Enable light client data backfill by tracking best SyncAggregate

Beacon nodes can only compute light client data locally if they have the
corresponding `BeaconState` available. This is not the case for blocks
before the initially synced checkpoint state. The p2p-interface defines
endpoints to sync light client data, but it only supports forward sync.

To enable beacon nodes to backfill light client data, we must ensure
that a malicious peer cannot convince us of fraudulent data. While it
is possible to verify light client data against the locally backfilled
blocks, blocks are not necessarily available anymore on libp2p as they
are subject to `MIN_EPOCHS_FOR_BLOCK_REQUESTS`. Light client data stays
relevant for more than 5 months, and without validating it against local
block data it is impossible to distinguish canonical light client data
from fraudulent light client data that eventually culminates in a shared
history; the old periods in that case could still be manipulated.
Furthermore, agreeing on canonical data improves caching performance and
is relevant, e.g., for the portal network.

To support efficient proof that a `LightClientUpdate` is canonical, it
is proposed to minimally extend the `BeaconState` to track the best
`SyncAggregate` of the current and previous sync committee period,
according to an implementation-independent ranking function.
The proposed ranking function is compatible with what consensus nodes
implementing ethereum#3553 are
already making available across libp2p and REST transports.
It is based on and compatible with the `is_better_update` function in
`specs/altair/light-client/sync-protocol.md`.

There are three minor differences to `is_better_update`:

1. `is_better_update` runs in the LC, so runs without fork choice.
   It needs extra conditions to prefer older data over newer data.
   The `BeaconState` ranking function can use simpler logic.
2. The LC is always initialized from a post-Altair finalized checkpoint.
   This assumption does not hold in theoretical edge cases, requiring an
   extra guard for `ALTAIR_FORK_EPOCH` in the `BeaconState` function.
3. `is_better_update` has to deal with BNs serving incomplete data while
   they are still backfilling. This is not the case with `BeaconState`.

Once the data is available in the `BeaconState`, a light client data
backfill protocol could be defined that serves, for past periods:

1. A `LightClientUpdate` from requested `period` + 1 that proves
   that the entirety of `period` is finalized.
2. `BeaconState.historical_summaries[period].block_summary_root`
   at (1)'s `attested_header.beacon.state_root` + Merkle proof.
3. For each epoch's slot 0 block within requested `period`, the
   corresponding `LightClientHeader` + Merkle multi-proof for the
   block's inclusion into (2)'s `block_summary_root`.
4. For each of the entries from (3) with `beacon.slot` within `period`,
   the `current_sync_committee_branch` + Merkle proof for constructing
   `LightClientBootstrap`.
5. If (4) is not empty, the requested `period`'s
   `current_sync_committee`.
6. The best `LightClientUpdate` from `period`, if one exists, +
   Merkle proof that its `sync_aggregate` + `signature_slot` is
   selected as the canonical best one in (1)'s
   `attested_header.beacon.state_root`.

Only the proof in (6) depends on `BeaconState` tracking the best
light client data. This modification would enshrine the logic of a
subset of `is_better_update`, but does not require adding any
`LightClientXyz` data structures to the `BeaconState`.

specs/electra/beacon-chain.md

@@ -0,0 +1,163 @@
+# Electra -- The Beacon Chain
+
+**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 -->
+
+- [Containers](#containers)
+  - [New containers](#new-containers)
+    - [`SyncData`](#syncdata)
+  - [Extended containers](#extended-containers)
+    - [`BeaconState`](#beaconstate)
+- [Beacon chain state transition function](#beacon-chain-state-transition-function)
+  - [Epoch processing](#epoch-processing)
+    - [Modified `process_sync_committee_updates`](#modified-process_sync_committee_updates)
+  - [Block processing](#block-processing)
+    - [New `process_best_sync_data`](#new-process_best_sync_data)
+
+<!-- END doctoc generated TOC please keep comment here to allow auto update -->
+<!-- /TOC -->
+
+## Containers
+
+### New containers
+
+#### `SyncData`
+
+```python
+class SyncData(Container):
+    # Sync committee aggregate signature
+    sync_aggregate: SyncAggregate
+    # Slot at which the aggregate signature was created
+    signature_slot: Slot
+```
+
+### Extended containers
+
+#### `BeaconState`
+
+```python
+class BeaconState(Container):
+    # Versioning
+    genesis_time: uint64
+    genesis_validators_root: Root
+    slot: Slot
+    fork: Fork
+    # History
+    latest_block_header: BeaconBlockHeader
+    block_roots: Vector[Root, SLOTS_PER_HISTORICAL_ROOT]
+    state_roots: Vector[Root, SLOTS_PER_HISTORICAL_ROOT]
+    historical_roots: List[Root, HISTORICAL_ROOTS_LIMIT]  # Frozen in Capella, replaced by historical_summaries
+    # Eth1
+    eth1_data: Eth1Data
+    eth1_data_votes: List[Eth1Data, EPOCHS_PER_ETH1_VOTING_PERIOD * SLOTS_PER_EPOCH]
+    eth1_deposit_index: uint64
+    # Registry
+    validators: List[Validator, VALIDATOR_REGISTRY_LIMIT]
+    balances: List[Gwei, VALIDATOR_REGISTRY_LIMIT]
+    # Randomness
+    randao_mixes: Vector[Bytes32, EPOCHS_PER_HISTORICAL_VECTOR]
+    # Slashings
+    slashings: Vector[Gwei, EPOCHS_PER_SLASHINGS_VECTOR]  # Per-epoch sums of slashed effective balances
+    # Participation
+    previous_epoch_participation: List[ParticipationFlags, VALIDATOR_REGISTRY_LIMIT]
+    current_epoch_participation: List[ParticipationFlags, VALIDATOR_REGISTRY_LIMIT]
+    # Finality
+    justification_bits: Bitvector[JUSTIFICATION_BITS_LENGTH]  # Bit set for every recent justified epoch
+    previous_justified_checkpoint: Checkpoint
+    current_justified_checkpoint: Checkpoint
+    finalized_checkpoint: Checkpoint
+    # Inactivity
+    inactivity_scores: List[uint64, VALIDATOR_REGISTRY_LIMIT]
+    # Sync
+    current_sync_committee: SyncCommittee
+    next_sync_committee: SyncCommittee
+    # Execution
+    latest_execution_payload_header: ExecutionPayloadHeader
+    # Withdrawals
+    next_withdrawal_index: WithdrawalIndex
+    next_withdrawal_validator_index: ValidatorIndex
+    # Deep history valid from Capella onwards
+    historical_summaries: List[HistoricalSummary, HISTORICAL_ROOTS_LIMIT]
+    # Sync history
+    previous_best_sync_data: SyncData  # [New in Electra]
+    current_best_sync_data: SyncData  # [New in Electra]
+    parent_block_has_sync_committee_finality: bool  # [New in Electra]
+```
+
+## Beacon chain state transition function
+
+### Epoch processing
+
+#### Modified `process_sync_committee_updates`
+
+```python
+def process_sync_committee_updates(state: BeaconState) -> None:
+    next_epoch = get_current_epoch(state) + Epoch(1)
+    if next_epoch % EPOCHS_PER_SYNC_COMMITTEE_PERIOD == 0:
+        state.current_sync_committee = state.next_sync_committee
+        state.next_sync_committee = get_next_sync_committee(state)
+
+        # [New in Electra]
+        state.previous_best_sync_data = state.current_best_sync_data
+        state.current_best_sync_data = SyncData()
+        state.parent_block_has_sync_committee_finality = False
+```
+
+### Block processing
+
+```python
+def process_block(state: BeaconState, block: BeaconBlock) -> None:
+    process_best_sync_data(state, block)  # [New in Electra]
+    process_block_header(state, block)
+    process_withdrawals(state, block.body.execution_payload)
+    process_execution_payload(state, block.body, EXECUTION_ENGINE)
+    process_randao(state, block.body)
+    process_eth1_data(state, block.body)
+    process_operations(state, block.body)
+    process_sync_aggregate(state, block.body.sync_aggregate)
+```
+
+#### New `process_best_sync_data`
+
+```python
+def process_best_sync_data(state: BeaconState, block: BeaconBlock) -> None:
+    signature_period = compute_sync_committee_period_at_slot(block.slot)
+    attested_period = compute_sync_committee_period_at_slot(state.latest_block_header.slot)
+
+    # Track sync committee finality
+    old_has_sync_committee_finality = state.parent_block_has_sync_committee_finality
+    if state.parent_block_has_sync_committee_finality:
+        new_has_sync_committee_finality = True
+    elif state.finalized_checkpoint.epoch < ALTAIR_FORK_EPOCH:
+        new_has_sync_committee_finality = False
+    else:
+        finalized_period = compute_sync_committee_period(state.finalized_checkpoint.epoch)
+        new_has_sync_committee_finality = (finalized_period == attested_period)
+    state.parent_block_has_sync_committee_finality = new_has_sync_committee_finality
+
+    # Track best sync data
+    if attested_period == signature_period:
+        max_active_participants = len(block.body.sync_aggregate.sync_committee_bits)
+        new_num_active_participants = sum(block.body.sync_aggregate.sync_committee_bits)
+        old_num_active_participants = sum(state.current_best_sync_data.sync_aggregate.sync_committee_bits)
+        new_has_supermajority = new_num_active_participants * 3 >= max_active_participants * 2
+        old_has_supermajority = old_num_active_participants * 3 >= max_active_participants * 2
+        if new_has_supermajority != old_has_supermajority:
+            is_better_sync_data = new_has_supermajority
+        elif not new_has_supermajority and new_num_active_participants != old_num_active_participants:
+            is_better_sync_data = new_num_active_participants > old_num_active_participants
+        elif new_has_sync_committee_finality != old_has_sync_committee_finality:
+            is_better_sync_data = new_has_sync_committee_finality
+        else:
+            is_better_sync_data = new_num_active_participants > old_num_active_participants
+        if is_better_sync_data:
+            state.current_best_sync_data = SyncData(
+                sync_aggregate=block.body.sync_aggregate,
+                signature_slot=block.slot,
+            )
+```