seed[0:8]) % len(persistent_committee) + persistent_committee = persistent_committee[random_index:] + persistent_committee[:random_index] + + # Search for an active proposer + for index in persistent_committee: if is_active_validator(state.validator_registry[index], get_current_epoch(state)): return index - return None -``` - -## Data Structures - -### Shard chain blocks - -A `ShardBlock` object has the following fields: - -```python -{ - # 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, 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.validator_registry[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), DOMAIN_SHARD_PROPOSER))` passes. -* Let `group_public_key = bls_aggregate_pubkeys([state.validator_registry[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), DOMAIN_SHARD_ATTESTER))` 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: - -```python -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 -``` -```python -def merkle_root_of_bytes(data: bytes) -> bytes: - return merkle_root([data[i:i + 32] for i in range(0, len(data), 32)]) + # No block can be proposed if no validator is active + return None ``` -We define the function for computing the commitment as follows: +### `get_shard_header` ```python -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 - ]) - ) +def get_shard_header(block: ShardBlock) -> ShardBlockHeader: + return ShardBlockHeader( + slot: block.slot, + shard: block.shard, + beacon_chain_root: block.beacon_chain_root, + previous_block_root: block.previous_block_root, + body_root: hash_tree_root(block.body), + state_root: block.state_root, + attestations: block.attestations, + signature: block.signature, ) ``` -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). - -# Updates to the beacon chain - -## Data structures - -### `Validator` - -Add member values to the end of the `Validator` object: - -```python - 'next_subkey_to_reveal': 'uint64', - 'reveal_max_periods_late': 'uint64', -``` - -And the initializers: - -```python - 'next_subkey_to_reveal': get_current_custody_period(state), - 'reveal_max_periods_late': 0, -``` - -### `BeaconBlockBody` - -Add member values to the `BeaconBlockBody` structure: - -```python - 'branch_challenges': [BranchChallenge], - 'branch_responses': [BranchResponse], - 'subkey_reveals': [SubkeyReveal], - 'interactive_custody_challenge_initiations': [InteractiveCustodyChallengeInitiation], - 'interactive_custody_challenge_responses': [InteractiveCustodyChallengeResponse], - 'interactive_custody_challenge_continuations': [InteractiveCustodyChallengeContinuation], - -``` - -And initialize to the following: - -```python - 'branch_challenges': [], - 'branch_responses': [], - 'subkey_reveals': [], -``` - -### `BeaconState` - -Add member values to the `BeaconState` structure: - -```python - 'branch_challenge_records': [BranchChallengeRecord], - 'next_branch_challenge_id': 'uint64', - 'custody_challenge_records': [InteractiveCustodyChallengeRecord], - 'next_custody_challenge_id': 'uint64', -``` - -### `BranchChallenge` - -Define a `BranchChallenge` as follows: - -```python -{ - 'responder_index': 'uint64', - 'data_index': 'uint64', - 'attestation': SlashableAttestation, -} -``` - -### `BranchResponse` - -Define a `BranchResponse` as follows: - -```python -{ - 'challenge_id': 'uint64', - 'responding_to_custody_challenge': 'bool', - 'data': 'bytes32', - 'branch': ['bytes32'], -} -``` - -### `BranchChallengeRecord` - -Define a `BranchChallengeRecord` as follows: - -```python -{ - 'challenge_id': 'uint64', - 'challenger_index': 'uint64', - 'responder_index': 'uint64', - 'root': 'bytes32', - 'depth': 'uint64', - 'deadline': 'uint64', - 'data_index': 'uint64', -} -``` - -### `InteractiveCustodyChallengeRecord` - -```python -{ - 'challenge_id': 'uint64', - 'challenger_index': 'uint64', - 'responder_index': 'uint64', - # Initial data root - 'data_root': 'bytes32', - # Initial custody bit - 'custody_bit': 'bool', - # Responder subkey - 'responder_subkey': 'bytes96', - # The hash in the PoC tree in the position that we are currently at - 'current_custody_tree_node': 'bytes32', - # The position in the tree, in terms of depth and position offset - 'depth': 'uint64', - 'offset': 'uint64', - # Max depth of the branch - 'max_depth': 'uint64', - # Deadline to respond (as an epoch) - 'deadline': 'uint64', -} -``` - -### `InteractiveCustodyChallengeInitiation` - -```python -{ - 'attestation': SlashableAttestation, - 'responder_index': 'uint64', - 'challenger_index': 'uint64', - 'responder_subkey': 'bytes96', - 'signature': 'bytes96', -} -``` - -### `InteractiveCustodyChallengeResponse` - -```python -{ - 'challenge_id': 'uint64', - 'hashes': ['bytes32'], - 'signature': 'bytes96', -} -``` - -### `InteractiveCustodyChallengeContinuation` - -```python -{ - 'challenge_id': 'uint64', - 'sub_index': 'uint64', - 'new_custody_tree_node': 'bytes32', - 'proof': ['bytes32'], - 'signature': 'bytes96', -} -``` - -### `SubkeyReveal` - -Define a `SubkeyReveal` as follows: - -```python -{ - 'validator_index': 'uint64', - 'period': 'uint64', - 'subkey': 'bytes96', - 'mask': 'bytes32', - 'revealer_index': 'uint64' -} -``` - -## Helpers - -### `get_branch_challenge_record_by_id` - -```python -def get_branch_challenge_record_by_id(state: BeaconState, id: int) -> BranchChallengeRecord: - return [c for c in state.branch_challenges if c.challenge_id == id][0] -``` - -### `get_custody_challenge_record_by_id` - -```python -def get_custody_challenge_record_by_id(state: BeaconState, id: int) -> BranchChallengeRecord: - return [c for c in state.branch_challenges if c.challenge_id == id][0] -``` - -### `get_attestation_merkle_depth` - -```python -def get_attestation_merkle_depth(attestation: Attestation) -> int: - start_epoch = attestation.data.latest_crosslink.epoch - end_epoch = slot_to_epoch(attestation.data.slot) - chunks_per_slot = SHARD_BLOCK_SIZE // 32 - chunks = (end_epoch - start_epoch) * EPOCH_LENGTH * chunks_per_slot - return log2(next_power_of_two(chunks)) -``` - -### `epoch_to_custody_period` - -```python -def epoch_to_custody_period(epoch: Epoch) -> int: - return epoch // CUSTODY_PERIOD_LENGTH +### `verify_shard_attestation_signature` + +```python +def verify_shard_attestation_signature(state: BeaconState, + attestation: ShardAttestation) -> None: + data = attestation.data + persistent_committee = get_persistent_committee(state, data.shard, data.slot) + assert verify_bitfield(attestation.aggregation_bitfield, len(persistent_committee)) + pubkeys = [] + for i, index in enumerate(persistent_committee): + if get_bitfield_bit(attestation.aggregation_bitfield, i) == 0b1 + validator = state.validator_registry[index] + assert is_active_validator(validator, get_current_epoch(state)) + pubkeys.append(validator.pubkey) + assert bls_verify( + pubkey=bls_aggregate_pubkeys(pubkeys), + message_hash=data.shard_block_root, + signature=attestation.aggregate_signature, + domain=get_domain(state, slot_to_epoch(data.slot), DOMAIN_SHARD_ATTESTER) + ) ``` -### `slot_to_custody_period` +### `compute_crosslink_data_root` ```python -def slot_to_custody_period(slot: Slot) -> int: - return epoch_to_custody_period(slot_to_epoch(slot)) -``` - -### `get_current_custody_period` +def compute_crosslink_data_root(blocks: List[ShardBlock]) -> Hash: + def is_power_of_two(value: int) -> bool: + return (value > 0) and (value & (value - 1) == 0) -```python -def get_current_custody_period(state: BeaconState) -> int: - return epoch_to_custody_period(get_current_epoch(state)) -``` + def pad_to_power_of_2(values: List[bytes]) -> List[bytes]: + while not is_power_of_two(len(values)): + values += [b'\x00' * BYTES_PER_SHARD_BLOCK_BODY] + return values -### `verify_custody_subkey_reveal` + def merkle_root_of_bytes(data: bytes) -> bytes: + return merkle_root([data[i:i + 32] for i in range(0, len(data), 32)]) -```python -def verify_custody_subkey_reveal(pubkey: bytes48, - subkey: bytes96, - mask: bytes32, - mask_pubkey: bytes48, - period: int) -> bool: - # Legitimate reveal: checking that the provided value actually is the subkey - if mask == ZERO_HASH: - pubkeys=[pubkey] - message_hashes=[hash(int_to_bytes8(period))] - - # Punitive early reveal: checking that the provided value is a valid masked subkey - # (masking done to prevent "stealing the reward" from a whistleblower by block proposers) - # Secure under the aggregate extraction infeasibility assumption described on page 11-12 - # of https://crypto.stanford.edu/~dabo/pubs/papers/aggreg.pdf - else: - pubkeys=[pubkey, mask_pubkey] - message_hashes=[hash(int_to_bytes8(period)), mask] - - return bls_multi_verify( - pubkeys=pubkeys, - message_hashes=message_hashes, - signature=subkey, - domain=get_domain( - fork=state.fork, - epoch=period * CUSTODY_PERIOD_LENGTH, - domain_type=DOMAIN_CUSTODY_SUBKEY, - ) + return hash( + merkle_root(pad_to_power_of_2([ + merkle_root_of_bytes(zpad(serialize(get_shard_header(block)), BYTES_PER_SHARD_BLOCK_BODY)) for block in blocks + ])) + + merkle_root(pad_to_power_of_2([ + merkle_root_of_bytes(block.body) for block in blocks + ])) ) ``` -### `verify_signed_challenge_message` +## Object validity -```python -def verify_signed_challenge_message(message: Any, pubkey: bytes48) -> bool: - return bls_verify( - message_hash=signed_root(message), - pubkey=pubkey, - signature=message.signature, - domain=get_domain(state, get_current_epoch(state), DOMAIN_CUSTODY_INTERACTIVE) - ) +### Shard blocks -``` +Let: -### `penalize_validator` - -Change the definition of `penalize_validator` as follows: +* `beacon_blocks` be the `BeaconBlock` list such that `beacon_blocks[slot]` is the canonical `BeaconBlock` at slot `slot` +* `beacon_state` be the canonical `BeaconState` after processing `beacon_blocks[-1]` +* `valid_shard_blocks` be the list of valid `ShardBlock`, recursively defined +* `unix_time` be the current unix time +* `candidate` be a candidate `ShardBlock` for which validity is to be determined by running `is_valid_shard_block` ```python -def penalize_validator(state: BeaconState, index: ValidatorIndex, whistleblower_index=None:ValidatorIndex) -> None: - """ - Penalize the validator of the given ``index``. - Note that this function mutates ``state``. - """ - exit_validator(state, index) - validator = state.validator_registry[index] - state.latest_penalized_balances[get_current_epoch(state) % LATEST_PENALIZED_EXIT_LENGTH] += get_effective_balance(state, index) - - block_proposer_index = get_beacon_proposer_index(state, state.slot) - whistleblower_reward = get_effective_balance(state, index) // WHISTLEBLOWER_REWARD_QUOTIENT - if whistleblower_index is None: - state.validator_balances[block_proposer_index] += whistleblower_reward - else: - state.validator_balances[whistleblower_index] += ( - whistleblower_reward * INCLUDER_REWARD_QUOTIENT / (INCLUDER_REWARD_QUOTIENT + 1) - ) - state.validator_balances[block_proposer_index] += whistleblower_reward / (INCLUDER_REWARD_QUOTIENT + 1) - state.validator_balances[index] -= whistleblower_reward - validator.penalized_epoch = get_current_epoch(state) - validator.withdrawable_epoch = get_current_epoch(state) + LATEST_PENALIZED_EXIT_LENGTH -``` - -The only change is that this introduces the possibility of a penalization where the "whistleblower" that takes credit is NOT the block proposer. +def is_valid_shard_block(beacon_blocks: List[BeaconBlock], + beacon_state: BeaconState, + valid_shard_blocks: List[ShardBlock], + unix_time: uint64, + candidate: ShardBlock) -> bool + # Check if block is already determined valid + for _, block in enumerate(valid_shard_blocks): + if candidate == block: + return True -## Per-slot processing - -### Operations - -Add the following operations to the per-slot processing, in order the given below and _after_ all other operations (specifically, right after exits). - -#### Branch challenges - -Verify that `len(block.body.branch_challenges) <= MAX_BRANCH_CHALLENGES`. - -For each `challenge` in `block.body.branch_challenges`, run: - -```python -def process_branch_challenge(state: BeaconState, - challenge: BranchChallenge) -> None: - # Check that it's not too late to challenge - assert slot_to_epoch(challenge.attestation.data.slot) >= get_current_epoch(state) - MAX_BRANCH_CHALLENGE_DELAY - assert state.validator_registry[responder_index].exit_epoch >= get_current_epoch(state) - MAX_BRANCH_CHALLENGE_DELAY - # Check the attestation is valid - assert verify_slashable_attestation(state, challenge.attestation) - # Check that the responder participated - assert challenger.responder_index in challenge.attestation.validator_indices - # Check the challenge is not a duplicate - assert [ - c for c in state.branch_challenge_records if c.root == challenge.attestation.data.crosslink_data_root and - c.data_index == challenge.data_index - ] == [] - # Check validity of depth - depth = get_attestation_merkle_depth(challenge.attestation) - assert c.data_index < 2**depth - # Add new challenge - state.branch_challenge_records.append(BranchChallengeRecord( - challenge_id=state.next_branch_challenge_id, - challenger_index=get_beacon_proposer_index(state, state.slot), - root=challenge.attestation.data.shard_chain_commitment, - depth=depth, - deadline=get_current_epoch(state) + CHALLENGE_RESPONSE_DEADLINE, - data_index=challenge.data_index - )) - state.next_branch_challenge_id += 1 -``` + # Check slot number + assert block.slot >= PHASE_1_GENESIS_SLOT + assert unix_time >= beacon_state.genesis_time + (block.slot - GENESIS_SLOT) * SECONDS_PER_SLOT -#### Branch responses + # Check shard number + assert block.shard <= SHARD_COUNT -Verify that `len(block.body.branch_responses) <= MAX_BRANCH_RESPONSES`. + # Check beacon block + beacon_block = beacon_blocks[block.slot] + assert block.beacon_block_root == signed_root(beacon_block) + assert beacon_block.slot <= block.slot: -For each `response` in `block.body.branch_responses`, if `response.responding_to_custody_challenge == False`, run: + # Check state root + assert block.state_root == ZERO_HASH # [to be removed in phase 2] -```python -def process_branch_exploration_response(state: BeaconState, - response: BranchResponse) -> None: - challenge = get_branch_challenge_record_by_id(response.challenge_id) - assert verify_merkle_branch( - leaf=response.data, - branch=response.branch, - depth=challenge.depth, - index=challenge.data_index, - root=challenge.root + # Check parent block + if block.slot == PHASE_1_GENESIS_SLOT: + assert candidate.previous_block_root == ZERO_HASH + else: + parent_block = next( + block for block in valid_shard_blocks if + signed_root(block) == candidate.previous_block_root + , None) + assert parent_block != None + assert parent_block.shard == block.shard + assert parent_block.slot < block.slot + assert signed_root(beacon_blocks[parent_block.slot]) == parent_block.beacon_chain_root + + # Check attestations + assert len(block.attestations) <= MAX_SHARD_ATTESTIONS + for _, attestation in enumerate(block.attestations): + assert max(GENESIS_SHARD_SLOT, block.slot - SLOTS_PER_EPOCH) <= attestation.data.slot + assert attesation.data.slot <= block.slot - MIN_ATTESTATION_INCLUSION_DELAY + assert attetation.data.shart == block.shard + verify_shard_attestation_signature(beacon_state, attestation) + + # Check signature + proposer_index = get_shard_proposer_index(beacon_state, block.shard, block.slot) + assert proposer_index is not None + assert bls_verify( + pubkey=validators[proposer_index].pubkey, + message_hash=signed_root(block), + signature=block.signature, + domain=get_domain(beacon_state, slot_to_epoch(block.slot), DOMAIN_SHARD_PROPOSER) ) - # Must wait at least ENTRY_EXIT_DELAY before responding to a branch challenge - assert get_current_epoch(state) >= challenge.inclusion_epoch + ENTRY_EXIT_DELAY - state.branch_challenge_records.pop(challenge) - # Reward the proposer - proposer_index = get_beacon_proposer_index(state, state.slot) - state.validator_balances[proposer_index] += base_reward(state, index) // MINOR_REWARD_QUOTIENT -``` -If `response.responding_to_custody_challenge == True`, run: - -```python -def process_branch_custody_response(state: BeaconState, - response: BranchResponse) -> None: - challenge = get_custody_challenge_record_by_id(response.challenge_id) - responder = state.validator_registry[challenge.responder_index] - # Verify we're not too late - assert get_current_epoch(state) < responder.withdrawable_epoch - # Verify the Merkle branch *of the data tree* - assert verify_merkle_branch( - leaf=response.data, - branch=response.branch, - depth=challenge.max_depth, - index=challenge.offset, - root=challenge.data_root - ) - # Responder wins - if hash(challenge.responder_subkey + response.data) == challenge.current_custody_tree_node: - penalize_validator(state, challenge.challenger_index, challenge.responder_index) - # Challenger wins - else: - penalize_validator(state, challenge.responder_index, challenge.challenger_index) - state.custody_challenge_records.pop(challenge) + return True ``` -#### Subkey reveals - -Verify that `len(block.body.early_subkey_reveals) <= MAX_EARLY_SUBKEY_REVEALS`. - -For each `reveal` in `block.body.early_subkey_reveals`: - -* Verify that `verify_custody_subkey_reveal(state.validator_registry[reveal.validator_index].pubkey, reveal.subkey, reveal.period, reveal.mask, state.validator_registry[reveal.revealer_index].pubkey)` returns `True`. -* Let `is_early_reveal = reveal.period > get_current_custody_period(state) or (reveal.period == get_current_custody_period(state) and state.validator_registry[reveal.validator_index].exit_epoch > get_current_epoch(state))` (ie. either the reveal is of a future period, or it's of the current period and the validator is still active) -* Verify that one of the following is true: - * (i) `is_early_reveal` is `True` - * (ii) `is_early_reveal` is `False` and `reveal.period == state.validator_registry[reveal.validator_index].next_subkey_to_reveal` (revealing a past subkey, or a current subkey for a validator that has exited) and `reveal.mask == ZERO_HASH` - -In case (i): - -* Verify that `state.validator_registry[reveal.validator_index].penalized_epoch > get_current_epoch(state). -* Run `penalize_validator(state, reveal.validator_index, reveal.revealer_index)`. -* Set `state.validator_balances[reveal.revealer_index] += base_reward(state, index) // MINOR_REWARD_QUOTIENT` - -In case (ii): +### Shard attestations -* Determine the proposer `proposer_index = get_beacon_proposer_index(state, state.slot)` and set `state.validator_balances[proposer_index] += base_reward(state, index) // MINOR_REWARD_QUOTIENT`. -* Set `state.validator_registry[reveal.validator_index].next_subkey_to_reveal += 1` -* Set `state.validator_registry[reveal.validator_index].reveal_max_periods_late = max(state.validator_registry[reveal.validator_index].reveal_max_periods_late, get_current_period(state) - reveal.period)`. +Let: -#### Interactive custody challenge initiations - -Verify that `len(block.body.interactive_custody_challenge_initiations) <= MAX_INTERACTIVE_CUSTODY_CHALLENGE_INITIATIONS`. - -For each `initiation` in `block.body.interactive_custody_challenge_initiations`, use the following function to process it: +* `valid_shard_blocks` be the list of valid `ShardBlock` +* `beacon_state` be the canonical `BeaconState` +* `candidate` be a candidate `ShardAttestation` for which validity is to be determined by running `is_valid_shard_attestation` ```python -def process_initiation(state: BeaconState, - initiation: InteractiveCustodyChallengeInitiation) -> None: - challenger = state.validator_registry[initiation.challenger_index] - responder = state.validator_registry[initiation.responder_index] - # Verify the signature - assert verify_signed_challenge_message(initiation, challenger.pubkey) - # Verify the attestation - assert verify_slashable_attestation(initiation.attestation, state) - # Check that the responder actually participated in the attestation - assert initiation.responder_index in attestation.validator_indices - # Any validator can be a challenger or responder of max 1 challenge at a time - for c in state.custody_challenge_records: - assert c.challenger_index != initiation.challenger_index - assert c.responder_index != initiation.responder_index - # Can't challenge if you've been penalized - assert challenger.penalized_epoch == FAR_FUTURE_EPOCH - # Make sure the revealed subkey is valid - assert verify_custody_subkey_reveal( - pubkey=state.validator_registry[responder_index].pubkey, - subkey=initiation.responder_subkey, - period=slot_to_custody_period(attestation.data.slot) - ) - # Verify that the attestation is still eligible for challenging - min_challengeable_epoch = responder.exit_epoch - CUSTODY_PERIOD_LENGTH * (1 + responder.reveal_max_periods_late) - assert min_challengeable_epoch <= slot_to_epoch(initiation.attestation.data.slot) - # Create a new challenge object - state.branch_challenge_records.append(InteractiveCustodyChallengeRecord( - challenge_id=state.next_branch_challenge_id, - challenger_index=initiation.challenger_index, - responder_index=initiation.responder_index, - data_root=attestation.custody_commitment, - custody_bit=get_bitfield_bit(attestation.custody_bitfield, attestation.validator_indices.index(responder_index)), - responder_subkey=responder_subkey, - current_custody_tree_node=ZERO_HASH, - depth=0, - offset=0, - max_depth=get_attestation_data_merkle_depth(initiation.attestation.data), - deadline=get_current_epoch(state) + CHALLENGE_RESPONSE_DEADLINE - )) - state.next_branch_challenge_id += 1 - # Responder can't withdraw yet! - state.validator_registry[responder_index].withdrawable_epoch = FAR_FUTURE_EPOCH -``` - -#### Interactive custody challenge responses - -A response provides 32 hashes that are under current known proof of custody tree node. Note that at the beginning the tree node is just one bit of the custody root, so we ask the responder to sign to commit to the top 5 levels of the tree and therefore the root hash; at all other stages in the game responses are self-verifying. - -Verify that `len(block.body.interactive_custody_challenge_responses) <= MAX_INTERACTIVE_CUSTODY_CHALLENGE_RESPONSES`. +def is_valid_shard_attestation(valid_shard_blocks: List[ShardBlock], + beacon_state: BeaconState, + candidate: Attestation) -> bool: + # Check shard block + shard_block = next( + block for block in valid_shard_blocks if + signed_root(block) == candidate.attestation.data.shard_block_root + , None) + assert shard_block != None + assert shard_block.slot == attestation.data.slot + assert shard_block.shard == attestation.data.shard -For each `response` in `block.body.interactive_custody_challenge_responses`, use the following function to process it: + # Check signature + verify_shard_attestation_signature(beacon_state, attestation) -```python -def process_response(state: BeaconState, - response: InteractiveCustodyChallengeResponse) -> None: - challenge = get_custody_challenge_record_by_id(state, response.challenge_id) - responder = state.validator_registry[challenge.responder_index] - # Check that the right number of hashes was provided - expected_depth = min(challenge.max_depth - challenge.depth, MAX_POC_RESPONSE_DEPTH) - assert 2**expected_depth == len(response.hashes) - # Must make some progress! - assert expected_depth > 0 - # Check the hashes match the previously provided root - root = merkle_root(response.hashes) - # If this is the first response check the bit and the signature and set the root - if challenge.depth == 0: - assert get_bitfield_bit(root, 0) == challenge.custody_bit - assert verify_signed_challenge_message(response, responder.pubkey) - challenge.current_custody_tree_node = root - # Otherwise just check the response against the root - else: - assert root == challenge_data.current_custody_tree_node - # Update challenge data - challenge.deadline=FAR_FUTURE_EPOCH - responder.withdrawable_epoch = get_current_epoch(state) + MAX_POC_RESPONSE_DEPTH + return True ``` -#### Interactive custody challenge continuations - -Once a response provides 32 hashes, the challenger has the right to choose any one of them that they feel is constructed incorrectly to continue the game. Note that eventually, the game will get to the point where the `new_custody_tree_node` is a leaf node. - -Verify that `len(block.body.interactive_custody_challenge_continuations) <= MAX_INTERACTIVE_CUSTODY_CHALLENGE_CONTINUATIONS`. - -For each `continuation` in `block.body.interactive_custody_challenge_continuations`, use the following function to process it: - -```python -def process_continuation(state: BeaconState, - continuation: InteractiveCustodyChallengeContinuation) -> None: - challenge = get_custody_challenge_record_by_id(state, continuation.challenge_id) - challenger = state.validator_registry[challenge.challenger_index] - responder = state.validator_registry[challenge.responder_index] - expected_depth = min(challenge_data.max_depth - challenge_data.depth, MAX_POC_RESPONSE_DEPTH) - # Verify we're not too late - assert get_current_epoch(state) < responder.withdrawable_epoch - # Verify the Merkle branch (the previous custody response provided the next level of hashes so the - # challenger has the info to make any Merkle branch) - assert verify_merkle_branch( - leaf=new_custody_tree_node, - branch=continuation.proof, - depth=expected_depth, - index=sub_index, - root=challenge_data.current_custody_tree_node - ) - # Verify signature - assert verify_signed_challenge_message(continuation, challenger.pubkey) - # Update the challenge data - challenge.current_custody_tree_node = continuation.new_custody_tree_node - challenge.depth += expected_depth - challenge.deadline = get_current_epoch(state) + MAX_POC_RESPONSE_DEPTH - responder.withdrawable_epoch = FAR_FUTURE_EPOCH - challenge.offset = challenge_data.offset * 2**expected_depth + sub_index -``` +### Beacon attestations -## Per-epoch processing +Let: -Add the following loop immediately below the `process_ejections` loop: +* `shard` be a valid `Shard` +* `shard_blocks` be the `ShardBlock` list such that `shard_blocks[slot]` is the canonical `ShardBlock` for shard `shard` at slot `slot` +* `beacon_state` be the canonical `BeaconState` +* `valid_attestations` be the list of valid `Attestation`, recursively defined +* `candidate` be a candidate `Attestation` which is valid under phase 0 rules, and for which validity is to be determined under phase 1 rules by running `is_valid_beacon_attestation` ```python -def process_challenge_absences(state: BeaconState) -> None: - """ - Iterate through the challenge list - and penalize validators with balance that did not answer challenges. - """ - for c in state.branch_challenge_records: - if get_current_epoch(state) > c.deadline: - penalize_validator(state, c.responder_index, c.challenger_index) - - for c in state.custody_challenge_records: - if get_current_epoch(state) > c.deadline: - penalize_validator(state, c.responder_index, c.challenger_index) - if get_current_epoch(state) > state.validator_registry[c.responder_index].withdrawable_epoch: - penalize_validator(state, c.challenger_index, c.responder_index) -``` - -In `process_penalties_and_exits`, change the definition of `eligible` to the following (note that it is not a pure function because `state` is declared in the surrounding scope): +def is_valid_beacon_attestation(shard: Shard, + shard_blocks: List[ShardBlock], + beacon_state: BeaconState, + valid_attestations: List[Attestation], + candidate: Attestation) -> bool: + # Check if attestation is already determined valid + for _, attestation in enumerate(valid_attestations): + if candidate == attestation: + return True -```python -def eligible(index): - validator = state.validator_registry[index] - # Cannot exit if there are still open branch challenges - if [c for c in state.branch_challenge_records if c.responder_index == index] != []: - return False - # Cannot exit if you have not revealed all of your subkeys - elif validator.next_subkey_to_reveal <= epoch_to_custody_period(validator.exit_epoch): - return False - # Cannot exit if you already have - elif validator.withdrawable_epoch < FAR_FUTURE_EPOCH: - return False - # Return minimum time + # Check previous attestation + if candidate.data.previous_crosslink.epoch <= PHASE_1_GENESIS_EPOCH: + assert candidate.data.previous_crosslink.crosslink_data_root == ZERO_HASH else: - return current_epoch >= validator.exit_epoch + MIN_VALIDATOR_WITHDRAWAL_EPOCHS -``` - -## One-time phase 1 initiation transition - -Run the following on the fork block after per-slot processing and before per-block and per-epoch processing. + previous_attestation = next( + attestation for attestation in valid_attestations if + attestation.data.crosslink_data_root == candidate.data.previous_crosslink.crosslink_data_root + , None) + assert previous_attestation != None + assert candidate.data.previous_attestation.epoch < slot_to_epoch(candidate.data.slot) -For all `validator` in `ValidatorRegistry`, update it to the new format and fill the new member values with: + # Check crosslink data root + start_epoch = state.latest_crosslinks[shard].epoch + end_epoch = min(slot_to_epoch(candidate.data.slot) - CROSSLINK_LOOKBACK, start_epoch + MAX_CROSSLINK_EPOCHS) + blocks = [] + for slot in range(start_epoch * SLOTS_PER_EPOCH, end_epoch * SLOTS_PER_EPOCH): + blocks.append(shard_blocks[slot]) + assert candidate.data.crosslink_data_root == compute_crosslink_data_root(blocks) -```python - 'next_subkey_to_reveal': get_current_custody_period(state), - 'reveal_max_periods_late': 0, + return True ``` -Update the `BeaconState` to the new format and fill the new member values with: +## Shard fork choice rule -```python - 'branch_challenge_records': [], - 'next_branch_challenge_id': 0, - 'custody_challenge_records': [], - 'next_custody_challenge_id': 0, -``` +The fork choice rule for any shard is LMD GHOST using the shard 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 (i.e. `state.crosslinks[shard].shard_block_root`). Only blocks whose `beacon_chain_root` 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.)