beacon/light: add CommitteeChain (#27766)

This change implements CommitteeChain which is a key component of the beacon light client. It is a passive data structure that can validate, hold and update a chain of beacon light sync committees and updates, starting from a checkpoint that proves the starting committee through a beacon block hash, header and corresponding state. Once synced to the current sync period, CommitteeChain can also validate signed beacon headers.
This commit is contained in:
Felföldi Zsolt 2023-12-08 13:38:00 +01:00 committed by GitHub
parent 1048e2d6a3
commit fff843cfaf
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
7 changed files with 1247 additions and 0 deletions

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beacon/light/canonical.go Normal file
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// Copyright 2023 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package light
import (
"encoding/binary"
"fmt"
"github.com/ethereum/go-ethereum/common/lru"
"github.com/ethereum/go-ethereum/ethdb"
"github.com/ethereum/go-ethereum/log"
"github.com/ethereum/go-ethereum/rlp"
)
// canonicalStore stores instances of the given type in a database and caches
// them in memory, associated with a continuous range of period numbers.
// Note: canonicalStore is not thread safe and it is the caller's responsibility
// to avoid concurrent access.
type canonicalStore[T any] struct {
keyPrefix []byte
periods periodRange
cache *lru.Cache[uint64, T]
}
// newCanonicalStore creates a new canonicalStore and loads all keys associated
// with the keyPrefix in order to determine the ranges available in the database.
func newCanonicalStore[T any](db ethdb.Iteratee, keyPrefix []byte) (*canonicalStore[T], error) {
cs := &canonicalStore[T]{
keyPrefix: keyPrefix,
cache: lru.NewCache[uint64, T](100),
}
var (
iter = db.NewIterator(keyPrefix, nil)
kl = len(keyPrefix)
first = true
)
defer iter.Release()
for iter.Next() {
if len(iter.Key()) != kl+8 {
log.Warn("Invalid key length in the canonical chain database", "key", fmt.Sprintf("%#x", iter.Key()))
continue
}
period := binary.BigEndian.Uint64(iter.Key()[kl : kl+8])
if first {
cs.periods.Start = period
} else if cs.periods.End != period {
return nil, fmt.Errorf("gap in the canonical chain database between periods %d and %d", cs.periods.End, period-1)
}
first = false
cs.periods.End = period + 1
}
return cs, nil
}
// databaseKey returns the database key belonging to the given period.
func (cs *canonicalStore[T]) databaseKey(period uint64) []byte {
return binary.BigEndian.AppendUint64(append([]byte{}, cs.keyPrefix...), period)
}
// add adds the given item to the database. It also ensures that the range remains
// continuous. Can be used either with a batch or database backend.
func (cs *canonicalStore[T]) add(backend ethdb.KeyValueWriter, period uint64, value T) error {
if !cs.periods.canExpand(period) {
return fmt.Errorf("period expansion is not allowed, first: %d, next: %d, period: %d", cs.periods.Start, cs.periods.End, period)
}
enc, err := rlp.EncodeToBytes(value)
if err != nil {
return err
}
if err := backend.Put(cs.databaseKey(period), enc); err != nil {
return err
}
cs.cache.Add(period, value)
cs.periods.expand(period)
return nil
}
// deleteFrom removes items starting from the given period.
func (cs *canonicalStore[T]) deleteFrom(db ethdb.KeyValueWriter, fromPeriod uint64) (deleted periodRange) {
keepRange, deleteRange := cs.periods.split(fromPeriod)
deleteRange.each(func(period uint64) {
db.Delete(cs.databaseKey(period))
cs.cache.Remove(period)
})
cs.periods = keepRange
return deleteRange
}
// get returns the item at the given period or the null value of the given type
// if no item is present.
func (cs *canonicalStore[T]) get(backend ethdb.KeyValueReader, period uint64) (T, bool) {
var null, value T
if !cs.periods.contains(period) {
return null, false
}
if value, ok := cs.cache.Get(period); ok {
return value, true
}
enc, err := backend.Get(cs.databaseKey(period))
if err != nil {
log.Error("Canonical store value not found", "period", period, "start", cs.periods.Start, "end", cs.periods.End)
return null, false
}
if err := rlp.DecodeBytes(enc, &value); err != nil {
log.Error("Error decoding canonical store value", "error", err)
return null, false
}
cs.cache.Add(period, value)
return value, true
}

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// Copyright 2023 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package light
import (
"errors"
"fmt"
"math"
"sync"
"time"
"github.com/ethereum/go-ethereum/beacon/params"
"github.com/ethereum/go-ethereum/beacon/types"
"github.com/ethereum/go-ethereum/common"
"github.com/ethereum/go-ethereum/common/lru"
"github.com/ethereum/go-ethereum/common/mclock"
"github.com/ethereum/go-ethereum/core/rawdb"
"github.com/ethereum/go-ethereum/ethdb"
"github.com/ethereum/go-ethereum/log"
)
var (
ErrNeedCommittee = errors.New("sync committee required")
ErrInvalidUpdate = errors.New("invalid committee update")
ErrInvalidPeriod = errors.New("invalid update period")
ErrWrongCommitteeRoot = errors.New("wrong committee root")
ErrCannotReorg = errors.New("can not reorg committee chain")
)
// CommitteeChain is a passive data structure that can validate, hold and update
// a chain of beacon light sync committees and updates. It requires at least one
// externally set fixed committee root at the beginning of the chain which can
// be set either based on a BootstrapData or a trusted source (a local beacon
// full node). This makes the structure useful for both light client and light
// server setups.
//
// It always maintains the following consistency constraints:
// - a committee can only be present if its root hash matches an existing fixed
// root or if it is proven by an update at the previous period
// - an update can only be present if a committee is present at the same period
// and the update signature is valid and has enough participants.
// The committee at the next period (proven by the update) should also be
// present (note that this means they can only be added together if neither
// is present yet). If a fixed root is present at the next period then the
// update can only be present if it proves the same committee root.
//
// Once synced to the current sync period, CommitteeChain can also validate
// signed beacon headers.
type CommitteeChain struct {
// chainmu guards against concurrent access to the canonicalStore structures
// (updates, committees, fixedCommitteeRoots) and ensures that they stay consistent
// with each other and with committeeCache.
chainmu sync.RWMutex
db ethdb.KeyValueStore
updates *canonicalStore[*types.LightClientUpdate]
committees *canonicalStore[*types.SerializedSyncCommittee]
fixedCommitteeRoots *canonicalStore[common.Hash]
committeeCache *lru.Cache[uint64, syncCommittee] // cache deserialized committees
clock mclock.Clock // monotonic clock (simulated clock in tests)
unixNano func() int64 // system clock (simulated clock in tests)
sigVerifier committeeSigVerifier // BLS sig verifier (dummy verifier in tests)
config *types.ChainConfig
signerThreshold int
minimumUpdateScore types.UpdateScore
enforceTime bool // enforceTime specifies whether the age of a signed header should be checked
}
// NewCommitteeChain creates a new CommitteeChain.
func NewCommitteeChain(db ethdb.KeyValueStore, config *types.ChainConfig, signerThreshold int, enforceTime bool) *CommitteeChain {
return newCommitteeChain(db, config, signerThreshold, enforceTime, blsVerifier{}, &mclock.System{}, func() int64 { return time.Now().UnixNano() })
}
// newCommitteeChain creates a new CommitteeChain with the option of replacing the
// clock source and signature verification for testing purposes.
func newCommitteeChain(db ethdb.KeyValueStore, config *types.ChainConfig, signerThreshold int, enforceTime bool, sigVerifier committeeSigVerifier, clock mclock.Clock, unixNano func() int64) *CommitteeChain {
s := &CommitteeChain{
committeeCache: lru.NewCache[uint64, syncCommittee](10),
db: db,
sigVerifier: sigVerifier,
clock: clock,
unixNano: unixNano,
config: config,
signerThreshold: signerThreshold,
enforceTime: enforceTime,
minimumUpdateScore: types.UpdateScore{
SignerCount: uint32(signerThreshold),
SubPeriodIndex: params.SyncPeriodLength / 16,
},
}
var err1, err2, err3 error
if s.fixedCommitteeRoots, err1 = newCanonicalStore[common.Hash](db, rawdb.FixedCommitteeRootKey); err1 != nil {
log.Error("Error creating fixed committee root store", "error", err1)
}
if s.committees, err2 = newCanonicalStore[*types.SerializedSyncCommittee](db, rawdb.SyncCommitteeKey); err2 != nil {
log.Error("Error creating committee store", "error", err2)
}
if s.updates, err3 = newCanonicalStore[*types.LightClientUpdate](db, rawdb.BestUpdateKey); err3 != nil {
log.Error("Error creating update store", "error", err3)
}
if err1 != nil || err2 != nil || err3 != nil || !s.checkConstraints() {
log.Info("Resetting invalid committee chain")
s.Reset()
}
// roll back invalid updates (might be necessary if forks have been changed since last time)
for !s.updates.periods.isEmpty() {
update, ok := s.updates.get(s.db, s.updates.periods.End-1)
if !ok {
log.Error("Sync committee update missing", "period", s.updates.periods.End-1)
s.Reset()
break
}
if valid, err := s.verifyUpdate(update); err != nil {
log.Error("Error validating update", "period", s.updates.periods.End-1, "error", err)
} else if valid {
break
}
if err := s.rollback(s.updates.periods.End); err != nil {
log.Error("Error writing batch into chain database", "error", err)
}
}
if !s.committees.periods.isEmpty() {
log.Trace("Sync committee chain loaded", "first period", s.committees.periods.Start, "last period", s.committees.periods.End-1)
}
return s
}
// checkConstraints checks committee chain validity constraints
func (s *CommitteeChain) checkConstraints() bool {
isNotInFixedCommitteeRootRange := func(r periodRange) bool {
return s.fixedCommitteeRoots.periods.isEmpty() ||
r.Start < s.fixedCommitteeRoots.periods.Start ||
r.Start >= s.fixedCommitteeRoots.periods.End
}
valid := true
if !s.updates.periods.isEmpty() {
if isNotInFixedCommitteeRootRange(s.updates.periods) {
log.Error("Start update is not in the fixed roots range")
valid = false
}
if s.committees.periods.Start > s.updates.periods.Start || s.committees.periods.End <= s.updates.periods.End {
log.Error("Missing committees in update range")
valid = false
}
}
if !s.committees.periods.isEmpty() {
if isNotInFixedCommitteeRootRange(s.committees.periods) {
log.Error("Start committee is not in the fixed roots range")
valid = false
}
if s.committees.periods.End > s.fixedCommitteeRoots.periods.End && s.committees.periods.End > s.updates.periods.End+1 {
log.Error("Last committee is neither in the fixed roots range nor proven by updates")
valid = false
}
}
return valid
}
// Reset resets the committee chain.
func (s *CommitteeChain) Reset() {
s.chainmu.Lock()
defer s.chainmu.Unlock()
if err := s.rollback(0); err != nil {
log.Error("Error writing batch into chain database", "error", err)
}
}
// CheckpointInit initializes a CommitteeChain based on the checkpoint.
// Note: if the chain is already initialized and the committees proven by the
// checkpoint do match the existing chain then the chain is retained and the
// new checkpoint becomes fixed.
func (s *CommitteeChain) CheckpointInit(bootstrap *types.BootstrapData) error {
s.chainmu.Lock()
defer s.chainmu.Unlock()
if err := bootstrap.Validate(); err != nil {
return err
}
period := bootstrap.Header.SyncPeriod()
if err := s.deleteFixedCommitteeRootsFrom(period + 2); err != nil {
s.Reset()
return err
}
if s.addFixedCommitteeRoot(period, bootstrap.CommitteeRoot) != nil {
s.Reset()
if err := s.addFixedCommitteeRoot(period, bootstrap.CommitteeRoot); err != nil {
s.Reset()
return err
}
}
if err := s.addFixedCommitteeRoot(period+1, common.Hash(bootstrap.CommitteeBranch[0])); err != nil {
s.Reset()
return err
}
if err := s.addCommittee(period, bootstrap.Committee); err != nil {
s.Reset()
return err
}
return nil
}
// addFixedCommitteeRoot sets a fixed committee root at the given period.
// Note that the period where the first committee is added has to have a fixed
// root which can either come from a BootstrapData or a trusted source.
func (s *CommitteeChain) addFixedCommitteeRoot(period uint64, root common.Hash) error {
if root == (common.Hash{}) {
return ErrWrongCommitteeRoot
}
batch := s.db.NewBatch()
oldRoot := s.getCommitteeRoot(period)
if !s.fixedCommitteeRoots.periods.canExpand(period) {
// Note: the fixed committee root range should always be continuous and
// therefore the expected syncing method is to forward sync and optionally
// backward sync periods one by one, starting from a checkpoint. The only
// case when a root that is not adjacent to the already fixed ones can be
// fixed is when the same root has already been proven by an update chain.
// In this case the all roots in between can and should be fixed.
// This scenario makes sense when a new trusted checkpoint is added to an
// existing chain, ensuring that it will not be rolled back (might be
// important in case of low signer participation rate).
if root != oldRoot {
return ErrInvalidPeriod
}
// if the old root exists and matches the new one then it is guaranteed
// that the given period is after the existing fixed range and the roots
// in between can also be fixed.
for p := s.fixedCommitteeRoots.periods.End; p < period; p++ {
if err := s.fixedCommitteeRoots.add(batch, p, s.getCommitteeRoot(p)); err != nil {
return err
}
}
}
if oldRoot != (common.Hash{}) && (oldRoot != root) {
// existing old root was different, we have to reorg the chain
if err := s.rollback(period); err != nil {
return err
}
}
if err := s.fixedCommitteeRoots.add(batch, period, root); err != nil {
return err
}
if err := batch.Write(); err != nil {
log.Error("Error writing batch into chain database", "error", err)
return err
}
return nil
}
// deleteFixedCommitteeRootsFrom deletes fixed roots starting from the given period.
// It also maintains chain consistency, meaning that it also deletes updates and
// committees if they are no longer supported by a valid update chain.
func (s *CommitteeChain) deleteFixedCommitteeRootsFrom(period uint64) error {
if period >= s.fixedCommitteeRoots.periods.End {
return nil
}
batch := s.db.NewBatch()
s.fixedCommitteeRoots.deleteFrom(batch, period)
if s.updates.periods.isEmpty() || period <= s.updates.periods.Start {
// Note: the first period of the update chain should always be fixed so if
// the fixed root at the first update is removed then the entire update chain
// and the proven committees have to be removed. Earlier committees in the
// remaining fixed root range can stay.
s.updates.deleteFrom(batch, period)
s.deleteCommitteesFrom(batch, period)
} else {
// The update chain stays intact, some previously fixed committee roots might
// get unfixed but are still proven by the update chain. If there were
// committees present after the range proven by updates, those should be
// removed if the belonging fixed roots are also removed.
fromPeriod := s.updates.periods.End + 1 // not proven by updates
if period > fromPeriod {
fromPeriod = period // also not justified by fixed roots
}
s.deleteCommitteesFrom(batch, fromPeriod)
}
if err := batch.Write(); err != nil {
log.Error("Error writing batch into chain database", "error", err)
return err
}
return nil
}
// deleteCommitteesFrom deletes committees starting from the given period.
func (s *CommitteeChain) deleteCommitteesFrom(batch ethdb.Batch, period uint64) {
deleted := s.committees.deleteFrom(batch, period)
for period := deleted.Start; period < deleted.End; period++ {
s.committeeCache.Remove(period)
}
}
// addCommittee adds a committee at the given period if possible.
func (s *CommitteeChain) addCommittee(period uint64, committee *types.SerializedSyncCommittee) error {
if !s.committees.periods.canExpand(period) {
return ErrInvalidPeriod
}
root := s.getCommitteeRoot(period)
if root == (common.Hash{}) {
return ErrInvalidPeriod
}
if root != committee.Root() {
return ErrWrongCommitteeRoot
}
if !s.committees.periods.contains(period) {
if err := s.committees.add(s.db, period, committee); err != nil {
return err
}
s.committeeCache.Remove(period)
}
return nil
}
// InsertUpdate adds a new update if possible.
func (s *CommitteeChain) InsertUpdate(update *types.LightClientUpdate, nextCommittee *types.SerializedSyncCommittee) error {
s.chainmu.Lock()
defer s.chainmu.Unlock()
period := update.AttestedHeader.Header.SyncPeriod()
if !s.updates.periods.canExpand(period) || !s.committees.periods.contains(period) {
return ErrInvalidPeriod
}
if s.minimumUpdateScore.BetterThan(update.Score()) {
return ErrInvalidUpdate
}
oldRoot := s.getCommitteeRoot(period + 1)
reorg := oldRoot != (common.Hash{}) && oldRoot != update.NextSyncCommitteeRoot
if oldUpdate, ok := s.updates.get(s.db, period); ok && !update.Score().BetterThan(oldUpdate.Score()) {
// a better or equal update already exists; no changes, only fail if new one tried to reorg
if reorg {
return ErrCannotReorg
}
return nil
}
if s.fixedCommitteeRoots.periods.contains(period+1) && reorg {
return ErrCannotReorg
}
if ok, err := s.verifyUpdate(update); err != nil {
return err
} else if !ok {
return ErrInvalidUpdate
}
addCommittee := !s.committees.periods.contains(period+1) || reorg
if addCommittee {
if nextCommittee == nil {
return ErrNeedCommittee
}
if nextCommittee.Root() != update.NextSyncCommitteeRoot {
return ErrWrongCommitteeRoot
}
}
if reorg {
if err := s.rollback(period + 1); err != nil {
return err
}
}
batch := s.db.NewBatch()
if addCommittee {
if err := s.committees.add(batch, period+1, nextCommittee); err != nil {
return err
}
s.committeeCache.Remove(period + 1)
}
if err := s.updates.add(batch, period, update); err != nil {
return err
}
if err := batch.Write(); err != nil {
log.Error("Error writing batch into chain database", "error", err)
return err
}
log.Info("Inserted new committee update", "period", period, "next committee root", update.NextSyncCommitteeRoot)
return nil
}
// NextSyncPeriod returns the next period where an update can be added and also
// whether the chain is initialized at all.
func (s *CommitteeChain) NextSyncPeriod() (uint64, bool) {
s.chainmu.RLock()
defer s.chainmu.RUnlock()
if s.committees.periods.isEmpty() {
return 0, false
}
if !s.updates.periods.isEmpty() {
return s.updates.periods.End, true
}
return s.committees.periods.End - 1, true
}
// rollback removes all committees and fixed roots from the given period and updates
// starting from the previous period.
func (s *CommitteeChain) rollback(period uint64) error {
max := s.updates.periods.End + 1
if s.committees.periods.End > max {
max = s.committees.periods.End
}
if s.fixedCommitteeRoots.periods.End > max {
max = s.fixedCommitteeRoots.periods.End
}
for max > period {
max--
batch := s.db.NewBatch()
s.deleteCommitteesFrom(batch, max)
s.fixedCommitteeRoots.deleteFrom(batch, max)
if max > 0 {
s.updates.deleteFrom(batch, max-1)
}
if err := batch.Write(); err != nil {
log.Error("Error writing batch into chain database", "error", err)
return err
}
}
return nil
}
// getCommitteeRoot returns the committee root at the given period, either fixed,
// proven by a previous update or both. It returns an empty hash if the committee
// root is unknown.
func (s *CommitteeChain) getCommitteeRoot(period uint64) common.Hash {
if root, ok := s.fixedCommitteeRoots.get(s.db, period); ok || period == 0 {
return root
}
if update, ok := s.updates.get(s.db, period-1); ok {
return update.NextSyncCommitteeRoot
}
return common.Hash{}
}
// getSyncCommittee returns the deserialized sync committee at the given period.
func (s *CommitteeChain) getSyncCommittee(period uint64) (syncCommittee, error) {
if c, ok := s.committeeCache.Get(period); ok {
return c, nil
}
if sc, ok := s.committees.get(s.db, period); ok {
c, err := s.sigVerifier.deserializeSyncCommittee(sc)
if err != nil {
return nil, fmt.Errorf("Sync committee #%d deserialization error: %v", period, err)
}
s.committeeCache.Add(period, c)
return c, nil
}
return nil, fmt.Errorf("Missing serialized sync committee #%d", period)
}
// VerifySignedHeader returns true if the given signed header has a valid signature
// according to the local committee chain. The caller should ensure that the
// committees advertised by the same source where the signed header came from are
// synced before verifying the signature.
// The age of the header is also returned (the time elapsed since the beginning
// of the given slot, according to the local system clock). If enforceTime is
// true then negative age (future) headers are rejected.
func (s *CommitteeChain) VerifySignedHeader(head types.SignedHeader) (bool, time.Duration, error) {
s.chainmu.RLock()
defer s.chainmu.RUnlock()
return s.verifySignedHeader(head)
}
func (s *CommitteeChain) verifySignedHeader(head types.SignedHeader) (bool, time.Duration, error) {
var age time.Duration
now := s.unixNano()
if head.Header.Slot < (uint64(now-math.MinInt64)/uint64(time.Second)-s.config.GenesisTime)/12 {
age = time.Duration(now - int64(time.Second)*int64(s.config.GenesisTime+head.Header.Slot*12))
} else {
age = time.Duration(math.MinInt64)
}
if s.enforceTime && age < 0 {
return false, age, nil
}
committee, err := s.getSyncCommittee(types.SyncPeriod(head.SignatureSlot))
if err != nil {
return false, 0, err
}
if committee == nil {
return false, age, nil
}
if signingRoot, err := s.config.Forks.SigningRoot(head.Header); err == nil {
return s.sigVerifier.verifySignature(committee, signingRoot, &head.Signature), age, nil
}
return false, age, nil
}
// verifyUpdate checks whether the header signature is correct and the update
// fits into the specified constraints (assumes that the update has been
// successfully validated previously)
func (s *CommitteeChain) verifyUpdate(update *types.LightClientUpdate) (bool, error) {
// Note: SignatureSlot determines the sync period of the committee used for signature
// verification. Though in reality SignatureSlot is always bigger than update.Header.Slot,
// setting them as equal here enforces the rule that they have to be in the same sync
// period in order for the light client update proof to be meaningful.
ok, age, err := s.verifySignedHeader(update.AttestedHeader)
if age < 0 {
log.Warn("Future committee update received", "age", age)
}
return ok, err
}

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// Copyright 2022 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package light
import (
"crypto/rand"
"testing"
"time"
"github.com/ethereum/go-ethereum/beacon/params"
"github.com/ethereum/go-ethereum/beacon/types"
"github.com/ethereum/go-ethereum/common/mclock"
"github.com/ethereum/go-ethereum/ethdb/memorydb"
)
var (
testGenesis = newTestGenesis()
testGenesis2 = newTestGenesis()
tfBase = newTestForks(testGenesis, types.Forks{
&types.Fork{Epoch: 0, Version: []byte{0}},
})
tfAlternative = newTestForks(testGenesis, types.Forks{
&types.Fork{Epoch: 0, Version: []byte{0}},
&types.Fork{Epoch: 0x700, Version: []byte{1}},
})
tfAnotherGenesis = newTestForks(testGenesis2, types.Forks{
&types.Fork{Epoch: 0, Version: []byte{0}},
})
tcBase = newTestCommitteeChain(nil, tfBase, true, 0, 10, 400, false)
tcBaseWithInvalidUpdates = newTestCommitteeChain(tcBase, tfBase, false, 5, 10, 200, false) // signer count too low
tcBaseWithBetterUpdates = newTestCommitteeChain(tcBase, tfBase, false, 5, 10, 440, false)
tcReorgWithWorseUpdates = newTestCommitteeChain(tcBase, tfBase, true, 5, 10, 400, false)
tcReorgWithWorseUpdates2 = newTestCommitteeChain(tcBase, tfBase, true, 5, 10, 380, false)
tcReorgWithBetterUpdates = newTestCommitteeChain(tcBase, tfBase, true, 5, 10, 420, false)
tcReorgWithFinalizedUpdates = newTestCommitteeChain(tcBase, tfBase, true, 5, 10, 400, true)
tcFork = newTestCommitteeChain(tcBase, tfAlternative, true, 7, 10, 400, false)
tcAnotherGenesis = newTestCommitteeChain(nil, tfAnotherGenesis, true, 0, 10, 400, false)
)
func TestCommitteeChainFixedCommitteeRoots(t *testing.T) {
for _, reload := range []bool{false, true} {
c := newCommitteeChainTest(t, tfBase, 300, true)
c.setClockPeriod(7)
c.addFixedCommitteeRoot(tcBase, 4, nil)
c.addFixedCommitteeRoot(tcBase, 5, nil)
c.addFixedCommitteeRoot(tcBase, 6, nil)
c.addFixedCommitteeRoot(tcBase, 8, ErrInvalidPeriod) // range has to be continuous
c.addFixedCommitteeRoot(tcBase, 3, nil)
c.addFixedCommitteeRoot(tcBase, 2, nil)
if reload {
c.reloadChain()
}
c.addCommittee(tcBase, 4, nil)
c.addCommittee(tcBase, 6, ErrInvalidPeriod) // range has to be continuous
c.addCommittee(tcBase, 5, nil)
c.addCommittee(tcBase, 6, nil)
c.addCommittee(tcAnotherGenesis, 3, ErrWrongCommitteeRoot)
c.addCommittee(tcBase, 3, nil)
if reload {
c.reloadChain()
}
c.verifyRange(tcBase, 3, 6)
}
}
func TestCommitteeChainCheckpointSync(t *testing.T) {
for _, enforceTime := range []bool{false, true} {
for _, reload := range []bool{false, true} {
c := newCommitteeChainTest(t, tfBase, 300, enforceTime)
if enforceTime {
c.setClockPeriod(6)
}
c.insertUpdate(tcBase, 3, true, ErrInvalidPeriod)
c.addFixedCommitteeRoot(tcBase, 3, nil)
c.addFixedCommitteeRoot(tcBase, 4, nil)
c.insertUpdate(tcBase, 4, true, ErrInvalidPeriod) // still no committee
c.addCommittee(tcBase, 3, nil)
c.addCommittee(tcBase, 4, nil)
if reload {
c.reloadChain()
}
c.verifyRange(tcBase, 3, 4)
c.insertUpdate(tcBase, 3, false, nil) // update can be added without committee here
c.insertUpdate(tcBase, 4, false, ErrNeedCommittee) // but not here as committee 5 is not there yet
c.insertUpdate(tcBase, 4, true, nil)
c.verifyRange(tcBase, 3, 5)
c.insertUpdate(tcBaseWithInvalidUpdates, 5, true, ErrInvalidUpdate) // signer count too low
c.insertUpdate(tcBase, 5, true, nil)
if reload {
c.reloadChain()
}
if enforceTime {
c.insertUpdate(tcBase, 6, true, ErrInvalidUpdate) // future update rejected
c.setClockPeriod(7)
}
c.insertUpdate(tcBase, 6, true, nil) // when the time comes it's accepted
if reload {
c.reloadChain()
}
if enforceTime {
c.verifyRange(tcBase, 3, 6) // committee 7 is there but still in the future
c.setClockPeriod(8)
}
c.verifyRange(tcBase, 3, 7) // now period 7 can also be verified
// try reverse syncing an update
c.insertUpdate(tcBase, 2, false, ErrInvalidPeriod) // fixed committee is needed first
c.addFixedCommitteeRoot(tcBase, 2, nil)
c.addCommittee(tcBase, 2, nil)
c.insertUpdate(tcBase, 2, false, nil)
c.verifyRange(tcBase, 2, 7)
}
}
}
func TestCommitteeChainReorg(t *testing.T) {
for _, reload := range []bool{false, true} {
for _, addBetterUpdates := range []bool{false, true} {
c := newCommitteeChainTest(t, tfBase, 300, true)
c.setClockPeriod(11)
c.addFixedCommitteeRoot(tcBase, 3, nil)
c.addFixedCommitteeRoot(tcBase, 4, nil)
c.addCommittee(tcBase, 3, nil)
for period := uint64(3); period < 10; period++ {
c.insertUpdate(tcBase, period, true, nil)
}
if reload {
c.reloadChain()
}
c.verifyRange(tcBase, 3, 10)
c.insertUpdate(tcReorgWithWorseUpdates, 5, true, ErrCannotReorg)
c.insertUpdate(tcReorgWithWorseUpdates2, 5, true, ErrCannotReorg)
if addBetterUpdates {
// add better updates for the base chain and expect first reorg to fail
// (only add updates as committees should be the same)
for period := uint64(5); period < 10; period++ {
c.insertUpdate(tcBaseWithBetterUpdates, period, false, nil)
}
if reload {
c.reloadChain()
}
c.verifyRange(tcBase, 3, 10) // still on the same chain
c.insertUpdate(tcReorgWithBetterUpdates, 5, true, ErrCannotReorg)
} else {
// reorg with better updates
c.insertUpdate(tcReorgWithBetterUpdates, 5, false, ErrNeedCommittee)
c.verifyRange(tcBase, 3, 10) // no success yet, still on the base chain
c.verifyRange(tcReorgWithBetterUpdates, 3, 5)
c.insertUpdate(tcReorgWithBetterUpdates, 5, true, nil)
// successful reorg, base chain should only match before the reorg period
if reload {
c.reloadChain()
}
c.verifyRange(tcBase, 3, 5)
c.verifyRange(tcReorgWithBetterUpdates, 3, 6)
for period := uint64(6); period < 10; period++ {
c.insertUpdate(tcReorgWithBetterUpdates, period, true, nil)
}
c.verifyRange(tcReorgWithBetterUpdates, 3, 10)
}
// reorg with finalized updates; should succeed even if base chain updates
// have been improved because a finalized update beats everything else
c.insertUpdate(tcReorgWithFinalizedUpdates, 5, false, ErrNeedCommittee)
c.insertUpdate(tcReorgWithFinalizedUpdates, 5, true, nil)
if reload {
c.reloadChain()
}
c.verifyRange(tcReorgWithFinalizedUpdates, 3, 6)
for period := uint64(6); period < 10; period++ {
c.insertUpdate(tcReorgWithFinalizedUpdates, period, true, nil)
}
c.verifyRange(tcReorgWithFinalizedUpdates, 3, 10)
}
}
}
func TestCommitteeChainFork(t *testing.T) {
c := newCommitteeChainTest(t, tfAlternative, 300, true)
c.setClockPeriod(11)
// trying to sync a chain on an alternative fork with the base chain data
c.addFixedCommitteeRoot(tcBase, 0, nil)
c.addFixedCommitteeRoot(tcBase, 1, nil)
c.addCommittee(tcBase, 0, nil)
// shared section should sync without errors
for period := uint64(0); period < 7; period++ {
c.insertUpdate(tcBase, period, true, nil)
}
c.insertUpdate(tcBase, 7, true, ErrInvalidUpdate) // wrong fork
// committee root #7 is still the same but signatures are already signed with
// a different fork id so period 7 should only verify on the alternative fork
c.verifyRange(tcBase, 0, 6)
c.verifyRange(tcFork, 0, 7)
for period := uint64(7); period < 10; period++ {
c.insertUpdate(tcFork, period, true, nil)
}
c.verifyRange(tcFork, 0, 10)
// reload the chain while switching to the base fork
c.config = tfBase
c.reloadChain()
// updates 7..9 should be rolled back now
c.verifyRange(tcFork, 0, 6) // again, period 7 only verifies on the right fork
c.verifyRange(tcBase, 0, 7)
c.insertUpdate(tcFork, 7, true, ErrInvalidUpdate) // wrong fork
for period := uint64(7); period < 10; period++ {
c.insertUpdate(tcBase, period, true, nil)
}
c.verifyRange(tcBase, 0, 10)
}
type committeeChainTest struct {
t *testing.T
db *memorydb.Database
clock *mclock.Simulated
config types.ChainConfig
signerThreshold int
enforceTime bool
chain *CommitteeChain
}
func newCommitteeChainTest(t *testing.T, config types.ChainConfig, signerThreshold int, enforceTime bool) *committeeChainTest {
c := &committeeChainTest{
t: t,
db: memorydb.New(),
clock: &mclock.Simulated{},
config: config,
signerThreshold: signerThreshold,
enforceTime: enforceTime,
}
c.chain = newCommitteeChain(c.db, &config, signerThreshold, enforceTime, dummyVerifier{}, c.clock, func() int64 { return int64(c.clock.Now()) })
return c
}
func (c *committeeChainTest) reloadChain() {
c.chain = newCommitteeChain(c.db, &c.config, c.signerThreshold, c.enforceTime, dummyVerifier{}, c.clock, func() int64 { return int64(c.clock.Now()) })
}
func (c *committeeChainTest) setClockPeriod(period float64) {
target := mclock.AbsTime(period * float64(time.Second*12*params.SyncPeriodLength))
wait := time.Duration(target - c.clock.Now())
if wait < 0 {
c.t.Fatalf("Invalid setClockPeriod")
}
c.clock.Run(wait)
}
func (c *committeeChainTest) addFixedCommitteeRoot(tc *testCommitteeChain, period uint64, expErr error) {
if err := c.chain.addFixedCommitteeRoot(period, tc.periods[period].committee.Root()); err != expErr {
c.t.Errorf("Incorrect error output from addFixedCommitteeRoot at period %d (expected %v, got %v)", period, expErr, err)
}
}
func (c *committeeChainTest) addCommittee(tc *testCommitteeChain, period uint64, expErr error) {
if err := c.chain.addCommittee(period, tc.periods[period].committee); err != expErr {
c.t.Errorf("Incorrect error output from addCommittee at period %d (expected %v, got %v)", period, expErr, err)
}
}
func (c *committeeChainTest) insertUpdate(tc *testCommitteeChain, period uint64, addCommittee bool, expErr error) {
var committee *types.SerializedSyncCommittee
if addCommittee {
committee = tc.periods[period+1].committee
}
if err := c.chain.InsertUpdate(tc.periods[period].update, committee); err != expErr {
c.t.Errorf("Incorrect error output from InsertUpdate at period %d (expected %v, got %v)", period, expErr, err)
}
}
func (c *committeeChainTest) verifySignedHeader(tc *testCommitteeChain, period float64, expOk bool) {
slot := uint64(period * float64(params.SyncPeriodLength))
signedHead := GenerateTestSignedHeader(types.Header{Slot: slot}, &tc.config, tc.periods[types.SyncPeriod(slot)].committee, slot+1, 400)
if ok, _, _ := c.chain.VerifySignedHeader(signedHead); ok != expOk {
c.t.Errorf("Incorrect output from VerifySignedHeader at period %f (expected %v, got %v)", period, expOk, ok)
}
}
func (c *committeeChainTest) verifyRange(tc *testCommitteeChain, begin, end uint64) {
if begin > 0 {
c.verifySignedHeader(tc, float64(begin)-0.5, false)
}
for period := begin; period <= end; period++ {
c.verifySignedHeader(tc, float64(period)+0.5, true)
}
c.verifySignedHeader(tc, float64(end)+1.5, false)
}
func newTestGenesis() types.ChainConfig {
var config types.ChainConfig
rand.Read(config.GenesisValidatorsRoot[:])
return config
}
func newTestForks(config types.ChainConfig, forks types.Forks) types.ChainConfig {
for _, fork := range forks {
config.AddFork(fork.Name, fork.Epoch, fork.Version)
}
return config
}
func newTestCommitteeChain(parent *testCommitteeChain, config types.ChainConfig, newCommittees bool, begin, end int, signerCount int, finalizedHeader bool) *testCommitteeChain {
tc := &testCommitteeChain{
config: config,
}
if parent != nil {
tc.periods = make([]testPeriod, len(parent.periods))
copy(tc.periods, parent.periods)
}
if newCommittees {
if begin == 0 {
tc.fillCommittees(begin, end+1)
} else {
tc.fillCommittees(begin+1, end+1)
}
}
tc.fillUpdates(begin, end, signerCount, finalizedHeader)
return tc
}
type testPeriod struct {
committee *types.SerializedSyncCommittee
update *types.LightClientUpdate
}
type testCommitteeChain struct {
periods []testPeriod
config types.ChainConfig
}
func (tc *testCommitteeChain) fillCommittees(begin, end int) {
if len(tc.periods) <= end {
tc.periods = append(tc.periods, make([]testPeriod, end+1-len(tc.periods))...)
}
for i := begin; i <= end; i++ {
tc.periods[i].committee = GenerateTestCommittee()
}
}
func (tc *testCommitteeChain) fillUpdates(begin, end int, signerCount int, finalizedHeader bool) {
for i := begin; i <= end; i++ {
tc.periods[i].update = GenerateTestUpdate(&tc.config, uint64(i), tc.periods[i].committee, tc.periods[i+1].committee, signerCount, finalizedHeader)
}
}

78
beacon/light/range.go Normal file
View File

@ -0,0 +1,78 @@
// Copyright 2023 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package light
// periodRange represents a (possibly zero-length) range of integers (sync periods).
type periodRange struct {
Start, End uint64
}
// isEmpty returns true if the length of the range is zero.
func (a periodRange) isEmpty() bool {
return a.End == a.Start
}
// contains returns true if the range includes the given period.
func (a periodRange) contains(period uint64) bool {
return period >= a.Start && period < a.End
}
// canExpand returns true if the range includes or can be expanded with the given
// period (either the range is empty or the given period is inside, right before or
// right after the range).
func (a periodRange) canExpand(period uint64) bool {
return a.isEmpty() || (period+1 >= a.Start && period <= a.End)
}
// expand expands the range with the given period.
// This method assumes that canExpand returned true: otherwise this is a no-op.
func (a *periodRange) expand(period uint64) {
if a.isEmpty() {
a.Start, a.End = period, period+1
return
}
if a.Start == period+1 {
a.Start--
}
if a.End == period {
a.End++
}
}
// split splits the range into two ranges. The 'fromPeriod' will be the first
// element in the second range (if present).
// The original range is unchanged by this operation
func (a *periodRange) split(fromPeriod uint64) (periodRange, periodRange) {
if fromPeriod <= a.Start {
// First range empty, everything in second range,
return periodRange{}, *a
}
if fromPeriod >= a.End {
// Second range empty, everything in first range,
return *a, periodRange{}
}
x := periodRange{a.Start, fromPeriod}
y := periodRange{fromPeriod, a.End}
return x, y
}
// each invokes the supplied function fn once per period in range
func (a *periodRange) each(fn func(uint64)) {
for p := a.Start; p < a.End; p++ {
fn(p)
}
}

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@ -0,0 +1,152 @@
// Copyright 2023 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package light
import (
"crypto/rand"
"crypto/sha256"
mrand "math/rand"
"github.com/ethereum/go-ethereum/beacon/merkle"
"github.com/ethereum/go-ethereum/beacon/params"
"github.com/ethereum/go-ethereum/beacon/types"
"github.com/ethereum/go-ethereum/common"
)
func GenerateTestCommittee() *types.SerializedSyncCommittee {
s := new(types.SerializedSyncCommittee)
rand.Read(s[:32])
return s
}
func GenerateTestUpdate(config *types.ChainConfig, period uint64, committee, nextCommittee *types.SerializedSyncCommittee, signerCount int, finalizedHeader bool) *types.LightClientUpdate {
update := new(types.LightClientUpdate)
update.NextSyncCommitteeRoot = nextCommittee.Root()
var attestedHeader types.Header
if finalizedHeader {
update.FinalizedHeader = new(types.Header)
*update.FinalizedHeader, update.NextSyncCommitteeBranch = makeTestHeaderWithMerkleProof(types.SyncPeriodStart(period)+100, params.StateIndexNextSyncCommittee, merkle.Value(update.NextSyncCommitteeRoot))
attestedHeader, update.FinalityBranch = makeTestHeaderWithMerkleProof(types.SyncPeriodStart(period)+200, params.StateIndexFinalBlock, merkle.Value(update.FinalizedHeader.Hash()))
} else {
attestedHeader, update.NextSyncCommitteeBranch = makeTestHeaderWithMerkleProof(types.SyncPeriodStart(period)+2000, params.StateIndexNextSyncCommittee, merkle.Value(update.NextSyncCommitteeRoot))
}
update.AttestedHeader = GenerateTestSignedHeader(attestedHeader, config, committee, attestedHeader.Slot+1, signerCount)
return update
}
func GenerateTestSignedHeader(header types.Header, config *types.ChainConfig, committee *types.SerializedSyncCommittee, signatureSlot uint64, signerCount int) types.SignedHeader {
bitmask := makeBitmask(signerCount)
signingRoot, _ := config.Forks.SigningRoot(header)
c, _ := dummyVerifier{}.deserializeSyncCommittee(committee)
return types.SignedHeader{
Header: header,
Signature: types.SyncAggregate{
Signers: bitmask,
Signature: makeDummySignature(c.(dummySyncCommittee), signingRoot, bitmask),
},
SignatureSlot: signatureSlot,
}
}
func GenerateTestCheckpoint(period uint64, committee *types.SerializedSyncCommittee) *types.BootstrapData {
header, branch := makeTestHeaderWithMerkleProof(types.SyncPeriodStart(period)+200, params.StateIndexSyncCommittee, merkle.Value(committee.Root()))
return &types.BootstrapData{
Header: header,
Committee: committee,
CommitteeRoot: committee.Root(),
CommitteeBranch: branch,
}
}
func makeBitmask(signerCount int) (bitmask [params.SyncCommitteeBitmaskSize]byte) {
for i := 0; i < params.SyncCommitteeSize; i++ {
if mrand.Intn(params.SyncCommitteeSize-i) < signerCount {
bitmask[i/8] += byte(1) << (i & 7)
signerCount--
}
}
return
}
func makeTestHeaderWithMerkleProof(slot, index uint64, value merkle.Value) (types.Header, merkle.Values) {
var branch merkle.Values
hasher := sha256.New()
for index > 1 {
var proofHash merkle.Value
rand.Read(proofHash[:])
hasher.Reset()
if index&1 == 0 {
hasher.Write(value[:])
hasher.Write(proofHash[:])
} else {
hasher.Write(proofHash[:])
hasher.Write(value[:])
}
hasher.Sum(value[:0])
index >>= 1
branch = append(branch, proofHash)
}
return types.Header{Slot: slot, StateRoot: common.Hash(value)}, branch
}
// syncCommittee holds either a blsSyncCommittee or a fake dummySyncCommittee used for testing
type syncCommittee interface{}
// committeeSigVerifier verifies sync committee signatures (either proper BLS
// signatures or fake signatures used for testing)
type committeeSigVerifier interface {
deserializeSyncCommittee(s *types.SerializedSyncCommittee) (syncCommittee, error)
verifySignature(committee syncCommittee, signedRoot common.Hash, aggregate *types.SyncAggregate) bool
}
// blsVerifier implements committeeSigVerifier
type blsVerifier struct{}
// deserializeSyncCommittee implements committeeSigVerifier
func (blsVerifier) deserializeSyncCommittee(s *types.SerializedSyncCommittee) (syncCommittee, error) {
return s.Deserialize()
}
// verifySignature implements committeeSigVerifier
func (blsVerifier) verifySignature(committee syncCommittee, signingRoot common.Hash, aggregate *types.SyncAggregate) bool {
return committee.(*types.SyncCommittee).VerifySignature(signingRoot, aggregate)
}
type dummySyncCommittee [32]byte
// dummyVerifier implements committeeSigVerifier
type dummyVerifier struct{}
// deserializeSyncCommittee implements committeeSigVerifier
func (dummyVerifier) deserializeSyncCommittee(s *types.SerializedSyncCommittee) (syncCommittee, error) {
var sc dummySyncCommittee
copy(sc[:], s[:32])
return sc, nil
}
// verifySignature implements committeeSigVerifier
func (dummyVerifier) verifySignature(committee syncCommittee, signingRoot common.Hash, aggregate *types.SyncAggregate) bool {
return aggregate.Signature == makeDummySignature(committee.(dummySyncCommittee), signingRoot, aggregate.Signers)
}
func makeDummySignature(committee dummySyncCommittee, signingRoot common.Hash, bitmask [params.SyncCommitteeBitmaskSize]byte) (sig [params.BLSSignatureSize]byte) {
for i, b := range committee[:] {
sig[i] = b ^ signingRoot[i]
}
copy(sig[32:], bitmask[:])
return
}

View File

@ -25,6 +25,24 @@ import (
"github.com/ethereum/go-ethereum/common" "github.com/ethereum/go-ethereum/common"
) )
// BootstrapData contains a sync committee where light sync can be started,
// together with a proof through a beacon header and corresponding state.
// Note: BootstrapData is fetched from a server based on a known checkpoint hash.
type BootstrapData struct {
Header Header
CommitteeRoot common.Hash
Committee *SerializedSyncCommittee `rlp:"-"`
CommitteeBranch merkle.Values
}
// Validate verifies the proof included in BootstrapData.
func (c *BootstrapData) Validate() error {
if c.CommitteeRoot != c.Committee.Root() {
return errors.New("wrong committee root")
}
return merkle.VerifyProof(c.Header.StateRoot, params.StateIndexSyncCommittee, c.CommitteeBranch, merkle.Value(c.CommitteeRoot))
}
// LightClientUpdate is a proof of the next sync committee root based on a header // LightClientUpdate is a proof of the next sync committee root based on a header
// signed by the sync committee of the given period. Optionally, the update can // signed by the sync committee of the given period. Optionally, the update can
// prove quasi-finality by the signed header referring to a previous, finalized // prove quasi-finality by the signed header referring to a previous, finalized

View File

@ -132,6 +132,10 @@ var (
CliqueSnapshotPrefix = []byte("clique-") CliqueSnapshotPrefix = []byte("clique-")
BestUpdateKey = []byte("update-") // bigEndian64(syncPeriod) -> RLP(types.LightClientUpdate) (nextCommittee only referenced by root hash)
FixedCommitteeRootKey = []byte("fixedRoot-") // bigEndian64(syncPeriod) -> committee root hash
SyncCommitteeKey = []byte("committee-") // bigEndian64(syncPeriod) -> serialized committee
preimageCounter = metrics.NewRegisteredCounter("db/preimage/total", nil) preimageCounter = metrics.NewRegisteredCounter("db/preimage/total", nil)
preimageHitCounter = metrics.NewRegisteredCounter("db/preimage/hits", nil) preimageHitCounter = metrics.NewRegisteredCounter("db/preimage/hits", nil)
) )