mirror of
https://github.com/kaspanet/kaspad.git
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1223 lines
42 KiB
Go
1223 lines
42 KiB
Go
// Copyright (c) 2013-2017 The btcsuite developers
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// Use of this source code is governed by an ISC
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// license that can be found in the LICENSE file.
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package blockdag
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import (
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"encoding/binary"
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"fmt"
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"math"
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"math/big"
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"sort"
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"time"
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"github.com/daglabs/btcd/dagconfig"
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"github.com/daglabs/btcd/dagconfig/daghash"
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"github.com/daglabs/btcd/txscript"
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"github.com/daglabs/btcd/util"
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"github.com/daglabs/btcd/util/subnetworkid"
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"github.com/daglabs/btcd/wire"
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)
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const (
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// MaxSigOpsPerBlock is the maximum number of signature operations
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// allowed for a block. It is a fraction of the max block payload size.
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MaxSigOpsPerBlock = wire.MaxBlockPayload / 50
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// MaxTimeOffsetSeconds is the maximum number of seconds a block time
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// is allowed to be ahead of the current time. This is currently 2
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// hours.
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MaxTimeOffsetSeconds = 2 * 60 * 60
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// MinCoinbaseScriptLen is the minimum length a coinbase script can be.
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MinCoinbaseScriptLen = 2
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// MaxCoinbaseScriptLen is the maximum length a coinbase script can be.
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MaxCoinbaseScriptLen = 100
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// medianTimeBlocks is the number of previous blocks which should be
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// used to calculate the median time used to validate block timestamps.
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medianTimeBlocks = 51
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// baseSubsidy is the starting subsidy amount for mined blocks. This
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// value is halved every SubsidyHalvingInterval blocks.
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baseSubsidy = 50 * util.SatoshiPerBitcoin
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// MaxOutputsPerBlock is the maximum number of transaction outputs there
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// can be in a block of max size.
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MaxOutputsPerBlock = wire.MaxBlockPayload / wire.MinTxOutPayload
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)
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// isNullOutpoint determines whether or not a previous transaction output point
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// is set.
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func isNullOutpoint(outpoint *wire.OutPoint) bool {
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if outpoint.Index == math.MaxUint32 && outpoint.TxID == daghash.ZeroTxID {
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return true
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}
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return false
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}
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// IsCoinBase determines whether or not a transaction is a coinbase. A coinbase
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// is a special transaction created by miners that has no inputs. This is
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// represented in the block dag by a transaction with a single input that has
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// a previous output transaction index set to the maximum value along with a
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// zero hash.
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func IsCoinBase(tx *util.Tx) bool {
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return tx.MsgTx().IsCoinBase()
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}
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// IsBlockReward determines whether or not a transaction is a block reward (a fee transaction or block reward)
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func IsBlockReward(tx *util.Tx) bool {
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return tx.MsgTx().IsBlockReward()
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}
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// IsFeeTransaction determines whether or not a transaction is a fee transaction. A fee
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// transaction is a special transaction created by miners that distributes fees to the
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// previous blocks' miners. Each input of the fee transaction should set index to maximum
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// value and reference the relevant block id, instead of previous transaction id.
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func IsFeeTransaction(tx *util.Tx) bool {
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return tx.MsgTx().IsFeeTransaction()
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}
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// SequenceLockActive determines if a transaction's sequence locks have been
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// met, meaning that all the inputs of a given transaction have reached a
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// height or time sufficient for their relative lock-time maturity.
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func SequenceLockActive(sequenceLock *SequenceLock, blockHeight int32,
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medianTimePast time.Time) bool {
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// If either the seconds, or height relative-lock time has not yet
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// reached, then the transaction is not yet mature according to its
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// sequence locks.
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if sequenceLock.Seconds >= medianTimePast.Unix() ||
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sequenceLock.BlockHeight >= blockHeight {
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return false
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}
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return true
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}
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// IsFinalizedTransaction determines whether or not a transaction is finalized.
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func IsFinalizedTransaction(tx *util.Tx, blockHeight int32, blockTime time.Time) bool {
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msgTx := tx.MsgTx()
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// Lock time of zero means the transaction is finalized.
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lockTime := msgTx.LockTime
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if lockTime == 0 {
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return true
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}
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// The lock time field of a transaction is either a block height at
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// which the transaction is finalized or a timestamp depending on if the
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// value is before the txscript.LockTimeThreshold. When it is under the
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// threshold it is a block height.
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blockTimeOrHeight := int64(0)
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if lockTime < txscript.LockTimeThreshold {
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blockTimeOrHeight = int64(blockHeight)
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} else {
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blockTimeOrHeight = blockTime.Unix()
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}
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if int64(lockTime) < blockTimeOrHeight {
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return true
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}
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// At this point, the transaction's lock time hasn't occurred yet, but
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// the transaction might still be finalized if the sequence number
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// for all transaction inputs is maxed out.
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for _, txIn := range msgTx.TxIn {
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if txIn.Sequence != math.MaxUint64 {
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return false
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}
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}
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return true
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}
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// CalcBlockSubsidy returns the subsidy amount a block at the provided height
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// should have. This is mainly used for determining how much the coinbase for
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// newly generated blocks awards as well as validating the coinbase for blocks
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// has the expected value.
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//
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// The subsidy is halved every SubsidyReductionInterval blocks. Mathematically
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// this is: baseSubsidy / 2^(height/SubsidyReductionInterval)
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//
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// At the target block generation rate for the main network, this is
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// approximately every 4 years.
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func CalcBlockSubsidy(height int32, dagParams *dagconfig.Params) uint64 {
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if dagParams.SubsidyReductionInterval == 0 {
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return baseSubsidy
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}
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// Equivalent to: baseSubsidy / 2^(height/subsidyHalvingInterval)
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return baseSubsidy >> uint(height/dagParams.SubsidyReductionInterval)
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}
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// CheckTransactionSanity performs some preliminary checks on a transaction to
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// ensure it is sane. These checks are context free.
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func CheckTransactionSanity(tx *util.Tx, subnetworkID *subnetworkid.SubnetworkID, isFeeTransaction bool) error {
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// A transaction must have at least one input.
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msgTx := tx.MsgTx()
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if len(msgTx.TxIn) == 0 {
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return ruleError(ErrNoTxInputs, "transaction has no inputs")
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}
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// A transaction must not exceed the maximum allowed block payload when
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// serialized.
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serializedTxSize := msgTx.SerializeSize()
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if serializedTxSize > wire.MaxBlockPayload {
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str := fmt.Sprintf("serialized transaction is too big - got "+
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"%d, max %d", serializedTxSize, wire.MaxBlockPayload)
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return ruleError(ErrTxTooBig, str)
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}
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// Ensure the transaction amounts are in range. Each transaction
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// output must not be negative or more than the max allowed per
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// transaction. Also, the total of all outputs must abide by the same
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// restrictions. All amounts in a transaction are in a unit value known
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// as a satoshi. One bitcoin is a quantity of satoshi as defined by the
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// SatoshiPerBitcoin constant.
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var totalSatoshi uint64
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for _, txOut := range msgTx.TxOut {
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satoshi := txOut.Value
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if satoshi > util.MaxSatoshi {
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str := fmt.Sprintf("transaction output value of %d is "+
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"higher than max allowed value of %d", satoshi,
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util.MaxSatoshi)
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return ruleError(ErrBadTxOutValue, str)
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}
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// Binary arithmetic guarantees that any overflow is detected and reported.
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// This is impossible for Bitcoin, but perhaps possible if an alt increases
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// the total money supply.
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newTotalSatoshi := totalSatoshi + satoshi
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if newTotalSatoshi < totalSatoshi {
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str := fmt.Sprintf("total value of all transaction "+
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"outputs exceeds max allowed value of %d",
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util.MaxSatoshi)
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return ruleError(ErrBadTxOutValue, str)
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}
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totalSatoshi = newTotalSatoshi
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if totalSatoshi > util.MaxSatoshi {
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str := fmt.Sprintf("total value of all transaction "+
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"outputs is %d which is higher than max "+
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"allowed value of %d", totalSatoshi,
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util.MaxSatoshi)
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return ruleError(ErrBadTxOutValue, str)
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}
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}
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// Check for duplicate transaction inputs.
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existingTxOut := make(map[wire.OutPoint]struct{})
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for _, txIn := range msgTx.TxIn {
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if _, exists := existingTxOut[txIn.PreviousOutPoint]; exists {
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return ruleError(ErrDuplicateTxInputs, "transaction "+
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"contains duplicate inputs")
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}
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existingTxOut[txIn.PreviousOutPoint] = struct{}{}
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}
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// Coinbase script length must be between min and max length.
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if IsCoinBase(tx) {
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slen := len(msgTx.TxIn[0].SignatureScript)
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if slen < MinCoinbaseScriptLen || slen > MaxCoinbaseScriptLen {
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str := fmt.Sprintf("coinbase transaction script length "+
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"of %d is out of range (min: %d, max: %d)",
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slen, MinCoinbaseScriptLen, MaxCoinbaseScriptLen)
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return ruleError(ErrBadCoinbaseScriptLen, str)
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}
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} else {
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// Previous transaction outputs referenced by the inputs to this
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// transaction must not be null.
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for _, txIn := range msgTx.TxIn {
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if isNullOutpoint(&txIn.PreviousOutPoint) {
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return ruleError(ErrBadTxInput, "transaction "+
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"input refers to previous output that "+
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"is null")
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}
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}
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}
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// Transactions in native and subnetwork registry subnetworks must have Gas = 0
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if (msgTx.SubnetworkID.IsEqual(subnetworkid.SubnetworkIDNative) ||
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msgTx.SubnetworkID.IsEqual(subnetworkid.SubnetworkIDRegistry)) &&
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msgTx.Gas > 0 {
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return ruleError(ErrInvalidGas, "transaction in the native or "+
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"registry subnetworks has gas > 0 ")
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}
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if msgTx.SubnetworkID.IsEqual(subnetworkid.SubnetworkIDNative) &&
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len(msgTx.Payload) > 0 {
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return ruleError(ErrInvalidPayload,
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"transaction in the native subnetwork includes a payload")
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}
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if msgTx.SubnetworkID.IsEqual(subnetworkid.SubnetworkIDRegistry) &&
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len(msgTx.Payload) != 8 {
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return ruleError(ErrInvalidPayload,
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"transaction in the subnetwork registry include a payload "+
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"with length != 8 bytes")
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}
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// If we are a partial node, only transactions on the Registry subnetwork
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// or our own subnetwork may have a payload
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isLocalNodeFull := subnetworkID.IsEqual(subnetworkid.SubnetworkIDSupportsAll)
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shouldTxBeFull := msgTx.SubnetworkID.IsEqual(subnetworkid.SubnetworkIDRegistry) ||
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msgTx.SubnetworkID.IsEqual(subnetworkID)
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if !isLocalNodeFull && !shouldTxBeFull && len(msgTx.Payload) > 0 {
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return ruleError(ErrInvalidPayload,
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"transaction that was expected to be partial has a payload "+
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"with length > 0")
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}
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return nil
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}
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// checkProofOfWork ensures the block header bits which indicate the target
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// difficulty is in min/max range and that the block hash is less than the
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// target difficulty as claimed.
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//
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// The flags modify the behavior of this function as follows:
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// - BFNoPoWCheck: The check to ensure the block hash is less than the target
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// difficulty is not performed.
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func (dag *BlockDAG) checkProofOfWork(header *wire.BlockHeader, flags BehaviorFlags) error {
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// The target difficulty must be larger than zero.
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target := CompactToBig(header.Bits)
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if target.Sign() <= 0 {
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str := fmt.Sprintf("block target difficulty of %064x is too low",
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target)
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return ruleError(ErrUnexpectedDifficulty, str)
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}
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// The target difficulty must be less than the maximum allowed.
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if target.Cmp(dag.dagParams.PowLimit) > 0 {
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str := fmt.Sprintf("block target difficulty of %064x is "+
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"higher than max of %064x", target, dag.dagParams.PowLimit)
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return ruleError(ErrUnexpectedDifficulty, str)
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}
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// The block hash must be less than the claimed target unless the flag
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// to avoid proof of work checks is set.
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if flags&BFNoPoWCheck != BFNoPoWCheck {
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// The block hash must be less than the claimed target.
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hash := header.BlockHash()
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hashNum := daghash.HashToBig(&hash)
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if hashNum.Cmp(target) > 0 {
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str := fmt.Sprintf("block hash of %064x is higher than "+
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"expected max of %064x", hashNum, target)
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return ruleError(ErrHighHash, str)
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}
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}
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return nil
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}
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// CountSigOps returns the number of signature operations for all transaction
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// input and output scripts in the provided transaction. This uses the
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// quicker, but imprecise, signature operation counting mechanism from
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// txscript.
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func CountSigOps(tx *util.Tx) int {
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msgTx := tx.MsgTx()
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// Accumulate the number of signature operations in all transaction
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// inputs.
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totalSigOps := 0
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for _, txIn := range msgTx.TxIn {
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numSigOps := txscript.GetSigOpCount(txIn.SignatureScript)
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totalSigOps += numSigOps
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}
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// Accumulate the number of signature operations in all transaction
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// outputs.
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for _, txOut := range msgTx.TxOut {
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numSigOps := txscript.GetSigOpCount(txOut.PkScript)
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totalSigOps += numSigOps
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}
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return totalSigOps
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}
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// CountP2SHSigOps returns the number of signature operations for all input
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// transactions which are of the pay-to-script-hash type. This uses the
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// precise, signature operation counting mechanism from the script engine which
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// requires access to the input transaction scripts.
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func CountP2SHSigOps(tx *util.Tx, isBlockReward bool, utxoSet UTXOSet) (int, error) {
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// Block reward transactions have no interesting inputs.
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if isBlockReward {
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return 0, nil
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}
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// Accumulate the number of signature operations in all transaction
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// inputs.
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msgTx := tx.MsgTx()
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totalSigOps := 0
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for txInIndex, txIn := range msgTx.TxIn {
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// Ensure the referenced input transaction is available.
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entry, ok := utxoSet.Get(txIn.PreviousOutPoint)
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if !ok {
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str := fmt.Sprintf("output %s referenced from "+
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"transaction %s:%d either does not exist or "+
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"has already been spent", txIn.PreviousOutPoint,
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tx.ID(), txInIndex)
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return 0, ruleError(ErrMissingTxOut, str)
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}
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// We're only interested in pay-to-script-hash types, so skip
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// this input if it's not one.
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pkScript := entry.PkScript()
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if !txscript.IsPayToScriptHash(pkScript) {
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continue
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}
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// Count the precise number of signature operations in the
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// referenced public key script.
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sigScript := txIn.SignatureScript
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numSigOps := txscript.GetPreciseSigOpCount(sigScript, pkScript,
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true)
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// We could potentially overflow the accumulator so check for
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// overflow.
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lastSigOps := totalSigOps
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totalSigOps += numSigOps
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if totalSigOps < lastSigOps {
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str := fmt.Sprintf("the public key script from output "+
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"%s contains too many signature operations - "+
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"overflow", txIn.PreviousOutPoint)
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return 0, ruleError(ErrTooManySigOps, str)
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}
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}
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return totalSigOps, nil
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}
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// checkBlockHeaderSanity performs some preliminary checks on a block header to
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// ensure it is sane before continuing with processing. These checks are
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// context free.
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//
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// The flags do not modify the behavior of this function directly, however they
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// are needed to pass along to checkProofOfWork.
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func (dag *BlockDAG) checkBlockHeaderSanity(header *wire.BlockHeader, flags BehaviorFlags) error {
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// Ensure the proof of work bits in the block header is in min/max range
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// and the block hash is less than the target value described by the
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// bits.
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err := dag.checkProofOfWork(header, flags)
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if err != nil {
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return err
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}
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if len(header.ParentHashes) == 0 {
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if header.BlockHash() != *dag.dagParams.GenesisHash {
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return ruleError(ErrNoParents, "block has no parents")
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}
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} else {
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err = checkBlockParentsOrder(header)
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if err != nil {
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return err
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}
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}
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// A block timestamp must not have a greater precision than one second.
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// This check is necessary because Go time.Time values support
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// nanosecond precision whereas the consensus rules only apply to
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// seconds and it's much nicer to deal with standard Go time values
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// instead of converting to seconds everywhere.
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if !header.Timestamp.Equal(time.Unix(header.Timestamp.Unix(), 0)) {
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str := fmt.Sprintf("block timestamp of %s has a higher "+
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"precision than one second", header.Timestamp)
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return ruleError(ErrInvalidTime, str)
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}
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// Ensure the block time is not too far in the future.
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maxTimestamp := dag.timeSource.AdjustedTime().Add(time.Second *
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MaxTimeOffsetSeconds)
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if header.Timestamp.After(maxTimestamp) {
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str := fmt.Sprintf("block timestamp of %s is too far in the "+
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"future", header.Timestamp)
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return ruleError(ErrTimeTooNew, str)
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}
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return nil
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}
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//checkBlockParentsOrder ensures that the block's parents are ordered by hash
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func checkBlockParentsOrder(header *wire.BlockHeader) error {
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sortedHashes := make([]daghash.Hash, 0, header.NumParentBlocks())
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for _, hash := range header.ParentHashes {
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sortedHashes = append(sortedHashes, hash)
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}
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sort.Slice(sortedHashes, func(i, j int) bool {
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return daghash.Less(&sortedHashes[i], &sortedHashes[j])
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})
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if !daghash.AreEqual(header.ParentHashes, sortedHashes) {
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return ruleError(ErrWrongParentsOrder, "block parents are not ordered by hash")
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}
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return nil
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}
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|
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// checkBlockSanity performs some preliminary checks on a block to ensure it is
|
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// sane before continuing with block processing. These checks are context free.
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//
|
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// The flags do not modify the behavior of this function directly, however they
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// are needed to pass along to checkBlockHeaderSanity.
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func (dag *BlockDAG) checkBlockSanity(block *util.Block, flags BehaviorFlags) error {
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msgBlock := block.MsgBlock()
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header := &msgBlock.Header
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err := dag.checkBlockHeaderSanity(header, flags)
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if err != nil {
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return err
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}
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// A block must have at least one transaction.
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numTx := len(msgBlock.Transactions)
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if numTx == 0 {
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return ruleError(ErrNoTransactions, "block does not contain "+
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"any transactions")
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}
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// A block must not have more transactions than the max block payload or
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// else it is certainly over the block size limit.
|
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if numTx > wire.MaxBlockPayload {
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str := fmt.Sprintf("block contains too many transactions - "+
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"got %d, max %d", numTx, wire.MaxBlockPayload)
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return ruleError(ErrBlockTooBig, str)
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}
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|
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// A block must not exceed the maximum allowed block payload when
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// serialized.
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serializedSize := msgBlock.SerializeSize()
|
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if serializedSize > wire.MaxBlockPayload {
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str := fmt.Sprintf("serialized block is too big - got %d, "+
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"max %d", serializedSize, wire.MaxBlockPayload)
|
|
return ruleError(ErrBlockTooBig, str)
|
|
}
|
|
|
|
// The first transaction in a block must be a coinbase.
|
|
transactions := block.Transactions()
|
|
if !IsCoinBase(transactions[0]) {
|
|
return ruleError(ErrFirstTxNotCoinbase, "first transaction in "+
|
|
"block is not a coinbase")
|
|
}
|
|
|
|
isGenesis := block.MsgBlock().Header.IsGenesis()
|
|
if !isGenesis && !IsFeeTransaction(transactions[1]) {
|
|
return ruleError(ErrSecondTxNotFeeTransaction, "second transaction in "+
|
|
"block is not a fee transaction")
|
|
}
|
|
|
|
txOffset := 2
|
|
if isGenesis {
|
|
txOffset = 1
|
|
}
|
|
|
|
// A block must not have more than one coinbase. And transactions must be
|
|
// ordered by subnetwork
|
|
for i, tx := range transactions[txOffset:] {
|
|
if IsCoinBase(tx) {
|
|
str := fmt.Sprintf("block contains second coinbase at "+
|
|
"index %d", i+2)
|
|
return ruleError(ErrMultipleCoinbases, str)
|
|
}
|
|
if IsFeeTransaction(tx) {
|
|
str := fmt.Sprintf("block contains second fee transaction at "+
|
|
"index %d", i+2)
|
|
return ruleError(ErrMultipleFeeTransactions, str)
|
|
}
|
|
if subnetworkid.Less(&tx.MsgTx().SubnetworkID, &transactions[i].MsgTx().SubnetworkID) {
|
|
return ruleError(ErrTransactionsNotSorted, "transactions must be sorted by subnetwork")
|
|
}
|
|
}
|
|
|
|
// Do some preliminary checks on each transaction to ensure they are
|
|
// sane before continuing.
|
|
for i, tx := range transactions {
|
|
isFeeTransaction := i == util.FeeTransactionIndex
|
|
err := CheckTransactionSanity(tx, dag.subnetworkID, isFeeTransaction)
|
|
if err != nil {
|
|
return err
|
|
}
|
|
}
|
|
|
|
// Build merkle tree and ensure the calculated merkle root matches the
|
|
// entry in the block header. This also has the effect of caching all
|
|
// of the transaction hashes in the block to speed up future hash
|
|
// checks. Bitcoind builds the tree here and checks the merkle root
|
|
// after the following checks, but there is no reason not to check the
|
|
// merkle root matches here.
|
|
hashMerkleTree := BuildHashMerkleTreeStore(block.Transactions())
|
|
calculatedHashMerkleRoot := hashMerkleTree.Root()
|
|
if !header.HashMerkleRoot.IsEqual(calculatedHashMerkleRoot) {
|
|
str := fmt.Sprintf("block hash merkle root is invalid - block "+
|
|
"header indicates %s, but calculated value is %s",
|
|
header.HashMerkleRoot, calculatedHashMerkleRoot)
|
|
return ruleError(ErrBadMerkleRoot, str)
|
|
}
|
|
|
|
idMerkleTree := BuildIDMerkleTreeStore(block.Transactions())
|
|
calculatedIDMerkleRoot := idMerkleTree.Root()
|
|
if !header.IDMerkleRoot.IsEqual(calculatedIDMerkleRoot) {
|
|
str := fmt.Sprintf("block ID merkle root is invalid - block "+
|
|
"header indicates %s, but calculated value is %s",
|
|
header.IDMerkleRoot, calculatedIDMerkleRoot)
|
|
return ruleError(ErrBadMerkleRoot, str)
|
|
}
|
|
|
|
// Check for duplicate transactions. This check will be fairly quick
|
|
// since the transaction IDs are already cached due to building the
|
|
// merkle tree above.
|
|
existingTxIDs := make(map[daghash.TxID]struct{})
|
|
for _, tx := range transactions {
|
|
id := tx.ID()
|
|
if _, exists := existingTxIDs[*id]; exists {
|
|
str := fmt.Sprintf("block contains duplicate "+
|
|
"transaction %s", id)
|
|
return ruleError(ErrDuplicateTx, str)
|
|
}
|
|
existingTxIDs[*id] = struct{}{}
|
|
}
|
|
|
|
// The number of signature operations must be less than the maximum
|
|
// allowed per block.
|
|
totalSigOps := 0
|
|
for _, tx := range transactions {
|
|
// We could potentially overflow the accumulator so check for
|
|
// overflow.
|
|
lastSigOps := totalSigOps
|
|
totalSigOps += CountSigOps(tx)
|
|
if totalSigOps < lastSigOps || totalSigOps > MaxSigOpsPerBlock {
|
|
str := fmt.Sprintf("block contains too many signature "+
|
|
"operations - got %d, max %d", totalSigOps,
|
|
MaxSigOpsPerBlock)
|
|
return ruleError(ErrTooManySigOps, str)
|
|
}
|
|
}
|
|
|
|
return nil
|
|
}
|
|
|
|
// CheckBlockSanity performs some preliminary checks on a block to ensure it is
|
|
// sane before continuing with block processing. These checks are context free.
|
|
func (dag *BlockDAG) CheckBlockSanity(block *util.Block, powLimit *big.Int,
|
|
timeSource MedianTimeSource) error {
|
|
|
|
return dag.checkBlockSanity(block, BFNone)
|
|
}
|
|
|
|
// ExtractCoinbaseHeight attempts to extract the height of the block from the
|
|
// scriptSig of a coinbase transaction.
|
|
func ExtractCoinbaseHeight(coinbaseTx *util.Tx) (int32, error) {
|
|
sigScript := coinbaseTx.MsgTx().TxIn[0].SignatureScript
|
|
if len(sigScript) < 1 {
|
|
str := "the coinbase signature script" +
|
|
"must start with the " +
|
|
"length of the serialized block height"
|
|
str = fmt.Sprintf(str)
|
|
return 0, ruleError(ErrMissingCoinbaseHeight, str)
|
|
}
|
|
|
|
// Detect the case when the block height is a small integer encoded with
|
|
// a single byte.
|
|
opcode := int(sigScript[0])
|
|
if opcode == txscript.Op0 {
|
|
return 0, nil
|
|
}
|
|
if opcode >= txscript.Op1 && opcode <= txscript.Op16 {
|
|
return int32(opcode - (txscript.Op1 - 1)), nil
|
|
}
|
|
|
|
// Otherwise, the opcode is the length of the following bytes which
|
|
// encode in the block height.
|
|
serializedLen := int(sigScript[0])
|
|
if len(sigScript[1:]) < serializedLen {
|
|
str := "the coinbase signature script " +
|
|
"must start with the " +
|
|
"serialized block height"
|
|
str = fmt.Sprintf(str, serializedLen)
|
|
return 0, ruleError(ErrMissingCoinbaseHeight, str)
|
|
}
|
|
|
|
serializedHeightBytes := make([]byte, 8)
|
|
copy(serializedHeightBytes, sigScript[1:serializedLen+1])
|
|
serializedHeight := binary.LittleEndian.Uint64(serializedHeightBytes)
|
|
|
|
return int32(serializedHeight), nil
|
|
}
|
|
|
|
// checkSerializedHeight checks if the signature script in the passed
|
|
// transaction starts with the serialized block height of wantHeight.
|
|
func checkSerializedHeight(block *util.Block) error {
|
|
coinbaseTx := block.CoinbaseTransaction()
|
|
serializedHeight, err := ExtractCoinbaseHeight(coinbaseTx)
|
|
if err != nil {
|
|
return err
|
|
}
|
|
|
|
wantHeight := block.Height()
|
|
if serializedHeight != wantHeight {
|
|
str := fmt.Sprintf("the coinbase signature script serialized "+
|
|
"block height is %d when %d was expected",
|
|
serializedHeight, wantHeight)
|
|
return ruleError(ErrBadCoinbaseHeight, str)
|
|
}
|
|
return nil
|
|
}
|
|
|
|
// checkBlockHeaderContext performs several validation checks on the block header
|
|
// which depend on its position within the block dag.
|
|
//
|
|
// The flags modify the behavior of this function as follows:
|
|
// - BFFastAdd: All checks except those involving comparing the header against
|
|
// the checkpoints are not performed.
|
|
//
|
|
// This function MUST be called with the dag state lock held (for writes).
|
|
func (dag *BlockDAG) checkBlockHeaderContext(header *wire.BlockHeader, bluestParent *blockNode, blockHeight int32, fastAdd bool) error {
|
|
if !fastAdd {
|
|
if err := dag.validateDifficulty(header, bluestParent); err != nil {
|
|
return err
|
|
}
|
|
|
|
if err := validateMedianTime(header, bluestParent); err != nil {
|
|
return err
|
|
}
|
|
}
|
|
|
|
return dag.validateCheckpoints(header, blockHeight)
|
|
}
|
|
|
|
func (dag *BlockDAG) validateCheckpoints(header *wire.BlockHeader, blockHeight int32) error {
|
|
// Ensure dag matches up to predetermined checkpoints.
|
|
blockHash := header.BlockHash()
|
|
if !dag.verifyCheckpoint(blockHeight, &blockHash) {
|
|
str := fmt.Sprintf("block at height %d does not match "+
|
|
"checkpoint hash", blockHeight)
|
|
return ruleError(ErrBadCheckpoint, str)
|
|
}
|
|
|
|
// Find the previous checkpoint and prevent blocks which fork the main
|
|
// dag before it. This prevents storage of new, otherwise valid,
|
|
// blocks which build off of old blocks that are likely at a much easier
|
|
// difficulty and therefore could be used to waste cache and disk space.
|
|
checkpointNode, err := dag.findPreviousCheckpoint()
|
|
if err != nil {
|
|
return err
|
|
}
|
|
if checkpointNode != nil && blockHeight < checkpointNode.height {
|
|
str := fmt.Sprintf("block at height %d forks the main dag "+
|
|
"before the previous checkpoint at height %d",
|
|
blockHeight, checkpointNode.height)
|
|
return ruleError(ErrForkTooOld, str)
|
|
}
|
|
|
|
return nil
|
|
}
|
|
|
|
func validateMedianTime(header *wire.BlockHeader, bluestParent *blockNode) error {
|
|
if !header.IsGenesis() {
|
|
// Ensure the timestamp for the block header is not before the
|
|
// median time of the last several blocks (medianTimeBlocks).
|
|
medianTime := bluestParent.PastMedianTime()
|
|
if header.Timestamp.Before(medianTime) {
|
|
str := "block timestamp of %s is not after expected %s"
|
|
str = fmt.Sprintf(str, header.Timestamp, medianTime)
|
|
return ruleError(ErrTimeTooOld, str)
|
|
}
|
|
}
|
|
|
|
return nil
|
|
}
|
|
|
|
func (dag *BlockDAG) validateDifficulty(header *wire.BlockHeader, bluestParent *blockNode) error {
|
|
// Ensure the difficulty specified in the block header matches
|
|
// the calculated difficulty based on the previous block and
|
|
// difficulty retarget rules.
|
|
expectedDifficulty, err := dag.calcNextRequiredDifficulty(bluestParent,
|
|
header.Timestamp)
|
|
if err != nil {
|
|
return err
|
|
}
|
|
blockDifficulty := header.Bits
|
|
if blockDifficulty != expectedDifficulty {
|
|
str := "block difficulty of %d is not the expected value of %d"
|
|
str = fmt.Sprintf(str, blockDifficulty, expectedDifficulty)
|
|
return ruleError(ErrUnexpectedDifficulty, str)
|
|
}
|
|
|
|
return nil
|
|
}
|
|
|
|
// validateParents validates that no parent is an ancestor of another parent
|
|
func validateParents(blockHeader *wire.BlockHeader, parents blockSet) error {
|
|
minHeight := int32(math.MaxInt32)
|
|
queue := NewHeap()
|
|
visited := newSet()
|
|
for _, parent := range parents {
|
|
if parent.height < minHeight {
|
|
minHeight = parent.height
|
|
}
|
|
for _, grandParent := range parent.parents {
|
|
if !visited.contains(grandParent) {
|
|
queue.Push(grandParent)
|
|
visited.add(grandParent)
|
|
}
|
|
}
|
|
}
|
|
for queue.Len() > 0 {
|
|
current := queue.pop()
|
|
if parents.contains(current) {
|
|
return fmt.Errorf("Block %s is both a parent of %s and an"+
|
|
" ancestor of another parent",
|
|
current.hash,
|
|
blockHeader.BlockHash())
|
|
}
|
|
if current.height > minHeight {
|
|
for _, parent := range current.parents {
|
|
if !visited.contains(parent) {
|
|
queue.Push(parent)
|
|
visited.add(parent)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return nil
|
|
}
|
|
|
|
// checkBlockContext peforms several validation checks on the block which depend
|
|
// on its position within the block DAG.
|
|
//
|
|
// The flags modify the behavior of this function as follows:
|
|
// - BFFastAdd: The transaction are not checked to see if they are finalized
|
|
// and the somewhat expensive BIP0034 validation is not performed.
|
|
//
|
|
// The flags are also passed to checkBlockHeaderContext. See its documentation
|
|
// for how the flags modify its behavior.
|
|
//
|
|
// This function MUST be called with the dag state lock held (for writes).
|
|
func (dag *BlockDAG) checkBlockContext(block *util.Block, parents blockSet, bluestParent *blockNode, flags BehaviorFlags) error {
|
|
fastAdd := flags&BFFastAdd == BFFastAdd
|
|
|
|
err := validateParents(&block.MsgBlock().Header, parents)
|
|
if err != nil {
|
|
return err
|
|
}
|
|
|
|
// Perform all block header related validation checks.
|
|
header := &block.MsgBlock().Header
|
|
if err = dag.checkBlockHeaderContext(header, bluestParent, block.Height(), fastAdd); err != nil {
|
|
return err
|
|
}
|
|
|
|
if !fastAdd {
|
|
if err := dag.validateAllTxsFinalized(block, header, bluestParent); err != nil {
|
|
return err
|
|
}
|
|
|
|
// Ensure coinbase starts with serialized block heights
|
|
err := checkSerializedHeight(block)
|
|
if err != nil {
|
|
return err
|
|
}
|
|
|
|
}
|
|
|
|
return nil
|
|
}
|
|
|
|
func (dag *BlockDAG) validateAllTxsFinalized(block *util.Block, header *wire.BlockHeader, bluestParent *blockNode) error {
|
|
blockTime := header.Timestamp
|
|
if !block.IsGenesis() {
|
|
blockTime = bluestParent.PastMedianTime()
|
|
}
|
|
|
|
// Ensure all transactions in the block are finalized.
|
|
for _, tx := range block.Transactions() {
|
|
if !IsFinalizedTransaction(tx, block.Height(), blockTime) {
|
|
str := fmt.Sprintf("block contains unfinalized "+
|
|
"transaction %s", tx.ID())
|
|
return ruleError(ErrUnfinalizedTx, str)
|
|
}
|
|
}
|
|
|
|
return nil
|
|
}
|
|
|
|
// ensureNoDuplicateTx ensures blocks do not contain duplicate transactions which
|
|
// 'overwrite' older transactions that are not fully spent. This prevents an
|
|
// attack where a coinbase and all of its dependent transactions could be
|
|
// duplicated to effectively revert the overwritten transactions to a single
|
|
// confirmation thereby making them vulnerable to a double spend.
|
|
//
|
|
// For more details, see
|
|
// https://github.com/bitcoin/bips/blob/master/bip-0030.mediawiki and
|
|
// http://r6.ca/blog/20120206T005236Z.html.
|
|
//
|
|
// This function MUST be called with the dag state lock held (for reads).
|
|
func ensureNoDuplicateTx(block *blockNode, utxoSet UTXOSet,
|
|
transactions []*util.Tx) error {
|
|
// Fetch utxos for all of the transaction ouputs in this block.
|
|
// Typically, there will not be any utxos for any of the outputs.
|
|
fetchSet := make(map[wire.OutPoint]struct{})
|
|
for _, tx := range transactions {
|
|
prevOut := wire.OutPoint{TxID: *tx.ID()}
|
|
for txOutIdx := range tx.MsgTx().TxOut {
|
|
prevOut.Index = uint32(txOutIdx)
|
|
fetchSet[prevOut] = struct{}{}
|
|
}
|
|
}
|
|
|
|
// Duplicate transactions are only allowed if the previous transaction
|
|
// is fully spent.
|
|
for outpoint := range fetchSet {
|
|
utxo, ok := utxoSet.Get(outpoint)
|
|
if ok {
|
|
str := fmt.Sprintf("tried to overwrite transaction %s "+
|
|
"at block height %d that is not fully spent",
|
|
outpoint.TxID, utxo.BlockHeight())
|
|
return ruleError(ErrOverwriteTx, str)
|
|
}
|
|
}
|
|
|
|
return nil
|
|
}
|
|
|
|
// CheckTransactionInputs performs a series of checks on the inputs to a
|
|
// transaction to ensure they are valid. An example of some of the checks
|
|
// include verifying all inputs exist, ensuring the block reward seasoning
|
|
// requirements are met, detecting double spends, validating all values and fees
|
|
// are in the legal range and the total output amount doesn't exceed the input
|
|
// amount. As it checks the inputs, it also calculates the total fees for the
|
|
// transaction and returns that value.
|
|
//
|
|
// NOTE: The transaction MUST have already been sanity checked with the
|
|
// CheckTransactionSanity function prior to calling this function.
|
|
func CheckTransactionInputs(tx *util.Tx, txHeight int32, utxoSet UTXOSet, dagParams *dagconfig.Params, fastAdd bool) (
|
|
txFeeInSatoshi uint64, err error) {
|
|
|
|
// Block reward transactions have no inputs.
|
|
if IsBlockReward(tx) {
|
|
return 0, nil
|
|
}
|
|
|
|
txID := tx.ID()
|
|
var totalSatoshiIn uint64
|
|
for txInIndex, txIn := range tx.MsgTx().TxIn {
|
|
// Ensure the referenced input transaction is available.
|
|
entry, ok := utxoSet.Get(txIn.PreviousOutPoint)
|
|
if !ok {
|
|
str := fmt.Sprintf("output %s referenced from "+
|
|
"transaction %s:%d either does not exist or "+
|
|
"has already been spent", txIn.PreviousOutPoint,
|
|
tx.ID(), txInIndex)
|
|
return 0, ruleError(ErrMissingTxOut, str)
|
|
}
|
|
|
|
if !fastAdd {
|
|
if err = validateBlockRewardMaturity(dagParams, entry, txHeight, txIn); err != nil {
|
|
return 0, err
|
|
}
|
|
}
|
|
|
|
// Ensure the transaction amounts are in range. Each of the
|
|
// output values of the input transactions must not be negative
|
|
// or more than the max allowed per transaction. All amounts in
|
|
// a transaction are in a unit value known as a satoshi. One
|
|
// bitcoin is a quantity of satoshi as defined by the
|
|
// SatoshiPerBitcoin constant.
|
|
originTxSatoshi := entry.Amount()
|
|
if originTxSatoshi > util.MaxSatoshi {
|
|
str := fmt.Sprintf("transaction output value of %s is "+
|
|
"higher than max allowed value of %d",
|
|
util.Amount(originTxSatoshi),
|
|
util.MaxSatoshi)
|
|
return 0, ruleError(ErrBadTxOutValue, str)
|
|
}
|
|
|
|
// The total of all outputs must not be more than the max
|
|
// allowed per transaction. Also, we could potentially overflow
|
|
// the accumulator so check for overflow.
|
|
lastSatoshiIn := totalSatoshiIn
|
|
totalSatoshiIn += originTxSatoshi
|
|
if totalSatoshiIn < lastSatoshiIn ||
|
|
totalSatoshiIn > util.MaxSatoshi {
|
|
str := fmt.Sprintf("total value of all transaction "+
|
|
"inputs is %d which is higher than max "+
|
|
"allowed value of %d", totalSatoshiIn,
|
|
util.MaxSatoshi)
|
|
return 0, ruleError(ErrBadTxOutValue, str)
|
|
}
|
|
}
|
|
|
|
// Calculate the total output amount for this transaction. It is safe
|
|
// to ignore overflow and out of range errors here because those error
|
|
// conditions would have already been caught by checkTransactionSanity.
|
|
var totalSatoshiOut uint64
|
|
for _, txOut := range tx.MsgTx().TxOut {
|
|
totalSatoshiOut += txOut.Value
|
|
}
|
|
|
|
// Ensure the transaction does not spend more than its inputs.
|
|
if totalSatoshiIn < totalSatoshiOut {
|
|
str := fmt.Sprintf("total value of all transaction inputs for "+
|
|
"transaction %s is %d which is less than the amount "+
|
|
"spent of %d", txID, totalSatoshiIn, totalSatoshiOut)
|
|
return 0, ruleError(ErrSpendTooHigh, str)
|
|
}
|
|
|
|
// NOTE: bitcoind checks if the transaction fees are < 0 here, but that
|
|
// is an impossible condition because of the check above that ensures
|
|
// the inputs are >= the outputs.
|
|
txFeeInSatoshi = totalSatoshiIn - totalSatoshiOut
|
|
return txFeeInSatoshi, nil
|
|
}
|
|
|
|
func validateBlockRewardMaturity(dagParams *dagconfig.Params, entry *UTXOEntry, txHeight int32, txIn *wire.TxIn) error {
|
|
// Ensure the transaction is not spending coins which have not
|
|
// yet reached the required block reward maturity.
|
|
if entry.IsBlockReward() {
|
|
originHeight := entry.BlockHeight()
|
|
blocksSincePrev := txHeight - originHeight
|
|
blockRewardMaturity := int32(dagParams.BlockRewardMaturity)
|
|
if blocksSincePrev < blockRewardMaturity {
|
|
str := fmt.Sprintf("tried to spend block reward "+
|
|
"transaction output %s from height %d "+
|
|
"at height %d before required maturity "+
|
|
"of %d blocks", txIn.PreviousOutPoint,
|
|
originHeight, txHeight,
|
|
blockRewardMaturity)
|
|
return ruleError(ErrImmatureSpend, str)
|
|
}
|
|
}
|
|
return nil
|
|
}
|
|
|
|
// checkConnectToPastUTXO performs several checks to confirm connecting the passed
|
|
// block to the DAG represented by the passed view does not violate any rules.
|
|
//
|
|
// An example of some of the checks performed are ensuring connecting the block
|
|
// would not cause any duplicate transaction hashes for old transactions that
|
|
// aren't already fully spent, double spends, exceeding the maximum allowed
|
|
// signature operations per block, invalid values in relation to the expected
|
|
// block subsidy, or fail transaction script validation.
|
|
//
|
|
// It also returns the feeAccumulator for this block.
|
|
//
|
|
// This function MUST be called with the dag state lock held (for writes).
|
|
func (dag *BlockDAG) checkConnectToPastUTXO(block *blockNode, pastUTXO UTXOSet,
|
|
transactions []*util.Tx, fastAdd bool) (compactFeeData, error) {
|
|
|
|
if !fastAdd {
|
|
err := ensureNoDuplicateTx(block, pastUTXO, transactions)
|
|
if err != nil {
|
|
return nil, err
|
|
}
|
|
|
|
if err := validateSigopsCount(pastUTXO, transactions); err != nil {
|
|
return nil, err
|
|
}
|
|
}
|
|
|
|
// Perform several checks on the inputs for each transaction. Also
|
|
// accumulate the total fees. This could technically be combined with
|
|
// the loop above instead of running another loop over the transactions,
|
|
// but by separating it we can avoid running the more expensive (though
|
|
// still relatively cheap as compared to running the scripts) checks
|
|
// against all the inputs when the signature operations are out of
|
|
// bounds.
|
|
// In addition - add all fees into a fee accumulator, to be stored and checked
|
|
// when validating descendants' fee transactions.
|
|
var totalFees uint64
|
|
compactFeeFactory := newCompactFeeFactory()
|
|
|
|
var feeData compactFeeData
|
|
for _, tx := range transactions {
|
|
txFee, err := CheckTransactionInputs(tx, block.height, pastUTXO,
|
|
dag.dagParams, fastAdd)
|
|
if err != nil {
|
|
return nil, err
|
|
}
|
|
|
|
// Sum the total fees and ensure we don't overflow the
|
|
// accumulator.
|
|
lastTotalFees := totalFees
|
|
totalFees += txFee
|
|
if totalFees < lastTotalFees {
|
|
return nil, ruleError(ErrBadFees, "total fees for block "+
|
|
"overflows accumulator")
|
|
}
|
|
|
|
err = compactFeeFactory.add(txFee)
|
|
if err != nil {
|
|
return nil, fmt.Errorf("Error adding tx %s fee to feeAccumulatorWriter: %s", tx.ID(), err)
|
|
}
|
|
feeData, err = compactFeeFactory.data()
|
|
if err != nil {
|
|
return nil, fmt.Errorf("Error getting bytes of fee data: %s", err)
|
|
}
|
|
}
|
|
|
|
if !fastAdd {
|
|
// The total output values of the coinbase transaction must not exceed
|
|
// the expected subsidy value plus total transaction fees gained from
|
|
// mining the block. It is safe to ignore overflow and out of range
|
|
// errors here because those error conditions would have already been
|
|
// caught by checkTransactionSanity.
|
|
var totalSatoshiOut uint64
|
|
for _, txOut := range transactions[0].MsgTx().TxOut {
|
|
totalSatoshiOut += txOut.Value
|
|
}
|
|
expectedSatoshiOut := CalcBlockSubsidy(block.height, dag.dagParams)
|
|
if totalSatoshiOut > expectedSatoshiOut {
|
|
str := fmt.Sprintf("coinbase transaction for block pays %d "+
|
|
"which is more than expected value of %d",
|
|
totalSatoshiOut, expectedSatoshiOut)
|
|
return nil, ruleError(ErrBadCoinbaseValue, str)
|
|
}
|
|
|
|
// Don't run scripts if this node is before the latest known good
|
|
// checkpoint since the validity is verified via the checkpoints (all
|
|
// transactions are included in the merkle root hash and any changes
|
|
// will therefore be detected by the next checkpoint). This is a huge
|
|
// optimization because running the scripts is the most time consuming
|
|
// portion of block handling.
|
|
checkpoint := dag.LatestCheckpoint()
|
|
runScripts := true
|
|
if checkpoint != nil && block.height <= checkpoint.Height {
|
|
runScripts = false
|
|
}
|
|
|
|
scriptFlags := txscript.ScriptNoFlags
|
|
|
|
// We obtain the MTP of the *previous* block (unless it's genesis block)
|
|
// in order to determine if transactions in the current block are final.
|
|
medianTime := block.Header().Timestamp
|
|
if !block.isGenesis() {
|
|
medianTime = block.selectedParent.PastMedianTime()
|
|
}
|
|
|
|
// We also enforce the relative sequence number based
|
|
// lock-times within the inputs of all transactions in this
|
|
// candidate block.
|
|
for _, tx := range transactions {
|
|
// A transaction can only be included within a block
|
|
// once the sequence locks of *all* its inputs are
|
|
// active.
|
|
sequenceLock, err := dag.calcSequenceLock(block, pastUTXO, tx, false)
|
|
if err != nil {
|
|
return nil, err
|
|
}
|
|
if !SequenceLockActive(sequenceLock, block.height,
|
|
medianTime) {
|
|
str := fmt.Sprintf("block contains " +
|
|
"transaction whose input sequence " +
|
|
"locks are not met")
|
|
return nil, ruleError(ErrUnfinalizedTx, str)
|
|
}
|
|
}
|
|
|
|
// Now that the inexpensive checks are done and have passed, verify the
|
|
// transactions are actually allowed to spend the coins by running the
|
|
// expensive ECDSA signature check scripts. Doing this last helps
|
|
// prevent CPU exhaustion attacks.
|
|
if runScripts {
|
|
err := checkBlockScripts(block, pastUTXO, transactions, scriptFlags, dag.sigCache)
|
|
if err != nil {
|
|
return nil, err
|
|
}
|
|
}
|
|
|
|
}
|
|
return feeData, nil
|
|
}
|
|
|
|
func validateSigopsCount(pastUTXO UTXOSet, transactions []*util.Tx) error {
|
|
// The number of signature operations must be less than the maximum
|
|
// allowed per block. Note that the preliminary sanity checks on a
|
|
// block also include a check similar to this one, but this check
|
|
// expands the count to include a precise count of pay-to-script-hash
|
|
// signature operations in each of the input transaction public key
|
|
// scripts.
|
|
totalSigOps := 0
|
|
for i, tx := range transactions {
|
|
numsigOps := CountSigOps(tx)
|
|
// Since the first transaction has already been verified to be a
|
|
// coinbase transaction, and the second transaction has already
|
|
// been verified to be a fee transaction, use i < 2 as an
|
|
// optimization for the flag to countP2SHSigOps for whether or
|
|
// not the transaction is a block reward transaction rather than
|
|
// having to do a full coinbase and fee transaction check again.
|
|
numP2SHSigOps, err := CountP2SHSigOps(tx, i < 2, pastUTXO)
|
|
if err != nil {
|
|
return err
|
|
}
|
|
numsigOps += numP2SHSigOps
|
|
|
|
// Check for overflow or going over the limits. We have to do
|
|
// this on every loop iteration to avoid overflow.
|
|
lastSigops := totalSigOps
|
|
totalSigOps += numsigOps
|
|
if totalSigOps < lastSigops || totalSigOps > MaxSigOpsPerBlock {
|
|
str := fmt.Sprintf("block contains too many "+
|
|
"signature operations - got %d, max %d",
|
|
totalSigOps, MaxSigOpsPerBlock)
|
|
return ruleError(ErrTooManySigOps, str)
|
|
}
|
|
}
|
|
|
|
return nil
|
|
}
|
|
|
|
// countSpentOutputs returns the number of utxos the passed block spends.
|
|
func countSpentOutputs(block *util.Block) int {
|
|
// Exclude the block reward transactions since they can't spend anything.
|
|
var numSpent int
|
|
for _, tx := range block.Transactions()[1:] {
|
|
if !IsFeeTransaction(tx) {
|
|
numSpent += len(tx.MsgTx().TxIn)
|
|
}
|
|
}
|
|
return numSpent
|
|
}
|
|
|
|
// CheckConnectBlockTemplate fully validates that connecting the passed block to
|
|
// the DAG does not violate any consensus rules, aside from the proof of
|
|
// work requirement. The block must connect to the current tip of the main dag.
|
|
//
|
|
// This function is safe for concurrent access.
|
|
func (dag *BlockDAG) CheckConnectBlockTemplate(block *util.Block) error {
|
|
dag.dagLock.Lock()
|
|
defer dag.dagLock.Unlock()
|
|
|
|
// Skip the proof of work check as this is just a block template.
|
|
flags := BFNoPoWCheck
|
|
|
|
// This only checks whether the block can be connected to the tip of the
|
|
// current dag.
|
|
tips := dag.virtual.tips()
|
|
header := block.MsgBlock().Header
|
|
parentHashes := header.ParentHashes
|
|
if !tips.hashesEqual(parentHashes) {
|
|
str := fmt.Sprintf("parent blocks must be the currents tips %s, "+
|
|
"instead got %v", tips, parentHashes)
|
|
return ruleError(ErrParentBlockNotCurrentTips, str)
|
|
}
|
|
|
|
err := dag.checkBlockSanity(block, flags)
|
|
if err != nil {
|
|
return err
|
|
}
|
|
|
|
parents, err := lookupParentNodes(block, dag)
|
|
if err != nil {
|
|
return err
|
|
}
|
|
|
|
err = dag.checkBlockContext(block, parents, dag.selectedTip(), flags)
|
|
if err != nil {
|
|
return err
|
|
}
|
|
|
|
_, err = dag.checkConnectToPastUTXO(newBlockNode(&header, dag.virtual.tips(), dag.dagParams.K),
|
|
dag.UTXOSet(), block.Transactions(), false)
|
|
|
|
return err
|
|
}
|