# Sharding -- The Beacon Chain **Notice**: This document is a work-in-progress for researchers and implementers. ## Table of contents - [Introduction](#introduction) - [Glossary](#glossary) - [Custom types](#custom-types) - [Constants](#constants) - [Misc](#misc) - [Domain types](#domain-types) - [Shard Work Status](#shard-work-status) - [Misc](#misc-1) - [Participation flag indices](#participation-flag-indices) - [Incentivization weights](#incentivization-weights) - [Preset](#preset) - [Misc](#misc-2) - [Shard blob samples](#shard-blob-samples) - [Precomputed size verification points](#precomputed-size-verification-points) - [Gwei values](#gwei-values) - [Configuration](#configuration) - [Updated containers](#updated-containers) - [`AttestationData`](#attestationdata) - [`BeaconBlockBody`](#beaconblockbody) - [`BeaconState`](#beaconstate) - [New containers](#new-containers) - [`Builder`](#builder) - [`DataCommitment`](#datacommitment) - [`AttestedDataCommitment`](#attesteddatacommitment) - [`ShardBlobBody`](#shardblobbody) - [`ShardBlobBodySummary`](#shardblobbodysummary) - [`ShardBlob`](#shardblob) - [`ShardBlobHeader`](#shardblobheader) - [`SignedShardBlob`](#signedshardblob) - [`SignedShardBlobHeader`](#signedshardblobheader) - [`PendingShardHeader`](#pendingshardheader) - [`ShardBlobReference`](#shardblobreference) - [`ShardProposerSlashing`](#shardproposerslashing) - [`ShardWork`](#shardwork) - [Helper functions](#helper-functions) - [Misc](#misc-3) - [`next_power_of_two`](#next_power_of_two) - [`compute_previous_slot`](#compute_previous_slot) - [`compute_updated_sample_price`](#compute_updated_sample_price) - [`compute_committee_source_epoch`](#compute_committee_source_epoch) - [`batch_apply_participation_flag`](#batch_apply_participation_flag) - [Beacon state accessors](#beacon-state-accessors) - [Updated `get_committee_count_per_slot`](#updated-get_committee_count_per_slot) - [`get_active_shard_count`](#get_active_shard_count) - [`get_shard_proposer_index`](#get_shard_proposer_index) - [`get_start_shard`](#get_start_shard) - [`compute_shard_from_committee_index`](#compute_shard_from_committee_index) - [`compute_committee_index_from_shard`](#compute_committee_index_from_shard) - [Block processing](#block-processing) - [Operations](#operations) - [Extended Attestation processing](#extended-attestation-processing) - [`process_shard_header`](#process_shard_header) - [`process_shard_proposer_slashing`](#process_shard_proposer_slashing) - [Epoch transition](#epoch-transition) - [`process_pending_shard_confirmations`](#process_pending_shard_confirmations) - [`reset_pending_shard_work`](#reset_pending_shard_work) ## Introduction This document describes the extensions made to the Phase 0 design of The Beacon Chain to support data sharding, based on the ideas [here](https://hackmd.io/G-Iy5jqyT7CXWEz8Ssos8g) and more broadly [here](https://arxiv.org/abs/1809.09044), using KZG10 commitments to commit to data to remove any need for fraud proofs (and hence, safety-critical synchrony assumptions) in the design. ### Glossary - **Data**: A list of KZG points, to translate a byte string into - **Blob**: Data with commitments and meta-data, like a flattened bundle of L2 transactions. - **Builder**: Independent actor that builds blobs and bids for proposal slots via fee-paying blob-headers, responsible for availability. - **Shard proposer**: Validator taking bids from blob builders for shard data opportunity, co-signs with builder to propose the blob. ## Custom types We define the following Python custom types for type hinting and readability: | Name | SSZ equivalent | Description | | - | - | - | | `Shard` | `uint64` | A shard number | | `BLSCommitment` | `Bytes48` | A G1 curve point | | `BLSPoint` | `uint256` | A number `x` in the range `0 <= x < MODULUS` | | `BuilderIndex` | `uint64` | Builder registry index | ## Constants The following values are (non-configurable) constants used throughout the specification. ### Misc | Name | Value | Notes | | - | - | - | | `PRIMITIVE_ROOT_OF_UNITY` | `5` | Primitive root of unity of the BLS12_381 (inner) modulus | | `DATA_AVAILABILITY_INVERSE_CODING_RATE` | `2**1` (= 2) | Factor by which samples are extended for data availability encoding | | `POINTS_PER_SAMPLE` | `uint64(2**3)` (= 8) | 31 * 8 = 248 bytes | | `MODULUS` | `0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001` (curve order of BLS12_381) | ### Domain types | Name | Value | | - | - | | `DOMAIN_SHARD_BLOB` | `DomainType('0x80000000')` | ### Shard Work Status | Name | Value | Notes | | - | - | - | | `SHARD_WORK_UNCONFIRMED` | `0` | Unconfirmed, nullified after confirmation time elapses | | `SHARD_WORK_CONFIRMED` | `1` | Confirmed, reduced to just the commitment | | `SHARD_WORK_PENDING` | `2` | Pending, a list of competing headers | ### Misc TODO: `PARTICIPATION_FLAG_WEIGHTS` backwards-compatibility is difficult, depends on usage. | Name | Value | | - | - | | `PARTICIPATION_FLAG_WEIGHTS` | `[TIMELY_SOURCE_WEIGHT, TIMELY_TARGET_WEIGHT, TIMELY_HEAD_WEIGHT, TIMELY_SHARD_WEIGHT]` | ### Participation flag indices | Name | Value | | - | - | | `TIMELY_SHARD_FLAG_INDEX` | `3` | ### Incentivization weights TODO: determine weight for shard attestations | Name | Value | | - | - | | `TIMELY_SHARD_WEIGHT` | `uint64(8)` | TODO: `WEIGHT_DENOMINATOR` needs to be adjusted, but this breaks a lot of Altair code. ## Preset ### Misc | Name | Value | Notes | | - | - | - | | `MAX_SHARDS` | `uint64(2**10)` (= 1,024) | Theoretical max shard count (used to determine data structure sizes) | | `INITIAL_ACTIVE_SHARDS` | `uint64(2**6)` (= 64) | Initial shard count | | `SAMPLE_PRICE_ADJUSTMENT_COEFFICIENT` | `uint64(2**3)` (= 8) | Sample price may decrease/increase by at most exp(1 / this value) *per epoch* | | `MAX_SHARD_PROPOSER_SLASHINGS` | `2**4` (= 16) | Maximum amount of shard proposer slashing operations per block | | `MAX_SHARD_HEADERS_PER_SHARD` | `4` | | | `SHARD_STATE_MEMORY_SLOTS` | `uint64(2**8)` (= 256) | Number of slots for which shard commitments and confirmation status is directly available in the state | | `BLOB_BUILDER_REGISTRY_LIMIT` | `uint64(2**40)` (= 1,099,511,627,776) | shard blob builders | ### Shard blob samples | Name | Value | Notes | | - | - | - | | `MAX_SAMPLES_PER_BLOB` | `uint64(2**11)` (= 2,048) | 248 * 2,048 = 507,904 bytes | | `TARGET_SAMPLES_PER_BLOB` | `uint64(2**10)` (= 1,024) | 248 * 1,024 = 253,952 bytes | ### Precomputed size verification points | Name | Value | | - | - | | `G1_SETUP` | Type `List[G1]`. The G1-side trusted setup `[G, G*s, G*s**2....]`; note that the first point is the generator. | | `G2_SETUP` | Type `List[G2]`. The G2-side trusted setup `[G, G*s, G*s**2....]` | | `ROOT_OF_UNITY` | `pow(PRIMITIVE_ROOT_OF_UNITY, (MODULUS - 1) // int(MAX_SAMPLES_PER_BLOB * POINTS_PER_SAMPLE), MODULUS)` | ### Gwei values | Name | Value | Unit | Description | | - | - | - | - | | `MAX_SAMPLE_PRICE` | `Gwei(2**33)` (= 8,589,934,592) | Gwei | Max sample charged for a TARGET-sized shard blob | | `MIN_SAMPLE_PRICE` | `Gwei(2**3)` (= 8) | Gwei | Min sample price charged for a TARGET-sized shard blob | ## Configuration Note: Some preset variables may become run-time configurable for testnets, but default to a preset while the spec is unstable. E.g. `INITIAL_ACTIVE_SHARDS`, `MAX_SAMPLES_PER_BLOB` and `TARGET_SAMPLES_PER_BLOB`. ## Updated containers The following containers have updated definitions to support Sharding. ### `AttestationData` ```python class AttestationData(Container): slot: Slot index: CommitteeIndex # LMD GHOST vote beacon_block_root: Root # FFG vote source: Checkpoint target: Checkpoint # Hash-tree-root of ShardBlob shard_blob_root: Root # [New in Sharding] ``` ### `BeaconBlockBody` ```python class BeaconBlockBody(merge.BeaconBlockBody): # [extends The Merge block body] shard_proposer_slashings: List[ShardProposerSlashing, MAX_SHARD_PROPOSER_SLASHINGS] shard_headers: List[SignedShardBlobHeader, MAX_SHARDS * MAX_SHARD_HEADERS_PER_SHARD] ``` ### `BeaconState` ```python class BeaconState(merge.BeaconState): # Blob builder registry. blob_builders: List[Builder, BLOB_BUILDER_REGISTRY_LIMIT] blob_builder_balances: List[Gwei, BLOB_BUILDER_REGISTRY_LIMIT] # A ring buffer of the latest slots, with information per active shard. shard_buffer: Vector[List[ShardWork, MAX_SHARDS], SHARD_STATE_MEMORY_SLOTS] shard_sample_price: uint64 ``` ## New containers ### `Builder` ```python class Builder(Container): pubkey: BLSPubkey # TODO: fields for either an expiry mechanism (refunding execution account with remaining balance) # and/or a builder-transaction mechanism. ``` ### `DataCommitment` ```python class DataCommitment(Container): # KZG10 commitment to the data point: BLSCommitment # Length of the data in samples samples_count: uint64 ``` ### `AttestedDataCommitment` ```python class AttestedDataCommitment(Container): # KZG10 commitment to the data, and length commitment: DataCommitment # hash_tree_root of the ShardBlobHeader (stored so that attestations can be checked against it) root: Root # The proposer who included the shard-header includer_index: ValidatorIndex ``` ### `ShardBlobBody` Unsigned shard data, bundled by a shard-builder. Unique, signing different bodies as shard proposer for the same `(slot, shard)` is slashable. ```python class ShardBlobBody(Container): # The actual data commitment commitment: DataCommitment # Proof that the degree < commitment.samples_count * POINTS_PER_SAMPLE degree_proof: BLSCommitment # The actual data. Should match the commitment and degree proof. data: List[BLSPoint, POINTS_PER_SAMPLE * MAX_SAMPLES_PER_BLOB] # fee payment fields (EIP 1559 like) # TODO: express in MWei instead? max_priority_fee_per_sample: Gwei max_fee_per_sample: Gwei ``` ### `ShardBlobBodySummary` Summary version of the `ShardBlobBody`, omitting the data payload, while preserving the data-commitments. The commitments are not further collapsed to a single hash, to avoid an extra network roundtrip between proposer and builder, to include the header on-chain more quickly. ```python class ShardBlobBodySummary(Container): # The actual data commitment commitment: DataCommitment # Proof that the degree < commitment.samples_count * POINTS_PER_SAMPLE degree_proof: BLSCommitment # Hash-tree-root as summary of the data field data_root: Root # fee payment fields (EIP 1559 like) # TODO: express in MWei instead? max_priority_fee_per_sample: Gwei max_fee_per_sample: Gwei ``` ### `ShardBlob` `ShardBlobBody` wrapped with the header data that is unique to the shard blob proposal. ```python class ShardBlob(Container): slot: Slot shard: Shard # Builder of the data, pays data-fee to proposer builder_index: BuilderIndex # Proposer of the shard-blob proposer_index: ValidatorIndex # Blob contents body: ShardBlobBody ``` ### `ShardBlobHeader` Header version of `ShardBlob`. ```python class ShardBlobHeader(Container): slot: Slot shard: Shard # Builder of the data, pays data-fee to proposer builder_index: BuilderIndex # Proposer of the shard-blob proposer_index: ValidatorIndex # Blob contents, without the full data body_summary: ShardBlobBodySummary ``` ### `SignedShardBlob` Full blob data, signed by the shard builder (ensuring fee payment) and shard proposer (ensuring a single proposal). ```python class SignedShardBlob(Container): message: ShardBlob signature: BLSSignature ``` ### `SignedShardBlobHeader` Header of the blob, the signature is equally applicable to `SignedShardBlob`. Shard proposers can accept `SignedShardBlobHeader` as a data-transaction by co-signing the header. ```python class SignedShardBlobHeader(Container): message: ShardBlobHeader # Signature by builder. # Once accepted by proposer, the signatures is the aggregate of both. signature: BLSSignature ``` ### `PendingShardHeader` ```python class PendingShardHeader(Container): # The commitment that is attested attested: AttestedDataCommitment # Who voted for the header votes: Bitlist[MAX_VALIDATORS_PER_COMMITTEE] # Sum of effective balances of votes weight: Gwei # When the header was last updated, as reference for weight accuracy update_slot: Slot ``` ### `ShardBlobReference` Reference version of `ShardBlobHeader`, substituting the body for just a hash-tree-root. ```python class ShardBlobReference(Container): slot: Slot shard: Shard # Builder of the data builder_index: BuilderIndex # Proposer of the shard-blob proposer_index: ValidatorIndex # Blob hash-tree-root for slashing reference body_root: Root ``` ### `ShardProposerSlashing` ```python class ShardProposerSlashing(Container): slot: Slot shard: Shard proposer_index: ValidatorIndex builder_index_1: BuilderIndex builder_index_2: BuilderIndex body_root_1: Root body_root_2: Root signature_1: BLSSignature signature_2: BLSSignature ``` ### `ShardWork` ```python class ShardWork(Container): # Upon confirmation the data is reduced to just the commitment. status: Union[ # See Shard Work Status enum None, # SHARD_WORK_UNCONFIRMED AttestedDataCommitment, # SHARD_WORK_CONFIRMED List[PendingShardHeader, MAX_SHARD_HEADERS_PER_SHARD] # SHARD_WORK_PENDING ] ``` ## Helper functions ### Misc #### `next_power_of_two` ```python def next_power_of_two(x: int) -> int: return 2 ** ((x - 1).bit_length()) ``` #### `compute_previous_slot` ```python def compute_previous_slot(slot: Slot) -> Slot: if slot > 0: return Slot(slot - 1) else: return Slot(0) ``` #### `compute_updated_sample_price` ```python def compute_updated_sample_price(prev_price: Gwei, samples_length: uint64, active_shards: uint64) -> Gwei: adjustment_quotient = active_shards * SLOTS_PER_EPOCH * SAMPLE_PRICE_ADJUSTMENT_COEFFICIENT if samples_length > TARGET_SAMPLES_PER_BLOB: delta = max(1, prev_price * (samples_length - TARGET_SAMPLES_PER_BLOB) // TARGET_SAMPLES_PER_BLOB // adjustment_quotient) return min(prev_price + delta, MAX_SAMPLE_PRICE) else: delta = max(1, prev_price * (TARGET_SAMPLES_PER_BLOB - samples_length) // TARGET_SAMPLES_PER_BLOB // adjustment_quotient) return max(prev_price, MIN_SAMPLE_PRICE + delta) - delta ``` #### `compute_committee_source_epoch` ```python def compute_committee_source_epoch(epoch: Epoch, period: uint64) -> Epoch: """ Return the source epoch for computing the committee. """ source_epoch = Epoch(epoch - epoch % period) if source_epoch >= period: source_epoch -= period # `period` epochs lookahead return source_epoch ``` #### `batch_apply_participation_flag` ```python def batch_apply_participation_flag(state: BeaconState, bits: Bitlist[MAX_VALIDATORS_PER_COMMITTEE], epoch: Epoch, full_committee: Sequence[ValidatorIndex], flag_index: int): if epoch == get_current_epoch(state): epoch_participation = state.current_epoch_participation else: epoch_participation = state.previous_epoch_participation for bit, index in zip(bits, full_committee): if bit: epoch_participation[index] = add_flag(epoch_participation[index], flag_index) ``` ### Beacon state accessors #### Updated `get_committee_count_per_slot` ```python def get_committee_count_per_slot(state: BeaconState, epoch: Epoch) -> uint64: """ Return the number of committees in each slot for the given ``epoch``. """ return max(uint64(1), min( get_active_shard_count(state, epoch), uint64(len(get_active_validator_indices(state, epoch))) // SLOTS_PER_EPOCH // TARGET_COMMITTEE_SIZE, )) ``` #### `get_active_shard_count` ```python def get_active_shard_count(state: BeaconState, epoch: Epoch) -> uint64: """ Return the number of active shards. Note that this puts an upper bound on the number of committees per slot. """ return INITIAL_ACTIVE_SHARDS ``` #### `get_shard_proposer_index` ```python def get_shard_proposer_index(state: BeaconState, slot: Slot, shard: Shard) -> ValidatorIndex: """ Return the proposer's index of shard block at ``slot``. """ epoch = compute_epoch_at_slot(slot) seed = hash(get_seed(state, epoch, DOMAIN_SHARD_BLOB) + uint_to_bytes(slot) + uint_to_bytes(shard)) indices = get_active_validator_indices(state, epoch) return compute_proposer_index(state, indices, seed) ``` #### `get_start_shard` ```python def get_start_shard(state: BeaconState, slot: Slot) -> Shard: """ Return the start shard at ``slot``. """ epoch = compute_epoch_at_slot(Slot(slot)) committee_count = get_committee_count_per_slot(state, epoch) active_shard_count = get_active_shard_count(state, epoch) return committee_count * slot % active_shard_count ``` #### `compute_shard_from_committee_index` ```python def compute_shard_from_committee_index(state: BeaconState, slot: Slot, index: CommitteeIndex) -> Shard: active_shards = get_active_shard_count(state, compute_epoch_at_slot(slot)) assert index < active_shards return Shard((index + get_start_shard(state, slot)) % active_shards) ``` #### `compute_committee_index_from_shard` ```python def compute_committee_index_from_shard(state: BeaconState, slot: Slot, shard: Shard) -> CommitteeIndex: epoch = compute_epoch_at_slot(slot) active_shards = get_active_shard_count(state, epoch) index = CommitteeIndex((active_shards + shard - get_start_shard(state, slot)) % active_shards) assert index < get_committee_count_per_slot(state, epoch) return index ``` ### Block processing ```python def process_block(state: BeaconState, block: BeaconBlock) -> None: process_block_header(state, block) # is_execution_enabled is omitted, execution is enabled by default. process_execution_payload(state, block.body.execution_payload, EXECUTION_ENGINE) process_randao(state, block.body) process_eth1_data(state, block.body) process_operations(state, block.body) # [Modified in Sharding] process_sync_aggregate(state, block.body.sync_aggregate) ``` #### Operations ```python def process_operations(state: BeaconState, body: BeaconBlockBody) -> None: # Verify that outstanding deposits are processed up to the maximum number of deposits assert len(body.deposits) == min(MAX_DEPOSITS, state.eth1_data.deposit_count - state.eth1_deposit_index) def for_ops(operations: Sequence[Any], fn: Callable[[BeaconState, Any], None]) -> None: for operation in operations: fn(state, operation) for_ops(body.proposer_slashings, process_proposer_slashing) for_ops(body.attester_slashings, process_attester_slashing) # New shard proposer slashing processing for_ops(body.shard_proposer_slashings, process_shard_proposer_slashing) # Limit is dynamic: based on active shard count assert len(body.shard_headers) <= MAX_SHARD_HEADERS_PER_SHARD * get_active_shard_count(state, get_current_epoch(state)) for_ops(body.shard_headers, process_shard_header) # New attestation processing for_ops(body.attestations, process_attestation) for_ops(body.deposits, process_deposit) for_ops(body.voluntary_exits, process_voluntary_exit) # TODO: to avoid parallel shards racing, and avoid inclusion-order problems, # update the fee price per slot, instead of per header. # state.shard_sample_price = compute_updated_sample_price(state.shard_sample_price, ?, shard_count) ``` ##### Extended Attestation processing ```python def process_attestation(state: BeaconState, attestation: Attestation) -> None: altair.process_attestation(state, attestation) process_attested_shard_work(state, attestation) ``` ```python def process_attested_shard_work(state: BeaconState, attestation: Attestation) -> None: attestation_shard = compute_shard_from_committee_index( state, attestation.data.slot, attestation.data.index, ) full_committee = get_beacon_committee(state, attestation.data.slot, attestation.data.index) buffer_index = attestation.data.slot % SHARD_STATE_MEMORY_SLOTS committee_work = state.shard_buffer[buffer_index][attestation_shard] # Skip attestation vote accounting if the header is not pending if committee_work.status.selector != SHARD_WORK_PENDING: # If the data was already confirmed, check if this matches, to apply the flag to the attesters. if committee_work.status.selector == SHARD_WORK_CONFIRMED: attested: AttestedDataCommitment = committee_work.status.value if attested.root == attestation.data.shard_blob_root: batch_apply_participation_flag(state, attestation.aggregation_bits, attestation.data.target.epoch, full_committee, TIMELY_SHARD_FLAG_INDEX) return current_headers: Sequence[PendingShardHeader] = committee_work.status.value # Find the corresponding header, abort if it cannot be found header_index = len(current_headers) for i, header in enumerate(current_headers): if attestation.data.shard_blob_root == header.attested.root: header_index = i break # Attestations for an unknown header do not count towards shard confirmations, but can otherwise be valid. if header_index == len(current_headers): # Note: Attestations may be re-included if headers are included late. return pending_header: PendingShardHeader = current_headers[header_index] # The weight may be outdated if it is not the initial weight, and from a previous epoch if pending_header.weight != 0 and compute_epoch_at_slot(pending_header.update_slot) < get_current_epoch(state): pending_header.weight = sum(state.validators[index].effective_balance for index, bit in zip(full_committee, pending_header.votes) if bit) pending_header.update_slot = state.slot full_committee_balance = Gwei(0) # Update votes bitfield in the state, update weights for i, bit in enumerate(attestation.aggregation_bits): weight = state.validators[full_committee[i]].effective_balance full_committee_balance += weight if bit: if not pending_header.votes[i]: pending_header.weight += weight pending_header.votes[i] = True # Check if the PendingShardHeader is eligible for expedited confirmation, requiring 2/3 of balance attesting if pending_header.weight * 3 >= full_committee_balance * 2: # participants of the winning header are remembered with participation flags batch_apply_participation_flag(state, pending_header.votes, attestation.data.target.epoch, full_committee, TIMELY_SHARD_FLAG_INDEX) if pending_header.attested.commitment == DataCommitment(): # The committee voted to not confirm anything state.shard_buffer[buffer_index][attestation_shard].status.change( selector=SHARD_WORK_UNCONFIRMED, value=None, ) else: state.shard_buffer[buffer_index][attestation_shard].status.change( selector=SHARD_WORK_CONFIRMED, value=pending_header.attested, ) ``` ##### `process_shard_header` ```python def process_shard_header(state: BeaconState, signed_header: SignedShardBlobHeader) -> None: header: ShardBlobHeader = signed_header.message slot = header.slot shard = header.shard # Verify the header is not 0, and not from the future. assert Slot(0) < slot <= state.slot header_epoch = compute_epoch_at_slot(slot) # Verify that the header is within the processing time window assert header_epoch in [get_previous_epoch(state), get_current_epoch(state)] # Verify that the shard is valid shard_count = get_active_shard_count(state, header_epoch) assert shard < shard_count # Verify that a committee is able to attest this (slot, shard) start_shard = get_start_shard(state, slot) committee_index = (shard_count + shard - start_shard) % shard_count committees_per_slot = get_committee_count_per_slot(state, header_epoch) assert committee_index <= committees_per_slot # Check that this data is still pending committee_work = state.shard_buffer[slot % SHARD_STATE_MEMORY_SLOTS][shard] assert committee_work.status.selector == SHARD_WORK_PENDING # Check that this header is not yet in the pending list current_headers: List[PendingShardHeader, MAX_SHARD_HEADERS_PER_SHARD] = committee_work.status.value header_root = hash_tree_root(header) assert header_root not in [pending_header.attested.root for pending_header in current_headers] # Verify proposer matches assert header.proposer_index == get_shard_proposer_index(state, slot, shard) # Verify builder and proposer aggregate signature blob_signing_root = compute_signing_root(header, get_domain(state, DOMAIN_SHARD_BLOB)) builder_pubkey = state.blob_builders[header.builder_index].pubkey proposer_pubkey = state.validators[header.proposer_index].pubkey assert bls.FastAggregateVerify([builder_pubkey, proposer_pubkey], blob_signing_root, signed_header.signature) # Verify the length by verifying the degree. body_summary = header.body_summary points_count = body_summary.commitment.samples_count * POINTS_PER_SAMPLE if points_count == 0: assert body_summary.degree_proof == G1_SETUP[0] assert ( bls.Pairing(body_summary.degree_proof, G2_SETUP[0]) == bls.Pairing(body_summary.commitment.point, G2_SETUP[-points_count]) ) # Charge EIP 1559 fee, builder pays for opportunity, and is responsible for later availability, # or fail to publish at their own expense. samples = body_summary.commitment.samples_count # TODO: overflows, need bigger int type max_fee = body_summary.max_fee_per_sample * samples # Builder must have sufficient balance, even if max_fee is not completely utilized assert state.blob_builder_balances[header.builder_index] >= max_fee base_fee = state.shard_sample_price * samples # Base fee must be paid assert max_fee >= base_fee # Remaining fee goes towards proposer for prioritizing, up to a maximum max_priority_fee = body_summary.max_priority_fee_per_sample * samples priority_fee = min(max_fee - base_fee, max_priority_fee) # Burn base fee, take priority fee # priority_fee <= max_fee - base_fee, thus priority_fee + base_fee <= max_fee, thus sufficient balance. state.blob_builder_balances[header.builder_index] -= base_fee + priority_fee # Pay out priority fee increase_balance(state, header.proposer_index, priority_fee) # Initialize the pending header index = compute_committee_index_from_shard(state, slot, shard) committee_length = len(get_beacon_committee(state, slot, index)) initial_votes = Bitlist[MAX_VALIDATORS_PER_COMMITTEE]([0] * committee_length) pending_header = PendingShardHeader( attested=AttestedDataCommitment( commitment=body_summary.commitment, root=header_root, includer_index=get_beacon_proposer_index(state), ), votes=initial_votes, weight=0, update_slot=state.slot, ) # Include it in the pending list current_headers.append(pending_header) ``` The degree proof works as follows. For a block `B` with length `l` (so `l` values in `[0...l - 1]`, seen as a polynomial `B(X)` which takes these values), the length proof is the commitment to the polynomial `B(X) * X**(MAX_DEGREE + 1 - l)`, where `MAX_DEGREE` is the maximum power of `s` available in the setup, which is `MAX_DEGREE = len(G2_SETUP) - 1`. The goal is to ensure that a proof can only be constructed if `deg(B) < l` (there are not hidden higher-order terms in the polynomial, which would thwart reconstruction). ##### `process_shard_proposer_slashing` ```python def process_shard_proposer_slashing(state: BeaconState, proposer_slashing: ShardProposerSlashing) -> None: slot = proposer_slashing.slot shard = proposer_slashing.shard proposer_index = proposer_slashing.proposer_index reference_1 = ShardBlobReference(slot=slot, shard=shard, proposer_index=proposer_index, builder_index=proposer_slashing.builder_index_1, body_root=proposer_slashing.body_root_1) reference_2 = ShardBlobReference(slot=slot, shard=shard, proposer_index=proposer_index, builder_index=proposer_slashing.builder_index_2, body_root=proposer_slashing.body_root_2) # Verify the signed messages are different assert reference_1 != reference_2 # Verify the proposer is slashable proposer = state.validators[proposer_index] assert is_slashable_validator(proposer, get_current_epoch(state)) # The builders are not slashed, the proposer co-signed with them builder_pubkey_1 = state.blob_builders[proposer_slashing.builder_index_1].pubkey builder_pubkey_2 = state.blob_builders[proposer_slashing.builder_index_2].pubkey domain = get_domain(state, DOMAIN_SHARD_PROPOSER, compute_epoch_at_slot(slot)) signing_root_1 = compute_signing_root(reference_1, domain) signing_root_2 = compute_signing_root(reference_2, domain) assert bls.FastAggregateVerify([builder_pubkey_1, proposer.pubkey], signing_root_1, proposer_slashing.signature_1) assert bls.FastAggregateVerify([builder_pubkey_2, proposer.pubkey], signing_root_2, proposer_slashing.signature_2) slash_validator(state, proposer_index) ``` ### Epoch transition This epoch transition overrides the Merge epoch transition: ```python def process_epoch(state: BeaconState) -> None: # Sharding pre-processing process_pending_shard_confirmations(state) reset_pending_shard_work(state) # Base functionality process_justification_and_finalization(state) process_inactivity_updates(state) process_rewards_and_penalties(state) # Note: modified, see new TIMELY_SHARD_FLAG_INDEX process_registry_updates(state) process_slashings(state) process_eth1_data_reset(state) process_effective_balance_updates(state) process_slashings_reset(state) process_randao_mixes_reset(state) process_historical_roots_update(state) process_participation_flag_updates(state) process_sync_committee_updates(state) ``` #### `process_pending_shard_confirmations` ```python def process_pending_shard_confirmations(state: BeaconState) -> None: # Pending header processing applies to the previous epoch. # Skip if `GENESIS_EPOCH` because no prior epoch to process. if get_current_epoch(state) == GENESIS_EPOCH: return previous_epoch = get_previous_epoch(state) previous_epoch_start_slot = compute_start_slot_at_epoch(previous_epoch) # Mark stale headers as unconfirmed for slot in range(previous_epoch_start_slot, previous_epoch_start_slot + SLOTS_PER_EPOCH): buffer_index = slot % SHARD_STATE_MEMORY_SLOTS for shard_index in range(len(state.shard_buffer[buffer_index])): committee_work = state.shard_buffer[buffer_index][shard_index] if committee_work.status.selector == SHARD_WORK_PENDING: winning_header = max(committee_work.status.value, key=lambda header: header.weight) if winning_header.attested.commitment == DataCommitment(): committee_work.status.change(selector=SHARD_WORK_UNCONFIRMED, value=None) else: committee_work.status.change(selector=SHARD_WORK_CONFIRMED, value=winning_header.attested) ``` #### `reset_pending_shard_work` ```python def reset_pending_shard_work(state: BeaconState) -> None: # Add dummy "empty" PendingShardHeader (default vote if no shard header is available) next_epoch = get_current_epoch(state) + 1 next_epoch_start_slot = compute_start_slot_at_epoch(next_epoch) committees_per_slot = get_committee_count_per_slot(state, next_epoch) active_shards = get_active_shard_count(state, next_epoch) for slot in range(next_epoch_start_slot, next_epoch_start_slot + SLOTS_PER_EPOCH): buffer_index = slot % SHARD_STATE_MEMORY_SLOTS # Reset the shard work tracking state.shard_buffer[buffer_index] = [ShardWork() for _ in range(active_shards)] start_shard = get_start_shard(state, slot) for committee_index in range(committees_per_slot): shard = (start_shard + committee_index) % active_shards # a committee is available, initialize a pending shard-header list committee_length = len(get_beacon_committee(state, slot, CommitteeIndex(committee_index))) state.shard_buffer[buffer_index][shard].status.change( selector=SHARD_WORK_PENDING, value=List[PendingShardHeader, MAX_SHARD_HEADERS_PER_SHARD]( PendingShardHeader( attested=AttestedDataCommitment(), votes=Bitlist[MAX_VALIDATORS_PER_COMMITTEE]([0] * committee_length), weight=0, update_slot=slot, ) ) ) # a shard without committee available defaults to SHARD_WORK_UNCONFIRMED. ```