The Bitcoin Lightning Network:
Scalable Off-Chain Instant Payments
Joseph Poon

Thaddeus Dryja

joseph@lightning.network

rx@awsomnet.org

January 14, 2016
DRAFT Version 0.5.9.2

Abstract
The bitcoin protocol can encompass the global financial transaction volume in all electronic payment systems today, without a single
custodial third party holding funds or requiring participants to haveanything more than a computer using a broadband connection. A
decentralized system is proposed whereby transactions are sent overa network of micropayment channels (a.k.a. payment channels ortransaction channels) whose transfer of value occurs off-blockchain.
If Bitcoin transactions can be signed with a new sighash type that
addresses malleability, these transfers may occur between untrusted
parties along the transfer route by contracts which, in the event of uncooperative or hostile participants, are enforceable via broadcast overthe bitcoin blockchain in the event of uncooperative or hostile participants, through a series of decrementing timelocks.

1

The Bitcoin Blockchain Scalability Problem

The Bitcoin[1] blockchain holds great promise for distributed ledgers, but
the blockchain as a payment platform, by itself, cannot cover the world’scommerce anytime in the near future. The blockchain is a gossip protocol
whereby all state modifications to the ledger are broadcast to all participants. It is through this “gossip protocol” that consensus of the state,everyone’s balances, is agreed upon. If each node in the bitcoin network
must know about every single transaction that occurs globally, that may
1

create a significant drag on the ability of the network to encompass all
global financial transactions. It would instead be desirable to encompass alltransactions in a way that doesn’t sacrifice the decentralization and security
that the network provides.
The payment network Visa achieved 47,000 peak transactions per second (tps) on its network during the 2013 holidays[2], and currently averages
hundreds of millions per day. Currently, Bitcoin supports less than 7 transactions per second with a 1 megabyte block limit. If we use an average of 300
bytes per bitcoin transaction and assumed unlimited block sizes, an equivalent capacity to peak Visa transaction volume of 47,000/tps would be nearly
8 gigabytes per Bitcoin block, every ten minutes on average. Continuously,that would be over 400 terabytes of data per year.
Clearly, achieving Visa-like capacity on the Bitcoin network isn’t feasible today. No home computer in the world can operate with that kind of
bandwidth and storage. If Bitcoin is to replace all electronic payments inthe future, and not just Visa, it would result in outright collapse of the Bitcoin network, or at best, extreme centralization of Bitcoin nodes and miners
to the only ones who could afford it. This centralization would then defeat
aspects of network decentralization that make Bitcoin secure, as the ability for entities to validate the chain is what allows Bitcoin to ensure ledger
accuracy and security.
Having fewer validators due to larger blocks not only implies fewer
individuals ensuring ledger accuracy, but also results in fewer entities thatwould be able to validate the blockchain as part of the mining process,which results in encouraging miner centralization. Extremely large blocks,
for example in the above case of 8 gigabytes every 10 minutes on average,
would imply that only a few parties would be able to do block validation.
This creates a great possibility that entities will end up trusting centralized
parties. Having privileged, trusted parties creates a social trap whereby
the central party will not act in the interest of an individual (principalagent problem), e.g. rentierism by charging higher fees to mitigate the
incentive to act dishonestly. In extreme cases, this manifests as individuals
sending funds to centralized trusted custodians who have full custody ofcustomers’ funds. Such arrangements, as are common today, create severecounterparty risk. A prerequisite to prevent that kind of centralization fromoccurring would require the ability for bitcoin to be validated by a single
2

consumer-level computer on a home broadband connection. By ensuringthat full validation can occur cheaply, Bitcoin nodes and miners will be able
to prevent extreme centralization and trust, which ensures extremely lowtransaction fees.
While it is possible that Moore’s Law will continue indefinitely, andthe computational capacity for nodes to cost-effectively compute multigigabyte blocks may exist in the future, it is not a certainty.
To achieve much higher than 47,000 transactions per second using
Bitcoin requires conducting transactions off the Bitcoin blockchain itself. It
would be even better if the bitcoin network supported a near-unlimited number of transactions per second with extremely low fees for micropayments.
Many micropayments can be sent sequentially between two parties to enable any size of payments. Micropayments would enable unbunding, lesstrust and commodification of services, such as payments for per-megabyteinternet service. To be able to achieve these micropayment use cases, however, would require severely reducing the amount of transactions that end
up being broadcast on the global Bitcoin blockchain.
While it is possible to scale at a small level, it is absolutely not possible
to handle a large amount of micropayments on the network or to encompass
all global transactions. For bitcoin to succeed, it requires confidence that if
it were to become extremely popular, its current advantages stemming fromdecentralization will continue to exist. In order for people today to believethat Bitcoin will work tomorrow, Bitcoin needs to resolve the issue of block
size centralization effects; large blocks implicitly create trusted custodiansand significantly higher fees.

2

A Network of Micropayment Channels Can
Solve Scalability“If a tree falls in the forest and no one is around to hear it, doesit make a sound?”

The above quote questions the relevance of unobserved events —if
nobody hears the tree fall, whether it made a sound or not is of no consequence. Similarly, in the blockchain, if only two participants care about aneveryday recurring transaction, it’s not necessary for all other nodes in the3bitcoin network to know about that transaction. It is instead preferable to
only have the bare minimum of information on the blockchain. By deferring telling the entire world about every transaction, doing net settlementof their relationship at a later date enables Bitcoin users to conduct manytransactions without bloating up the blockchain or creating trust in a centralized counterparty. An effectively trustless structure can be achieved byusing time locks as a component to global consensus.
Currently the solution to micropayments and scalability is to offload
the transactions to a custodian, whereby one is trusting third party custodians to hold one’s coins and to update balances with other parties. Trusting
third parties to hold all of one’s funds creates counterparty risk and transaction costs.
Instead, using a network of these micropayment channels, Bitcoin
can scale to billions of transactions per day with the computational power
available on a modern desktop computer today. Sending many payments
inside a given micropayment channel enables one to send large amountsof funds to another party in a decentralized manner. These channels are
not a separate trusted network on top of bitcoin. They are real bitcointransactions.
Micropayment channels[3][4] create a relationship between two parties to perpetually update balances, deferring what is broadcast to theblockchain in a single transaction netting out the total balance between
those two parties. This permits the financial relationships between two parties to be trustlessly deferred to a later date, without risk of counterparty
default. Micropayment channels use real bitcoin transactions, only electing
to defer the broadcast to the blockchain in such a way that both parties
can guarantee their current balance on the blockchain; this is not a trusted
overlay network —payments in micropayment channels are real bitcoin communicated and exchanged off-chain.

2.1

Micropayment Channels Do Not Require Trust

Like the age-old question of whether the tree falling in the woods makes asound, if all parties agree that the tree fell at 2:45 in the afternoon, then thetree really did fall at 2:45 in the afternoon. Similarly, if both counterparties
agree that the current balance inside a channel is 0.07 BTC to Alice and 0.03

4

BTC to Bob, then that’s the true balance. However, without cryptography,
an interesting problem is created: If one’s counterparty disagrees about thecurrent balance of funds (or time the tree fell), then it is one’s word against
another. Without cryptographic signatures, the blockchain will not know
who owns what.
If the balance in the channel is 0.05 BTC to Alice and 0.05 BTC to
Bob, and the balance after a transaction is 0.07 BTC to Alice and 0.03
BTC to Bob, the network needs to know which set of balances is correct.
Blockchain transactions solve this problem by using the blockchain ledger
as a timestamping system. At the same time, it is desirable to create a system which does not actively use this timestamping system unless absolutely
necessary, as it can become costly to the network.
Instead, both parties can commit to signing a transaction and not
broadcasting this transaction. So if Alice and Bob commit funds into a 2of-2 multisignature address (where it requires consent from both parties tocreate spends), they can agree on the current balance state. Alice and Bob
can agree to create a refund from that 2-of-2 transaction to themselves, 0.05
BTC to each. This refund is not broadcast on the blockchain. Either party
may do so, but they may elect to instead hold onto that transaction, knowingthat they are able to redeem funds whenever they feel comfortable doing so.
By deferring broadcast of this transaction, they may elect to change thisbalance at a future date.
To update the balance, both parties create a new spend from the2-of-2 multisignature address, for example 0.07 to Alice and 0.03 to Bob.
Without proper design, though, there is the timestamping problem of notknowing which spend is correct: the new spend or the original refund.
The restriction on timestamping and dates, however, is not as complex as full ordering of all transactions as in the bitcoin blockchain. In thecase of micropayment channels, only two states are required: the current
correct balance, and any old deprecated balances. There would only be asingle correct current balance, and possibly many old balances which are
deprecated.
Therefore, it is possible in bitcoin to devise a bitcoin script whereby
all old transactions are invalidated, and only the new transaction is valid.
Invalidation is enforced by a bitcoin output script and dependent transactions which force the other party to give all their funds to the channel
5counterparty. By taking all funds as a penalty to give to the other, all oldtransactions are thereby invalidated.
This invalidation process can exist through a process of channel consensus where if both parties agree on current ledger states (and building newstates), then the real balance gets updated. The balance is reflected on theblockchain only when a single party disagrees. Conceptually, this system is
not an independent overlay network; it is more a deferral of state on thecurrent system, as the enforcement is still occurring on the blockchain itself(albeit deferred to future dates and transactions).

2.2

A Network of Channels

Thus, micropayment channels only create a relationship between two parties.
Requiring everyone to create channels with everyone else does not solve thescalability problem. Bitcoin scalability can be achieved using a large networkof micropayment channels.
If we presume a large network of channels on the Bitcoin blockchain,
and all Bitcoin users are participating on this graph by having at least one
channel open on the Bitcoin blockchain, it is possible to create a near-infinite
amount of transactions inside this network. The only transactions that arebroadcasted on the Bitcoin blockchain prematurely are with uncooperative
channel counterparties.
By encumbering the Bitcoin transaction outputs with a hashlock andtimelock, the channel counterparty will be unable to outright steal funds
and Bitcoins can be exchanged without outright counterparty theft. Further, by using staggered timeouts, it’s possible to send funds via multiple
intermediaries in a network without the risk of intermediary theft of funds.

3

Bidirectional Payment Channels

Micropayment channels permit a simple deferral of a transaction state to
be broadcast at a later time. The contracts are enforced by creating a
responsibility for one party to broadcast transactions before or after certain
dates. If the blockchain is a decentralized timestamping system, it is possible
to use clocks as a component of decentralized consensus[5] to determine data
validity, as well as present states as a method to order events[6].

6By creating timeframes where certain states can be broadcast andlater invalidated, it is possible to create complex contracts using bitcointransaction scripts. There has been prior work for Hub-and-Spoke Micropayment Channels[7][8][9] (and trusted payment channel networks[10][11])looking at building a hub-and-spoke network today. However, Lightning
Network’s bidirectional micropayment channel requires the malleability softfork described in Appendix A to enable near-infinite scalability while mitigating risks of intermediate node default.
By chaining together multiple micropayment channels, it is possible
to create a network of transaction paths. Paths can be routed using a BGPlike system, and the sender may designate a particular path to the recipient.
The output scripts are encumbered by a hash, which is generated by therecipient. By disclosing the input to that hash, the recipient’s counterparty
will be able to pull funds along the route.

3.1

The Problem of Blame in Channel Creation

In order to participate in this payment network, one must create a micropayment channel with another participant on this network.
3.1.1

Creating an Unsigned Funding Transaction

An initial channel Funding Transaction is created whereby one or both channel counterparties fund the inputs of this transaction. Both parties create
the inputs and outputs for this transaction but do not sign the transaction.
The output for this Funding Transaction is a single 2-of-2 multisignature script with both participants in this channel, henceforth named Aliceand Bob. Both participants do not exchange signatures for the Funding
Transaction until they have created spends from this 2-of-2 output refunding the original amount back to its respective funders. The purpose of not
signing the transaction allows for one to spend from a transaction which
does not yet exist. If Alice and Bob exchange the signatures from the Funding Transaction without being able to broadcast spends from the Funding
Transaction, the funds may be locked up forever if Alice and Bob do notcooperate (or other coin loss may occur through hostage scenarios whereby
one pays for the cooperation from the counterparty).
Alice and Bob both exchange inputs to fund the Funding Transaction7

(to know which inputs are used to determine the total value of the channel),and exchange one key to use to sign with later. This key is used for the
2-of-2 output for the Funding Transaction; both signatures are needed tospend from the Funding Transaction, in other words, both Alice and Bob
need to agree to spend from the Funding Transaction.
3.1.2

Spending from an Unsigned Transaction

The Lightning Network uses a SIGHASH NOINPUT transaction tospend from this 2-of-2 Funding Transaction output, as it is necessary tospend from a transaction for which the signatures are not yet exchanged.
SIGHASH NOINPUT, implemented using a soft-fork, ensures transactions
can be spent from before it is signed by all parties, as transactions would
need to be signed to get a transaction ID without new sighash flags.
Without SIGHASH NOINPUT, Bitcoin transactions cannot be spent frombefore they may be broadcast —it’s as if one could not draft a contract
without paying the other party first. SIGHASH NOINPUT resolves thisproblem. See Appendix A for more information and implementation.
Without SIGHASH NOINPUT, it is not possible to generate a spend
from a transaction without exchanging signatures, since spending the Funding Transaction requires a transaction ID as part of the signature in thechild’s input. A component of the Transaction ID is the parent’s (Funding
Transaction’s) signature, so both parties need to exchange their signatures ofthe parent transaction before the child can be spent. Since one or both parties must know the parent’s signatures to spend from it, that means one orboth parties are able to broadcast the parent (Funding Transaction) before
the child even exists. SIGHASH NOINPUT gets around this by permitting
the child to spend without signing the input. With SIGHASH NOINPUT,
the order of operations are to:
1. Create the parent (Funding Transaction)
2. Create the children (Commitment Transactions and all spends fromthe commitment transactions)
3. Sign the children
4. Exchange the signatures for the children85. Sign the parent
6. Exchange the signatures for the parent
7. Broadcast the parent on the blockchain
One is not able to broadcast the parent (Step 7) until Step 6 is complete. Both parties have not given their signature to spend from the Funding
Transaction until step 6. Further, if one party fails during Step 6, the parent
can either be spent to become the parent transaction or the inputs to theparent transaction can be double-spent (so that this entire transaction path
is invalidated).
3.1.3

Commitment Transactions: Unenforcible Construction

After the unsigned (and unbroadcasted) Funding Transaction has been created, both parties sign and exchange an initial Commitment Transaction.
These Commitment Transactions spends from the 2-of-2 output of the Funding Transaction (parent). However, only the Funding Transaction is broadcast on the blockchain.
Since the Funding Transaction has already entered into theblockchain, and the output is a 2-of-2 multisignature transaction which
requires the agreement of both parties to spend from, Commitment Transactions are used to express the present balance. If only one 2-of-2 signed
Commitment Transaction is exchanged between both parties, then bothparties will be sure that they are able to get their money back after theFunding Transaction enters the blockchain. Both parties do not broadcast
the Commitment Transactions onto the blockchain until they want to closeout the current balance in the channel. They do so by broadcasting thepresent Commitment Transaction.
Commitment Transactions pay out the respective current balances toeach party. A naive (broken) implementation would construct an unbroadcasted transaction whereby there is a 2-of-2 spend from a single transaction
which have two outputs that return all current balances to both channel
counterparties. This will return all funds to the original party when creating an initial Commitment Transaction.

9

Figure 1: A naive broken funding transaction is described in this diagram. The Funding
Transaction (F), designated in green, is broadcast on the blockchain after all other transactions are signed. All other transactions spending from the funding transactions are notyet broadcast, in case the counterparties wish to update their balance. Only the Funding
Transaction is broadcast on the blockchain at this time.

For instance, if Alice and Bob agree to create a Funding Transaction with a single 2-of-2 output worth 1.0 BTC (with 0.5 BTC contribution
from each), they create a Commitment Transaction where there are two 0.5
BTC outputs for Alice and Bob. The Commitment Transactions are signed
first and keys are exchanged so either is able to broadcast the Commitment
Transaction at any time contingent upon the Funding Transaction entering into the blockchain. At this point, the Funding Transaction signatures
can safely be exchanged, as either party is able to redeem their funds bybroadcasting the Commitment Transaction.
This construction breaks, however, when one wishes to update thepresent balance. In order to update the balance, they must update their
Commitment Transaction output values (the Funding Transaction has already entered into the blockchain and cannot be changed).
When both parties agree to a new Commitment Transaction and exchange signatures for the new Commitment Transaction, either Commitment Transactions can be broadcast. As the output from the Funding
Transaction can only be redeemed once, only one of those transactions will
be valid. For instance, if Alice and Bob agree that the balance of the channel
10

is now 0.4 to Alice and 0.6 to Bob, and a new Commitment Transaction iscreated to reflect that, either Commitment Transaction can be broadcast.
In effect, one would be unable to restrict which Commitment Transaction isbroadcast, since both parties have signed and exchanged the signatures for
either balance to be broadcast.

Figure 2: Either of the Commitment Transactions can be broadcast any any time byeither party, only one will successfully spend from the single Funding Transaction. Thiscannot work because one party will not want to broadcast the most recent transaction.

Since either party may broadcast the Commitment Transaction at any
time, the result would be after the new Commitment Transaction is generated, the one who receives less funds has significant incentive to broadcast
the transaction which has greater values for themselves in the Commitment
Transaction outputs. As a result, the channel would be immediately closed
and funds stolen. Therefore, one cannot create payment channels under thismodel.
3.1.4

Commitment Transactions: Ascribing Blame

Since any signed Commitment Transaction may be broadcast on theblockchain, and only one can be successfully broadcast, it is necessary
to prevent old Commitment Transactions from being broadcast. It is
not possible to revoke tens of thousands of transactions in Bitcoin, so analternate method is necessary. Instead of active revocation enforced by
the blockchain, it’s necessary to construct the channel itself in similarmanner to a Fidelity Bond, whereby both parties make commitments, and11

violations of these commitments are enforced by penalties. If one party
violates their agreement, then they will lose all the money in the channel.
For this payment channel, the contract terms are that both parties
commit to broadcasting only the most recent transaction. Any broadcast ofolder transactions will cause a violation of the contract, and all funds are
given to the other party as a penalty.
This can only be enforced if one is able to ascribe blame for broadcasting an old transaction. In order to do so, one must be able to uniquely
identify who broadcast an older transaction. This can be done if each counterparty has a uniquely identifiable Commitment Transaction. Both parties
must sign the inputs to the Commitment Transaction which the other party
is responsible for broadcasting. Since one has a version of the Commitment
Transaction that is signed by the other party, one can only broadcast one’s
own version of the Commitment Transaction.
For the Lightning Network, all spends from the Funding Transaction
output, Commitment Transactions, have two half-signed transactions. One
Commitment Transaction in which Alice signs and gives to Bob (C1b), andanother which Bob signs and gives to Alice (C1a). These two Commitment
Transactions spend from the same output (Funding Transaction), and havedifferent contents; only one can be broadcast on the blockchain, as bothpairs of Commitment Transactions spend from the same Funding Transaction. Either party may broadcast their received Commitment Transaction
by signing their version and including the counterparty’s signature. For example, Bob can broadcast Commitment C1b, since he has already received
the signature for C1b from Alice —he includes Alice’s signature and signs
C1b himself. The transaction will be a valid spend from the Funding Transaction’s 2-of-2 output requiring both Alice and Bob’s signature.

12

Figure 3: Purple boxes are unbroadcasted transactions which only Alice can broadcast.
Blue boxes are unbroadcasted transaction which only Bob can broadcast. Alice can only
broadcast Commitment 1a, Bob can only broadcast Commitment 1b. Only one Commitment Transaction can be spent from the Funding Transaction output. Blame is ascribed,
but either one can still be spent with no penalty.

However, even with this construction, one has only merely allocatedblame. It is not yet possible to enforce this contract on the Bitcoin
blockchain. Bob still trusts Alice not to broadcast an old Commitment
Transaction. At this time, he is only able to prove that Alice has done so
via a half-signed transaction proof.

3.2

Creating a Channel with Contract Revocation

To be able to actually enforce the terms of the contract, it’s necessary toconstruct a Commitment Transaction (along with its spends) where one isable to revoke a transaction. This revocation is achievable by using data
about when a transaction enters into a blockchain and using the maturityof the transaction to determine validation paths.

3.3

Sequence Number Maturity

Mark Freidenbach has proposed that Sequence Numbers can be enforcible via a relative block maturity of the parent transaction via asoft-fork[12]. This would allow some basic ability to ensure some formof relative block confirmation time lock on the spending script. In addi-

13

tion, an additional opcode, OP CHECKSEQUENCEVERIFY[13] (a.k.a.
OP RELATIVECHECKLOCKTIMEVERIFY)[14], would permit further
abilities, including allowing a stop-gap solution before a more permanent
solution for resolving transaction malleability. A future version of thispaper will include proposed solutions.
To summarize, Bitcoin was released with a sequence number which
was only enforced in the mempool of unconfirmed transactions. The original behavior permitted transaction replacement by replacing transactions in
the mempool with newer transactions if they have a higher sequence number. Due to transaction replacement rules, it is not enforced due to denialof service attack risks. It appears as though the intended purpose of thesequence number is to replace unbroadcasted transactions. However, thishigher sequence number replacement behavior is unenforcible. One cannot
be assured that old versions of transactions were replaced in the mempool
and a block contains the most recent version of the transaction. A way to
enforce transaction versions off-chain is via time commitments.
A Revocable Transaction spends from a unique output where thetransaction has a unique type of output script. This parent’s output has
two redemption paths where the first can be redeemed immediately, and thesecond can only be redeemed if the child has a minimum number of confirmations between transactions. This is achieved by making the sequencenumber of the child transaction require a minimum number of confirmations
from the parent. In essence, this new sequence number behavior will only
permit a spend from this output to be valid if the number of blocks between
the output and the redeeming transaction is above a specified block height.
A transaction can be revoked with this sequence number behavior bycreating a restriction with some defined number of blocks defined in thesequence number, which will result in the spend being only valid after theparent has entered into the blockchain for some defined number of blocks.
This creates a structure whereby the parent transaction with this output
becomes a bonded deposit, attesting that there is no revocation. A time
period exists which anyone on the blockchain can refute this attestation bybroadcasting a spend immediately after the transaction is broadcast.
If one wishes to permit revocable transactions with a 1000confirmation delay, the output transaction construction would remain a2-of-2 multisig:
14

2 <A l i c e 1 > <Bob1> 2 OP CHECKMULTISIG
However, the child spending transaction would contain a nSequencevalue of 1000. Since this transaction requires the signature of both counterparties to be valid, both parties include the nSequence number of 1000
as part of the signature. Both parties may, at their discretion, agree tocreate another transaction which supersedes that transaction without any
nSequence number.
This construction, a Revocable Sequence Maturity Contract (RSMC),
creates two paths, with very specific contract terms.
The contract terms are:
1. All parties pay into a contract with an output enforcing this contract
2. Both parties may agree to send funds to some contract, with somewaiting period (1000 confirmations in our example script). This is therevocable output balance.
3. One or both parties may elect to not broadcast (enforce) the payouts
until some future date; either party may redeem the funds after thewaiting period at any time.
4. If neither party has broadcast this transaction (redeemed the funds),
they may revoke the above payouts if and only if both parties agree todo so by placing in a new payout term in a superseding transaction payout. The new transaction payout can be immediately redeemed after
the contract is disclosed to the world (broadcast on the blockchain).
5. In the event that the contract is disclosed and the new payout structure
is not redeemed, the prior revoked payout terms may be redeemed byeither party (so it is the responsibility of either party to enforce the
new terms).
The pre-signed child transaction can be redeemed after the parent
transaction has entered into the blockchain with 1000 confirmations, due tothe child’s nSequence number on the input spending the parent.
In order to revoke this signed child transaction, both parties just agree
to create another child transaction with the default field of the nSequencenumber of MAX INT, which has special behavior permitting spending at
any time.
15

This new signed spend supersedes the revocable spend so long as the
new signed spend enters into the blockchain within 1000 confirmations of
the parent transaction entering into the blockchain. In effect, if Alice andBob agree to monitor the blockchain for incorrect broadcast of Commitment
Transactions, the moment the transaction gets broadcast, they are able tospend using the superseding transaction immediately. In order to broadcast
the revocable spend (deprecated transaction), which spends from the same
output as the superseding transaction, they must wait 1000 confirmations.
So long as both parties watch the blockchain, the revocable spend will neverenter into the transaction if either party prefers the superseding transaction.
Using this construction, anyone could create a transaction, not broadcast the transaction, and then later create incentives to not ever broadcast
that transaction in the future via penalties. This permits participants on the
Bitcoin network to defer many transactions from ever hitting the blockchain.
3.3.1

Timestop

To mitigate a flood of transactions by a malicious attacker requires a credible
threat that the attack will fail.
Greg Maxwell proposed using a timestop to mitigate a malicious floodon the blockchain:
There are many ways to address this [flood risk] which haven’t
been adequately explored yet —for example, the clock can stop
when blocks are full; turning the security risk into more hold-up
delay in the event of a dos attack.[15]This can be mitigated by allowing the miner to specify whether thecurrent (fee paid) mempool is presently being flooded with transactions.
They can enter a “1” value into the last bit in the version number of the blockheader. If the last bit in the block header contains a “1”, then that block will
not count towards the relative height maturity for the nSequence value andthe block is designated as a congested block. There is an uncongested blockheight (which is always lower than the normal block height). This blockheight is used for the nSequence value, which only counts block maturity(confirmations).
A miner can elect to define the block as a congested block or not. The
default code could automatically set the congested block flag as “1” if the16

mempool is above some size and the average fee for that set size is abovesome value. However, a miner has full discretion to change the rules onwhat automatically sets as a congested block, or can select to permanently
set the congestion flag to be permanently on or off. It’s expected that mosthonest miners would use the default behavior defined in their miner and notorganize a 51% attack.
For example, if a parent transaction output is spent by a child with anSequence value of 10, one must wait 10 confirmations before the transaction
becomes valid. However, if the timestop flag has been set, the counting ofconfirmations stops, even with new blocks. If 6 confirmations have elapsed(4 more are necessary for the transaction to be valid), and the timestop
block has been set on the 7th block, that block does not count towards thenSequence requirement of 10 confirmations; the child is still at 6 blocks forthe relative confirmation value. Functionally, this will be stored as somekind of auxiliary timestop block height which is used only for tracking thetimestop value. When the timestop bit is set, all transactions using an nSequence value will stop counting until the timestop bit has been unset. This
gives sufficient time and block-space for transactions at the current auxiliary timestop block height to enter into the blockchain, which can prevent
systemic attackers from successfully attacking the system.
However, this requires some kind of flag in the block to designate
whether it is a timestop block. For full SPV compatibility (Simple Payment
Verification; lightweight clients), it is desirable for this to be within the 80byte block header instead of in the coinbase. There are two places which
may be a good place to put in this flag in the block header: in the block
time and in the block version. The block time may not be safe due to thelast bits being used as an entropy source for some ASIC miners, therefore
a bit may need to be consumed for timestop flags. Another option would
be to hardcode timestop activation as a hard consensus rule (e.g. via blocksize), however this may make things less flexible. By setting sane defaults
for timestop rules, these rules can be changed without consensus soft-forks.
If the block version is used as a flag, the contextual information mustmatch the Chain ID used in some merge-mined coins.

173.3.2

Revocable Commitment Transactions

By combining the ascribing of blame as well as the revocable transaction,
one is able to determine when a party is not abiding by the terms of thecontract, and enforce penalties without trusting the counterparty.

Figure 4: The Funding Transaction F, designated in green, is broadcast on the blockchain
after all other transactions are signed. All transactions which only Alice can broadcast arein purple. All transactions which only Bob can broadcast is are blue. Only the Funding
Transaction is broadcast on the blockchain at this time.

The intent of creating a new Commitment Transaction is to invalidate
all old Commitment Transactions when updating the new balance with a
new Commitment Transaction. Invalidation of old transactions can happen
by making an output be a Revocable Sequence Maturity Contract (RSMC).
To invalidate a transaction, a superseding transaction will be signed andexchanged by both parties that gives all funds to the counterparty in theevent an older transaction is incorrectly broadcast. The incorrect broadcast

18

is identified by creating two different Commitment Transactions with thesame final balance outputs, however the payment to oneself is encumberedby an RSMC.
In effect, there are two Commitment Transactions from a single Funding Transaction 2-of-2 outputs. Of these two Commitment Transactions,only one can enter into the blockchain. Each party within a channel has one
version of this contract. So if this is the first Commitment Transaction pair,
Alice’s Commitment Transaction is defined as C1a, and Bob’s Commitment
Transaction is defined as C1b. By broadcasting a Commitment Transaction, one is requesting for the channel to close out and end. The first two
outputs for the Commitment Transaction include a Delivery Transaction(payout) of the present unallocated balance to the channel counterparties.
If Alice broadcasts C1a, one of the output is spendable by D1a, which sends
funds to Bob. For Bob, C1b is spendable by D1b, which sends funds to
Alice. The Delivery Transaction (D1a/D1b) is immediately redeemable andis not encumbered in any way in the event the Commitment Transaction isbroadcast.
For each party’s Commitment Transaction, they are attesting thatthey are broadcasting the most recent Commitment Transaction which theyown. Since they are attesting that this is the current balance, the balance
paid to the counterparty is assumed to be true, since one has no direct
benefit by paying some funds to the counterparty as a penalty.
The balance paid to the person who broadcast the Commitment
Transaction, however, is unverified. The participants on the blockchain
have no idea if the Commitment Transaction is the most recent or not. Ifthey do not broadcast their most recent version, they will be penalized bytaking all the funds in the channel and giving it to the counterparty. Since
their own funds are encumbered in their own RSMC, they will only beable to claim their funds after some set number of confirmations after theCommitment Transaction has been included in a block (in our example,
1000 confirmations). If they do broadcast their most recent Commitment
Transaction, there should be no revocation transaction superseding the
revocable transaction, so they will be able to receive their funds after some
set amount of time (1000 confirmations).
By knowing who broadcast the Commitment Transaction and encumbering one’s own payouts to be locked up for a predefined period of time,19both parties will be able to revoke the Commitment Transaction in the future.
3.3.3

Redeeming Funds from the Channel: Cooperative Counterparties

Either party may redeem the funds from the channel. However, the party
that broadcasts the Commitment Transaction must wait for the predefined
number of confirmations described in the RSMC. The counterparty which
did not broadcast the Commitment Transaction may redeem the funds immediately.
For example, if the Funding Transaction is committed with 1 BTC(half to each counterparty) and Bob broadcasts the most recent Commitment Transaction, C1b, he must wait 1000 confirmations to receive his 0.5
BTC, while Alice can spend 0.5 BTC. For Alice, this transaction is fully
closed if Alice agrees that Bob broadcast the correct Commitment Transaction (C1b).

20

Figure 5: When Bob broadcasts C1b, Alice can immediately redeem her portion. Bob
must wait 1000 confirmations. When the block is immediately broadcast, it is in thisstate. Transactions in green are transactions which are committed into the blockchain.

After the Commitment Transaction has been in the blockchain for1000 blocks, Bob can then broadcast the Revocable Delivery transaction.
He must wait 1000 blocks to prove he has not revoked this Commitment
Transaction (C1b). After 1000 blocks, the Revocable Delivery transaction
will be able to be included in a block. If a party attempt to include the
Revocable Delivery transaction in a block before 1000 confirmations, thetransaction will be invalid up until after 1000 confirmations have passed (atwhich point it will become valid if the output has not yet been redeemed).

21

Figure 6: Alice agrees that Bob broadcast the correct Commitment Transaction and1000 confirmations have passed. Bob then is able to broadcast the Revocable Delivery(RD1b) transaction on the blockchain.

After Bob broadcasts the Revocable Delivery transaction, the channel
is fully closed for both Alice and Bob, everyone has received the funds which
they both agree are the current balance they each own in the channel.
If it was instead Alice who broadcast the Commitment Transaction(C1a), she is the one who must wait 1000 confirmations instead of Bob.
3.3.4

Creating a new Commitment Transaction and Revoking
Prior Commitments

While each party may close out the most recent Commitment Transaction
at any time, they may also elect to create a new Commitment Transaction
and invalidate the old one.
Suppose Alice and Bob now want to update their current balancesfrom 0.5 BTC each refunded to 0.6 BTC for Bob and 0.4 BTC for Alice.

22

When they both agree to do so, they generate a new pair of Commitment
Transactions.

Figure 7: Four possible transactions can exist, a pair with the old commitments, andanother pair with the new commitments. Each party inside the channel can only broadcast
half of the total commitments (two each). There is no explicit enforcement preventing any
particular Commitment being broadcast other than penalty spends, as they are all valid
unbroadcasted spends. The Revocable Commitment still exists with the C1a/C1b pair,
but are not displayed for brevity.

When a new pair of Commitment Transactions (C2a/C2b) is agreed
upon, both parties will sign and exchange signatures for the new Commitment Transaction, then invalidate the old Commitment Transaction. This
invalidation occurs by having both parties sign a Breach Remedy Transaction (BR1), which supersedes the Revocable Delivery Transaction (RD1).
Each party hands to the other a half-signed revocation (BR1) from their own
Revocable Delivery (RD1), which is a spend from the Commitment Transaction. The Breach Remedy Transaction will send all coins to the counterparty
within the current balance of the channel. For example, if Alice and Bob
both generate a new pair of Commitment Transactions (C2a/C2b) and invalidate prior commitments (C1a/C1b), and later Bob incorrectly broadcasts
C1b on the blockchain, Alice can take all of Bob’s money from the channel.
Alice can do this because Bob has proved to Alice via penalty that he will
never broadcast C1b, since the moment he broadcasts C1b, Alice is able totake all of Bob’s money in the channel. In effect, by constructing a Breach23

Remedy transaction for the counterparty, one has attested that one will not
be broadcasting any prior commitments. The counterparty can accept this,because they will get all the money in the channel when this agreement isviolated.

Figure 8: When C2a and C2b exist, both parties exchange Breach Remedy transactions.
Both parties now have explicit economic incentive to avoid broadcasting old Commitment
Transactions (C1a/C1b). If either party wishes to close out the channel, they will only use
C2a (Alice) or C2b (Bob). If Alice broadcasts C1a, all her money will go to Bob. If Bob
broadcasts C1b, all his money will go to Alice. See previous figure for C2a/C2b outputs.

Due to this fact, one will likely delete all prior Commitment Transactions when a Breach Remedy Transaction has been passed to the counterparty. If one broadcasts an incorrect (deprecated and invalidated Commitment Transaction), all the money will go to one’s counterparty. For example,
if Bob broadcasts C1b, so long as Alice watches the blockchain within thepredefined number of blocks (in this case, 1000 blocks), Alice will be able
to take all the money in this channel by broadcasting RD1b. Even if the24

present balance of the Commitment state (C2a/C2b) is 0.4 BTC to Aliceand 0.6 BTC to Bob, because Bob violated the terms of the contract, all themoney goes to Alice as a penalty. Functionally, the Revocable Transaction
acts as a proof to the blockchain that Bob has violated the terms in thechannel and this is programatically adjudicated by the blockchain.

Figure 9: Transactions in green are committed to the blockchain. Bob incorrectly broadcasts C1b (only Bob is able to broadcast C1b/C2b). Because both agreed that the current
state is the C2a/C2b Commitment pair, and have attested to each party that old commitments are invalidated via Breach Remedy Transactions, Alice is able to broadcast BR1b
and take all the money in the channel, provided she does it within 1000 blocks after C1b
is broadcast.

However, if Alice does not broadcast BR1b within 1000 blocks, Bob
may be able to steal some money, since his Revocable Delivery Transaction (RD1b) becomes valid after 1000 blocks. When an incorrect Commitment Transaction is broadcast, only the Breach Remedy Transaction canbe broadcast for 1000 blocks (or whatever number of confirmations both25

parties agree to). After 1000 block confirmations, both the Breach Remedy(BR1b) and Revocable Delivery Transactions (RD1b) are able to be broadcast at any time. Breach Remedy transactions only have exclusivity within
this predefined time period, and any time after of that is functionally an
expiration of the statute of limitations —according to Bitcoin blockchain
consensus, the time for dispute has ended.
For this reason, one should periodically monitor the blockchain to see
if one’s counterparty has broadcast an invalidated Commitment Transaction,
or delegate a third party to do so. A third party can be delegated by only
giving the Breach Remedy transaction to this third party. They can be
incentivized to watch the blockchain broadcast such a transaction in theevent of counterparty maliciousness by giving these third parties some feein the output. Since the third party is only able to take action when the
counterparty is acting maliciously, this third party does not have any power
to force close of the channel.
3.3.5

Process for Creating Revocable Commitment Transactions

To create revocable Commitment Transactions, it requires proper construction of the channel from the beginning, and only signing transactions which
may be broadcast at any time in the future, while ensuring that one will
not lose out due to uncooperative or malicious counterparties. This requires determining which public key to use for new commitments, as using SIGHASH NOINPUT requires using unique keys for each Commitment
Transaction RSMC (and HTLC) output. We use P to designate pubkeys
and K to designate the corresponding private key used to sign.
When generating the first Commitment Transaction, Alice and Bob
agree to create a multisig output from a Funding Transaction with a single
multisig(PAliceF , PBobF ) output, funded with 0.5 BTC from Alice and Bob
for a total of 1 BTC. This output is a Pay to Script Hash[16] transaction,
which requires both Alice and Bob to both agree to spend from the Funding
Transaction. They do not yet make the Funding Transaction (F) spendable.
Additionally, PAliceF and PBobF are only used for the Funding Transaction,
they are not used for anything else.
Since the Delivery transaction is just a P2PKH output (bitcoin addresses beginning with 1) or P2SH transaction (commonly recognized as addresses beginning with the 3) which the counterparties designate beforehand,26this can be generated as an output of PAliceD and PBobD . For simplicity,
these output addresses will remain the same throughout the channel, since
its funds are fully controlled by its designated recipient after the Commitment Transaction enters the blockchain. If desired, but not necessary, bothparties may update and change PAliceD and PBobD for future Commitment
Transactions.
Both parties exchange pubkeys they intend to use for the RSMC (andHTLC described in future sections) for the Commitment Transaction. Eachset of Commitment Transactions use their own public keys and are notever reused. Both parties may already know all future pubkeys by using
a BIP 0032[17] HD Wallet construction by exchanging Master Public Keys
during channel construction. If they wish to generate a new Commitment
Transaction pair C2a/C2b, they use multisig(PAliceRSM C2 , PBobRSM C2 ) for
the RSMC output.
After both parties know the output values from the Commitment
Transactions, both parties create the pair of Commitment Transactions,e.g. C2a/C2b, but do not exchange signatures for the Commitment Transactions. They both sign the Revocable Delivery transaction (RD2a/RD2b)
and exchange the signatures. Bob signs RD1a and gives it to Alice(using KBobRSM C2 ), while Alice signs RD1b and gives it to Bob (using
KAliceRSM C2 ).
When both parties have the Revocable Delivery transaction, they exchange signatures for the Commitment Transactions. Bob signs C1a using
KBobF and gives it to Alice, and Alice signs C1b using KAliceF and gives it
to Bob.
At this point, the prior Commitment Transaction as well as the new
Commitment Transaction can be broadcast; both C1a/C1b and C2a/C2b
are valid. (Note that Commitments older than the prior Commitment areinvalidated via penalties.) In order to invalidate C1a and C1b, both parties
exchange Breach Remedy Transaction (BR1a/BR1b) signatures for the priorcommitment C1a/C1b. Alice sends BR1a to Bob using KAliceRSM C1 , andBob sends BR1b to Alice using KBobRSM C1 . When both Breach Remedy
signatures have been exchanged, the channel state is now at the current
Commitment C2a/C2b and the balances are now committed.
However, instead of disclosing the BR1a/BR1b signatures, it’s also
possible to just disclose the private keys to the counterparty. This is more27

effective as described later in the key storage section. One can disclose theprivate keys used in one’s own Commitment Transaction. For example, if
Bob wishes to invalidate C1b, he sends his private keys used in C1b to Alice(he does NOT disclose his keys used in C1a, as that would permit cointheft). Similarly, Alice discloses all her private key outputs in C1a to Bob
to invalidate C1a.
If Bob incorrectly broadcasts C1b, then because Alice has all theprivate keys used in the outputs of C1b, she can take the money. However,
only Bob is able to broadcast C1b. To prevent this coin theft risk, Bob
should destroy all old Commitment Transactions.

3.4

Cooperatively Closing Out a Channel

Both parties are able to send as many payments to their counterparty as
they wish, as long as they have funds available in the channel, knowingthat in the event of disagreements they can broadcast to the blockchain thecurrent state at any time.
In the vast majority of cases, all the outputs from the Funding Transaction will never be broadcast on the blockchain. They are just there incase the other party is non-cooperative, much like how a contract is rarely
enforced in the courts. A proven ability for the contract to be enforced in a
deterministic manner is sufficient incentive for both parties to act honestly.
When either party wishes to close out a channel cooperatively, they
will be able to do so by contacting the other party and spending fromthe Funding Transaction with an output of the most current Commitment
Transaction directly with no script encumbering conditions. No further payments may occur in the channel.

28

Figure 10: If both counterparties are cooperative, they take the balances in the current Commitment Transaction and spend from the Funding Transaction with a Exercise
Settlement Transaction (ES). If the most recent Commitment Transaction gets broadcast
instead, the payout (less fees) will be the same.

The purpose of closing out cooperatively is to reduce the numberof transactions that occur on the blockchain and both parties will be able
to receive their funds immediately (instead of one party waiting for the
Revocation Delivery transaction to become valid).
Channels may remain in perpetuity until they decide to cooperatively
close out the transaction, or when one party does not cooperate with anotherand the channel gets closed out and enforced on the blockchain.

3.5

Bidirectional Channel Implications and Summary

By ensuring channels can update only with the consent of both parties, it
is possible to construct channels which perpetually exist in the blockchain.
Both parties can update the balance inside the channel with whatever output
balances they wish, so long as it’s equal or less than the total funds committed inside the Funding Transaction; balances can move in both directions.
If one party becomes malicious, either party may immediately close out thechannel and broadcast the most current state to the blockchain. By usinga fidelity bond construction (Revocable Delivery Transactions), if a party
violates the terms of the channel, the funds will be sent to the counterparty,

29

provided the proof of violation (Breach Remedy Transaction) is entered into
the blockchain in a timely manner. If both parties are cooperative, the channel can remain open indefinitely, possibly for many years.
This type of construction is only possible because adjudication occurs
programatically over the blockchain as part of the Bitcoin consensus, so
one does not need to trust the other party. As a result, one’s channel
counterparty does not possess full custody or control of the funds.

4

Hashed Timelock Contract (HTLC)

A bidirectional payment channel only permits secure transfer of funds insidea channel. To be able to construct secure transfers using a network ofchannels across multiple hops to the final destination requires an additional
construction, a Hashed Timelock Contract (HTLC).
The purpose of an HTLC is to allow for global state across multiple
nodes via hashes. This global state is ensured by time commitments andtime-based unencumbering of resources via disclosure of preimages. Transactional “locking” occurs globally via commitments, at any point in time asingle participant is responsible for disclosing to the next participant whether
they have knowledge of the preimage R. This construction does not require
custodial trust in one’s channel counterparty, nor any other participant in
the network.
In order to achieve this, an HTLC must be able to create certaintransactions which are only valid after a certain date, using nLockTime, as
well as information disclosure to one’s channel counterparty. Additionally,
this data must be revocable, as one must be able to undo an HTLC.
An HTLC is also a channel contract with one’s counterparty which isenforcible via the blockchain. The counterparties in a channel agree to thefollowing terms for a Hashed Timelock Contract:
1. If Bob can produce to Alice an unknown 20-byte random input data
R from a known hash H, within three days, then Alice will settle thecontract by paying Bob 0.1 BTC.
2. If three days have elapsed, then the above clause is null and void andthe clearing process is invalidated, both parties must not attempt tosettle and claim payment after three days.
30

3. Either party may (and should) pay out according to the terms of thiscontract in any method of the participants choosing and close out thiscontract early so long as both participants in this contract agree.
4. Violation of the above terms will incur a maximum penalty of the funds
locked up in this contract, to be paid to the non-violating counterparty
as a fidelity bond.
For clarity of examples, we use days for HTLCs and block height for
RSMCs. In reality, the HTLC should also be defined as a block height (e.g.
3 days is equivalent to 432 blocks).
In effect, one desires to construct a payment which is contingent uponknowledge of R by the recipient within a certain timeframe. After thistimeframe, the funds are refunded back to the sender.
Similar to RSMCs, these contract terms are programatically enforcedon the Bitoin blockchain and do not require trust in the counterparty toadhere to the contract terms, as all violations are penalized via unilaterally
enforced fidelity bonds, which are constructed using penalty transactions
spending from commitment states. If Bob knows R within three days, thenhe can redeem the funds by broadcasting a transaction; Alice is unable towithhold the funds in any way, because the script returns as valid when thetransaction is spent on the Bitcoin blockchain.
An HTLC is an additional output in a Commitment Transaction witha unique output script:
OP IF
OP HASH160 <Hash160 (R)> OP EQUALVERIFY
2 <A l i c e 2 > <Bob2> OP CHECKMULTISIG
OP ELSE
2 <A l i c e 1 > <Bob1> OP CHECKMULTISIG
OP ENDIF
Conceptually, this script has two possible paths spending from a single
HTLC output. The first path (defined in the OP IF) sends funds to Bob if
Bob can produce R. The second path is redeemed using a 3-day timelockedrefund to Alice. The 3-day timelock is enforced using nLockTime from thespending transaction.

31

4.1

Non-revocable HTLC Construction

Figure 11: This is a non-functional naive implementation of an HTLC. Only the HTLC
path from the Commitment Transaction is displayed. Note that there are two possible
spends from an HTLC output. If Bob can produce the preimage R within 3 days and hecan redeem path 1. After three days, Alice is able to broadcast path 2. When 3 days haveelapsed either is valid. This model, however, doesn’t work with multiple Commitment
Transactions.

If R is produced within 3 days, then Bob can redeem the funds by broadcasting the “Delivery” transaction. A requirement for the “Delivery” transaction
to be valid requires R to be included with the transaction. If R is not included, then the “Delivery” transaction is invalid. However, if 3 days haveelapsed, the funds can be sent back to Alice by broadcasting transaction“Timeout”. When 3 days have elapsed and R has been disclosed, eithertransaction may be valid.
It is within both parties individual responsibility to ensure that they
can get their transaction into the blockchain in order to ensure the balances
are correct. For Bob, in order to receive the funds, he must either broadcast
the “Delivery” transaction on the Bitcoin blockchain, or otherwise settlewith Alice (while cancelling the HTLC). For Alice, she must broadcast the“Timeout” 3 days from now to receive the refund, or cancel the HTLC
entirely with Bob.
Yet this kind of simplistic construction has similar problems as an

32

incorrect bidirectional payment channel construction. When an old Commitment Transaction gets broadcast, either party may attempt to steal funds
as both paths may be valid after the fact. For example, if R gets disclosed 1
year later, and an incorrect Commitment Transaction gets broadcast, both
paths are valid and are redeemable by either party; the contract is not yet
enforcible on the blockchain. Closing out the HTLC is absolutely necessary,
because in order for Alice to get her refund, she must terminate the contract
and receive her refund. Otherwise, when Bob discovers R after 3 days haveelapsed, he may be able to steal the funds which should be going to Alice.
With uncooperative counterparties it’s not possible to terminate an HTLC
without broadcasting it to the bitcoin blockchain as the uncooperative party
is unwilling to create a new Commitment Transaction.

4.2

Off-chain Revocable HTLC

To be able to terminate this contract off-chain without a broadcast to the
Bitcoin blockchain requires embedding RSMCs in the output, which will
have a similar construction to the bidirectional channel.

33

Figure 12: If Alice broadcasts C2a, then the left half will execute. If Bob broadcasts
C2b, then the right half will execute. Either party may broadcast their Commitment
transaction at any time. HTLC Timeout is only valid after 3 days. HTLC Executions canonly be broadcast if the preimage to the hash R is known. Prior Commitments (and theirdependent transactions) are not displayed for brevity.

Presume Alice and Bob wish to update their balance in the channel
at Commitment 1 with a balance of 0.5 to Alice and 0.5 to Bob.
Alice wishes to send 0.1 to Bob contingent upon knowledge of R within
3 days, after 3 days she wants her money back if Bob does not produce R.
The new Commitment Transaction will have a full refund of the current balance to Alice and Bob (Outputs 0 and 1), with output 2 being the
HTLC, which describes the funds in transit. As 0.1 will be encumbered in
an HTLC, Alice’s balance is reduced to 0.4 and Bob’s remains the same at

34

0.5.
This new Commitment Transaction (C2a/C2b) will have an HTLC
output with two possible spends. Each spend is different depending oneach counterparty’s version of the Commitment Transaction. Similar to thebidirectional payment channel, when one party broadcasts their Commitment, payments to the counterparty will be assumed to be valid and notinvalidated. This can occur because when one broadcasts a Commitment
Transaction, one is attesting this is the most recent Commitment Transaction. If it is the most recent, then one is also attesting that the HTLC exists
and was not invalidated before, so potential payments to one’s counterparty
should be valid.
Note that HTLC transaction names (beginning with the letter H) will
begin with the number 1, whose values do not correlate with Commitment
Transactions. This is simply the first HTLC transaction. HTLC transactions may persist between Commitment Transactions. Each HTLC has 4
keys per side of the transaction (C2a and C2b) for a total of 8 keys per
counterparty.
The HTLC output in the Commitment Transaction has two sets ofkeys per counterparty in the output.
For Alice’s Commitment Transaction (C2a), the HTLC output script
requires multisig(PAlice2 , PBob2 ) encumbered by disclosure of R, as well as
multisig(PAlice1 , PBob1 ) with no encumbering.
For Bob’s Commitment Transaction (C2b), the HTLC output script
requires multisig(PAlice6 , PBob6 ) encumbered by disclosure of R, as well as
multisig(PAlice5 , PBob5 ) with no encumbering.
The HTLC output states are different depending upon which Commitment Transaction is broadcast.
4.2.1

HTLC when the Sender Broadcasts the Commitment
Transaction

For the sender (Alice), the “Delivery” transaction is sent as an HTLC Execution Delivery transaction (HED1a), which is not encumbered in an RSMC.
It assumes that this HTLC has never been terminated off-chain, as Alice is
attesting that the broadcasted Commitment Transaction is the most recent.
If Bob can produce the preimage R, he will be able to redeem funds from the
HTLC after the Commitment Transaction is broadcast on the blockchain.
35

This transaction consumes multisig(PAlice2 , PBob2 ) if Alice broadcasts her
Commitment C2a. Only Bob can broadcast HED1a since only Alice gave
her signature for HED1a to Bob.
However, if 3 days have elapsed since forming the HTLC, thenAlice will be able broadcast a “Timeout” transaction, the HTLC Timeout transaction (HT1a). This transaction is an RSMC. It consumes
the output multisig(PAlice1 , PBob1 ) without requiring disclosure of R if
Alice broadcasts C2a. This transaction cannot enter into the blockchain
until 3 days have elapsed. The output for this transaction is an RSMC
with multisig(PAlice3 , PBob3 ) with relative maturity of 1000 blocks, andmultisig(PAlice4 , PBob4 ) with no requirement for confirmation maturity.
Only Alice can broadcast HT1a since only Bob gave his signature for HT1a
to Alice.
After HT1a enters into the blockchain and 1000 block confirmations
occur, an HTLC Timeout Revocable Delivery transaction (HTRD1a)
may be broadcast by Alice which consumes multisig(PAlice3 , PBob3 ).
Only Alice can broadcast HTRD1a 1000 blocks after HT1a is broadcast
since only Bob gave his signature for HTRD1a to Alice. This transaction can be revocable when another transaction supersedes HTRD1ausing multisig(PAlice4 , PBob4 ) which does not have any block maturity
requirements.
4.2.2

HTLC when the Receiver Broadcasts the Commitment
Transaction

For the potential receiver (Bob), the “Timeout” of receipt is refunded as an
HTLC Timeout Delivery transaction (HTD1b). This transaction directly
refunds the funds to the original sender (Alice) and is not encumbered in
an RSMC. It assumes that this HTLC has never been terminated off-chain,
as Bob is attesting that the broadcasted Commitment Transaction (C2b)is the most recent. If 3 days have elapsed, Alice can broadcast HTD1b
and take the refund. This transaction consumes multisig(PAlice5 , PAlice5 ) if
Bob broadcasts C2b. Only Alice can broadcast HTD1b since Bob gave hissignature for HTD1b to Alice.
However, if HTD1b is not broadcast (3 days have not elapsed) andBob knows the preimage R, then Bob will be able to broadcast the HTLC
Execution transaction (HE1b) if he can produce R. This transaction is an
36

RSMC. It consumes the output multisig(PAlice6 , PBob6 ) and requires disclosure of R if Bob broadcasts C2b. The output for this transaction is an
RSMC with multisig(PAlice7 , PBob7 ) with relative maturity of 1000 blocks,
and multisig(PAlice8 , PBob8 ) which does not have any block maturity requirements. Only Bob can broadcast HE1b since only Alice gave her signaturefor HE1b to Bob.
After HE1b enters into the blockchain and 1000 block confirmations
occur, an HTLC Execution Revocable Delivery transaction (HERD1b)
may be broadcast by Bob which consumes multisig(PAlice7 , PBob7 ).
Only Bob can broadcast HERD1b 1000 blocks after HE1b is broadcast
since only Alice gave her signature for HERD1b to Bob. This transaction can be revocable when another transaction supersedes HERD1b
using multisig(PAlice8 , PBob8 ) which does not have any block maturity
requirements.

4.3

HTLC Off-chain Termination

After an HTLC is constructed, to terminate an HTLC off-chain requires
both parties to agree on the state of the channel. If the recipient can proveknowledge of R to the counterparty, the recipient is proving that they areable to immediately close out the channel on the Bitcoin blockchain and receive the funds. At this point, if both parties wish to keep the channel open,
they should terminate the HTLC off-chain and create a new Commitment
Transaction reflecting the new balance.

37

Figure 13: Since Bob proved to Alice he knows R by telling Alice R, Alice is willing to
update the balance with a new Commitment Transaction. The payout will be the same
whether C2 or C3 is broadcast at this time.

Similarly, if the recipient is not able to prove knowledge of R by
disclosing R, both parties should agree to terminate the HTLC and create
a new Commitment Transaction with the balance in the HTLC refunded tothe sender.
If the counterparties cannot come to an agreement or become otherwise unresponsive, they should close out the channel by broadcasting thenecessary channel transactions on the Bitcoin blockchain.
However, if they are cooperative, they can do so by first generating a new Commitment Transaction with the new balances, then invalidate the prior Commitment by exchanging Breach Remedy transactions(BR2a/BR2b). Additionally, if they are terminating a particular HTLC,
they should also exchange some of their own private keys used in the HTLC
transactions.
For example, Alice wishes to terminate the HTLC, Alice will disclose
KAlice1 and KAlice4 to Bob. Correspondingly if Bob wishes to terminate the
HTLC, Bob will disclose KBob6 and KBob8 to Alice. After the private keys
are disclosed to the counterparty, if Alice broadcasts C2a, Bob will be able
to take all the funds from the HTLC immediately. If Bob broadcasts C2b,
Alice will be able to take all funds from the HTLC immediately. Note thatwhen an HTLC is terminated, the older Commitment Transaction must be
revoked as well.

38

Figure 14: A fully revoked Commitment Transaction and terminated HTLC. If either
party broadcasts Commitment 2, they will lose all their money to the counterparty. Other
commitments (e.g. if Commitment 3 is the current Commitment) are not displayed forbrevity.

39

Since both parties are able to prove the current state to each other,
they can come to agreement on the current balance inside the channel. Since
they may broadcast the current state on the blockchain, they are able tocome to agreement on netting out and terminating the HTLC with a new
Commitment Transaction.

4.4

HTLC Formation and Closing OrderTo create a new HTLC, it is the same process as creating a new Commitment
Transaction, except the signatures for the HTLC are exchanged before the
new Commitment Transaction’s signatures.
To close out an HTLC, the process is as follows (from C2 to C3):
1. Alice signs and sends her signature for RD3b and C3b. At this point
Bob can elect to broadcast C3b or C2b (with the HTLC) with thesame payout. Bob is willing after receiving C3b to close out C2b.
2. Bob signs and sends his signature for RD3a and C3a, as well as his
private keys used for Commitment 2 and the HTLC being terminated;he sends Alice KBobRSM C2 , KBob5 , and KBob8 . At this point Bob
should only broadcast C3b and should not broadcast C2b as he willlose all his money if he does so. Bob has fully revoked C2b and the
HTLC. Alice is willing after receiving C3a to close out C2b.
3. Alice signs and sends her signature for RD3b and C3b, as well as her
private keys used for Commitment 2 and the HTLC being terminated;
she sends Bob KAliceRSM C2 , KBob1 , and KBob4 . At this point neither
party should broadcast Commitment 2, if they do so, their funds will
be going to the counterparty. The old Commitment and old HTLC
are now revoked and fully terminated. Only the new Commitment 3
remains, which does not have an HTLC.
When the HTLC has been closed, the funds are updated so that thepresent balance in the channel is what would occur had the HTLC contract
been completed and broadcast on the blockchain. Instead, both parties electto do off-chain novation and update their payments inside the channel.
It is absolutely necessary for both parties to complete off-chain novation within their designated time window. For the receiver (Bob), he must40

know R and update his balance with Alice within 3 days (or whatever time
was selected), else Alice will be able to redeem it within 3 days. For Alice,
very soon after her timeout becomes valid, she must novate or broadcast the
HTLC Timeout transaction. She must also novate or broadcast the HTLC
Timeout Revocable Delivery transaction as soon as it becomes valid. If thecounterparty is unwilling to novate or is stalling, then one must broadcast
the current channel state, including HTLC transactions) onto the Bitcoin
blockchain.
The amount of time flexibility with these offers to novate are dependent upon one’s contingent dependencies on the hashlock R. If one establishes a contract that the HTLC must be resolved within 1 day, then if thetransaction times out Alice must resolve it by day 4 (3 days plus 1), else
Alice risks losing funds.

5

Key Storage

Keys are generated using BIP 0032 Hierarchical Deterministic Wallets[17].
Keys are pre-generated by both parties. Keys are generated in a merkle
tree and are very deep within the tree. For instance, Alice pre-generates
one million keys, each key being a child of the previous key. Alice allocates
which keys to use according to some deterministic manner. For example,
she starts with the child deepest in the tree to generate many sub-keys forday 1. This key is used as a master key for all keys generated on day 1.
She gives Bob the address she wishes to use for the next transaction, anddiscloses the private key to Bob when it becomes invalidated. When Alicediscloses to Bob all private keys derived from the day 1 master key and does
not wish to continue using that master key, she can disclose the day 1 masterkey to Bob. At this point, Bob does not need to store all the keys derived
from the day 1 master key. Bob does the same for Alice and gives her his
day 1 key.
When all Day 2 private keys have been exchanged, for example byday 5, Alice discloses her Day 2 key. Bob is able to generate the Day 1 key
from the Day 2 key, as the Day 1 key is a child of the Day 2 key as well.
If a counterparty broadcasts the wrong Commitment Transaction,
which private key to use in a transaction to recover funds can either bebrute forced, or if both parties agree, they can use the sequence id number
41when creating the transaction to identify which sets of keys are used.
This enables participants in a channel to have prior output states(transactions) invalidated by both parties without using much data at all.
By disclosing private keys pre-arranged in a merkle-tree, it is possible toinvalidate millions of old transactions with only a few kilobytes of data perchannel. Core channels in the Lightning Network can conduct billions oftransactions without a need for significant storage costs.

6

Blockchain Transaction Fees for Bidirectional
Channels

It is possible for each participant to generate different versions of transactions to ascribe blame as to who broadcast the transaction on the blockchain.
By having knowledge of who broadcast a transaction and the ability to ascribe blame, a third party service can be used to hold fees in a 2-of-3 multisig
escrow. If one wishes to broadcast the transaction chain instead of agreeing
to do a Funding Close or replacement with a new Commitment Transaction,
one would communicate with the third party and broadcast the chain to theblockchain. If the counterparty refuses the notice from the third party tocooperate, the penalty is rewarded to the non-cooperative party. In most
instances, participants may be indifferent to the transaction fees in the eventof an uncooperative counterparty.
One should pick counterparties in the channel who will be cooperative,
but is not an absolute necessity for the system to function. Note that thisdoes not require trust among the rest of the network, and is only relevant
for the comparatively minor transaction fees. The less trusted party may
just be the one responsible for transaction fees.
The Lightning Network fees will likely be significantly lower thanblockchain transaction fees. The fees are largely derived from the time-valueof locking up funds for a particular route, as well as paying for the chanceof channel close on the blockchain. These should be significantly lower thanon-chain transactions, as many transactions on a Lightning Network channel can be settled into one single blockchain transaction. With a sufficiently
robust and interconnected network, the fees should asymptotically approach
negligibility for many types of transactions. With cheap fees and fast transactions, it will be possible to build scalable micropayments, even amongst
42

high-frequency systems such as Internet of Things applications or per-unit
micro-billing.

7

Pay to Contract

It is possible construct a cryptographically provable “Delivery Versus Payment” contract, or pay-to-contract[18], as proof of payment. This proof canbe established as knowledge of the input R from hash(R) as payment of acertain value. By embedding a clause into the contract between the buyer
and seller stating that knowing R is proof of funds sent, the recipient offunds has no incentive to disclose R unless they have certainty that they
will receive payment. When the funds eventually get pulled from the buyer
by their counterparty in their micropayment channel, R is disclosed as partof that pull of funds. One can design paper legal documents that specify
that knowledge or disclosure of R implies fulfillment of payment. The sender
can then arrange a cryptographically signed contract with knowledge of inputs for hashes treated as fulfillment of the paper contract before payment
occurs.

8

The Bitcoin Lightning Network

By having a micropayment channel with contracts encumbered by hashlocks
and timelocks, it is possible to clear transactions over a multi-hop payment
network using a series of decrementing timelocks without additional central
clearinghouses.
Traditionally, financial markets clear transactions by transferring theobligation for delivery at a central point and settle by transferring ownership
through this central hub. Bank wire and fund transfer systems (such as ACH
and the Visa card network), or equities clearinghouses (such as the DTCC)
operate in this manner.
As Bitcoin enables programmatic money, it is possible to create transactions without contacting a central clearinghouse. Transactions can executeoff-chain with no third party which collects all funds before disbursing it –only transactions with uncooperative channel counterparties become automatically adjudicated on the blockchain.

43

The obligation to deliver funds to an end-recipient is achieved througha process of chained delegation. Each participant along the path assumes
the obligation to deliver to a particular recipient. Each participant passeson this obligation to the next participant in the path. The obligation of eachsubsequent participant along the path, defined in their respective HTLCs,
has a shorter time to completion compared to the prior participant. Thisway each participant is sure that they will be able to claim funds when the
obligation is sent along the path.
Bitcoin Transaction Scripting, a form of what some call an implementation of “Smart Contracts”[19], enables systems without trusted custodial
clearinghouses or escrow services.

8.1

Decrementing Timelocks

Presume Alice wishes to send 0.001 BTC to Dave. She locates a route
through Bob and Carol. The transfer path would be Alice to Bob to Carol
to Dave.

Figure 15: Payment over the Lightning Network using HTLCs.

When Alice sends payment to Dave through Bob and Carol, she requests from Dave hash(R) to use for this payment. Alice then counts theamount of hops until the recipient and uses that as the HTLC expiry. In thiscase, she sets the HTLC expiry at 3 days. Bob then creates an HTLC with
Carol with an expiry of 2 days, and Carol does the same with Dave with an
expiry of 1 day. Dave is now free to disclose R to Carol, and both parties will
likely agree to immediate settlement via novation with a replacement Commitment Transaction. This then occurs step-by-step back to Alice. Notethat this occurs off-chain, and nothing is broadcast to the blockchain when
all parties are cooperative.

44

Figure 16: Settlement of HTLC, Alice’s funds get sent to Dave.

Decrementing timelocks are used so that all parties along the pathknow that the disclosure of R will allow the disclosing party to pull funds,
since they will at worst be pulling funds after the date whereby they mustreceive R. If Dave does not produce R within 1 day to Carol, then Carol will
be able to close out the HTLC. If Dave broadcasts R after 1 day, then he will
not be able to pull funds from Carol. Carol’s responsibility to Bob occurs
on day 2, so Carol will never be responsible for payment to Dave without
an ability to pull funds from Bob provided that she updates her transaction
with Dave via transmission to the blockchain or via novation.
In the event that R gets disclosed to the participants halfway throughexpiry along the path (e.g. day 2), then it is possible for some parties along
the path to be enriched. The sender will be able to know R, so due to Pay
to Contract, the payment will have been fulfilled even though the receiver
did not receive the funds. Therefore, the receiver must never disclose R
unless they have received an HTLC from their channel counterparty; they
are guaranteed to receive payment from one of their channel counterparties
upon disclosure of the preimage.
In the event a party outright disconnects, the counterparty will be responsible for broadcasting the current Commitment Transaction state in thechannel to the blockchain. Only the failed non-responsive channel state getsclosed out on the blockchain, all other channels should continue to update
their Commitment Transactions via novation inside the channel. Therefore,
counterparty risk for transaction fees are only exposed to direct channel
counterparties. If a node along the path decides to become unresponsive, theparticipants not directly connected to that node suffer only decreased timevalue of their funds by not conducting early settlement before the HTLC
close.

45

Figure 17: Only the non-responsive channels get broadcast on the blockchain, all others
are settled off-chain via novation.

8.2

Payment Amount

It is preferable to use a small payment per HTLC. One should not use an
extremely high payment, in case the payment does not fully route to its
destination. If the payment does not reach its destination and one of theparticipants along the path is uncooperative, it is possible that the sendermust wait until the expiry before receiving a refund. Delivery may be lossy,
similar to packets on the internet, but the network cannot outright steal
funds in transit. Since transactions don’t hit the blockchain with cooperative
channel counterparties, it is recommended to use as small of a payment
as possible. A tradeoff exists between locking up transaction fees on eachhop versus the desire to use as small a transaction amount as possible (thelatter of which may incur higher total fees). Smaller transfers with moreintermediaries imply a higher percentage paid as Lightning Network fees tothe intermediaries.

8.3

Clearing Failure and Rerouting

If a transaction fails to reach its final destination, the receiver should sendan equal payment to the sender with the same hash, but not disclose R.
This will net out the disclosure of the hash for the sender, but may not for
the receiver. The receiver, who generated the hash, should discard R andnever broadcast it. If one channel along the path cannot be contacted, thenthe channels may elect to wait until the path expires, which all participants46

will likely close out the HTLC as unsettled without any payment with a new
Commitment Transaction.

Figure 18: Dave creates a path back to Alice after Alice fails to send funds to Dave,because Carol is uncooperative. The input R from hash(R) is never brodcast by Dave,because Carol did not complete her actions. If R was broadcast, Alice will break-even.
Dave, who controls R should never broadcast R because he may not receive funds from
Carol, he should let the contracts expire. Alice and Bob have the option to net out andclose the contract early, as well, in this diagram.

If the refund route is the same as the payment route, and there areno half-signed contracts whereby one party may be able to steal funds, it ispossible to outright cancel the transaction by replacing it with a new Commitment Transaction starting with the most recent node who participatedin the HTLC.
It is also possible to clear out a channel by creating an alternate route
path in which payment will occur in the opposite direction (netting out
to zero) and/or creating an entirely alternate route for the payment path.
This will create a time-value of money for disclosing inputs to hashes on
the Lightning Network. Participants may specialize in high connectivity
between nodes and offering to offload contract hashlocks from other nodes
for a fee. These participants will agree to payments which net out to zero(plus fees), but are loaning bitcoins for a set time period. Most likely,
these entities with low demand for channel resources will be end-users who
are already connected to multiple well-connected nodes. When an end-user
connects to a node, the node may ask the client to lock up their funds forseveral days to another channel the client has established for a fee. Thiscan be achieved by having the new transactions require a new hash(Y) from
input Y in addition to the existing hash which may be generated by any
participant, but must disclose Y only after a full circle is established. The
new participant has the same responsibility as well as the same timelocks
47

as the old participant being replaced. It is also possible that the one newparticipant replaces multiple hops.

Figure 19: Erin is connected to both Bob and Dave. If Bob wishes to free up his channel
with Carol, since that channel is active and very profitable, Bob can offload the payment
to Dave via Erin. Since Erin has extra bitcoin available, she will be able to collect somefee for offloading the channel between Bob and Carol as well as between Carol and Dave.
The channels between Bob and Carol as well as Carol and Dave are undone and no longer
have the HTLC, nor has payment occurred on that path. Payment will occur on thepath involving Erin. This is achieved by creating a new payment from Dave to Carol to
Bob contingent upon Erin constructing an HTLC. The payment in dashed lines (red) arenetted out to zero and settled via a new Commitment Contract.

8.4

Payment Routing

It is theoretically possible to build a route map implicitly from observing
2-of-2 multisigs on the blockchain to build a routing table. Note, however,this is not feasible with pay-to-script-hash transaction outputs, which canbe resolved out-of-band from the bitcoin protocol via a third party routing
service. Building a routing table will become necessary for large operators(e.g. BGP, Cjdns). Eventually, with optimizations, the network will look a
lot like the correspondent banking network, or Tier-1 ISPs. Similar to how
packets still reach their destination on your home network connection, notall participants need to have a full routing table. The core Tier-1 routes
can be online all the time —while nodes at the edges, such as average users,
would be connected intermittently.
Node discovery can occur along the edges by pre-selecting and offering
partial routes to well-known nodes.

48

8.5

Fees

Lightning Network fees, which differ from blockchain fees, are paid directly
between participants within the channel. The fees pay for the time-valueof money for consuming the channel for a determined maximum period oftime, and for counterparty risk of non-communication.
Counterparty risk for fees only exist with one’s direct channel counterparty. If a node two hops away decides to disconnect and their transaction
gets broadcast on the blockchain, one’s direct counterparties should not
broadcast on the blockchain, but continue to update via novation with a
new Commitment Transaction. See the Decrementing Timelocks entry in
the HTLC section for more information about counterparty risk.
The time-value of fees pays for consuming time (e.g. 3 days) and isconceptually equivalent to a gold lease rate without custodial risk; it is thetime-value for using up the access to money for a very short duration. Since
certain paths may become very profitable in one direction, it is possible
for fees to be negative to encourage the channel to be available for those
profitable paths.

9

Risks

The primary risks relate to timelock expiration. Additionally, for core nodes
and possibly some merchants to be able to route funds, the keys must be
held online for lower latency. However, end-users and nodes are able to keep
their private keys firewalled off in cold storage.

9.1

Improper Timelocks

Participants must choose timelocks with sufficient amounts of time. If insufficient time is given, it is possible that timelocked transactions believed to
be invalid will become valid, enabling coin theft by the counterparty. Thereis a trade-off between longer timelocks and the time-value of money. When
writing wallet and Lightning Network application software, it is necessary
to ensure that sufficient time is given and users are able to have their transactions enter into the blockchain when interacting with non-cooperative or
malicious channel counterparties.

49

9.2

Forced Expiration SpamForced expiration of many transactions may be the greatest systemic risk
when using the Lightning Network. If a malicious participant creates manychannels and forces them all to expire at once, these may overwhelm block
data capacity, forcing expiration and broadcast to the blockchain. The result would be mass spam on the bitcoin network. The spam may delaytransactions to the point where other locktimed transactions become valid.
This may be mitigated by permitting one transaction replacement on
all pending transactions. Anti-spam can be used by permitting only one
transaction replacement of a higher sequence number by the inverse of aneven or odd number. For example, if an odd sequence number was broadcast, permit a replacement to a higher even number only once. Transactions
would use the sequence number in an orderly way to replace other transactions. This mitigates the risk assuming honest miners. This attack isextremely high risk, as incorrect broadcast of Commitment Transactions
entail a full penalty of all funds in the channel.
Additionally, one may attempt to steal HTLC transactions by forcing
a timeout transaction to go through when it should not. This can be easily
mitigated by having each transfer inside the channel be lower than the totaltransaction fees used. Since transactions are extremely cheap and do not
hit the blockchain with cooperative channel counterparties, large transfersof value can be split into many small transfers. This attempt can only work
if the blocks are completely full for a long time. While it is possible tomitigate it using a longer HTLC timeout duration, variable block sizes may
become common, which may need mitigations.
If this type of transaction becomes the dominant form of transactions
which are included on the blockchain, it may become necessary to increase
the block size and run a variable blocksize structure and timestop flags
as described in the section below. This can create sufficient penalties anddisincentives to be highly unprofitable and unsuccessful for attackers, asattackers lose all their funds from broadcasting the wrong transaction, tothe point where it will never occur.

50

9.3

Coin Theft via Cracking

As parties must be online and using private keys to sign, there is a possibility
that, if the computer where the private keys are stored is compromised, coins
will be stolen by the attacker. While there may be methods to mitigate
the threat for the sender and the receiver, the intermediary nodes must be
online and will likely be processing the transaction automatically. For thisreason, the intermediary nodes will be at risk and should not be holding
a substantial amount of money in this “hot wallet.” Intermediary nodes
which have better security will likely be able to out-compete others in thelong run and be able to conduct greater transaction volume due to lower
fees. Historically, one of the largest component of fees and interest in thefinancial system are from various forms of counterparty risk – in Bitcoin it
is possible that the largest component in fees will be derived from security
risk premiums.
A Funding Transaction may have multiple outputs with multiple Commitment Transactions, with the Funding Transaction key and some Commitment Transactions keys stored offline. It is possible to create an equivalentof a “Checking Account” and “Savings Account” by moving funds between
outputs from a Funding Transaction, with the “Savings Account” storedoffline and requiring additional signatures from security services.

9.4

Data Loss

When one party loses data, it is possible for the counterparty to steal funds.
This can be mitigated by having a third party data storage service whereencrypted data gets sent to this third party service which the party cannot
decrypt. Additionally, one should choose channel counterparties who areresponsible and willing to provide the current state, with some periodic
tests of honesty.

9.5

Forgetting to Broadcast the Transaction in Time

If one does not broadcast a transaction at the correct time, the counterparty
may steal funds. This can be mitigated by having a designated third party
to send funds. An output fee can be added to create an incentive for thisthird party to watch the network. Further, this can also be mitigated by
implementing OP CHECKSEQUENCEVERIFY.
51

9.6

Inability to Make Necessary Soft-Forks

Changes are necessary to bitcoin, such as the malleability soft-fork. Additionally, if this system becomes popular, it will be necessary for the system
to securely transact with many users and some kind of structure like a
blockheight timestop will be desirable. This system assumes such changes
to enable Lightning Network to exist entirely, as well as soft-forks ensuring
the security is robust against attackers will occur. While the system maycontinue to operate with only some time lock and malleability soft-forks,
there will be necessary soft-forks regarding systemic risks. Without proper
community foresight, an inability to establish a timestop or similar function will allow systemic attacks to take place and may not be recognized as
imperative until an attack actually occurs.

9.7

Colluding Miner Attacks

Miners may elect to refuse to enter in particular transactions (e.g. BreachRemedy transactions) in order to assist in timeout coin theft. An attacker
can pay off all miners to refuse to include certain transactions in their mempool and blocks. The miners can identify their own blocks in an attempt toprove their behavior to the paying attacker.
This can be mitigated by encouraging miners to avoid identifying
their own blocks. Further, it should be expected that this kind of payment
to miners is malicious activity and the contract is unenforcible. Miners may
then take payment and surreptitiously mine a block without identifying theblock to the attacker. Since the attacker is paying for this, they will quickly
run out of money by losing the fee to the miner, as well as losing all theirmoney in the channel. This attack is unlikely and fairly unattractive as it
is far too difficult and requires a high degree of collusion with extreme risk.
The risk model of this attack occurirng is similar to that of miners
colluding to do reorg attacks: Extremely unlikely with many uncoordinatedminers.

10

Block Size Increases and Consensus

If we presume that a decentralized payment network exists and one user will
make 3 blockchain transactions per year on average, Bitcoin will be able52

to support over 35 million users with 1MB blocks in ideal circumstances(assuming 2000 transactions/MB, or 500 bytes/Tx). This is quite limited,
and an increase of the block size may be necessary to support everyone in
the world using Bitcoin. A simple increase of the block size would be a hard
fork, meaning all nodes will need to update their wallets if they wish toparticipate in the network with the larger blocks.
While it may appear as though this system will mitigate the block size
increases in the short term, if it achieves global scale, it will necessitate ablock size increase in the long term. Creating a credible tool to help prevent
blockchain spam designed to encourage transactions to timeout becomes
imperative.
To mitigate timelock spam vulnerabilities, non-miner and miners’ consensus rules may also differ if the miners’ consensus rules are more restrictive.
Non-miners may accept blocks over 1MB, while miners may have different
soft-caps on block sizes. If a block size is above that cap, then that is viewed
as an invalid block by other miners, but not by non-miners. The miners will
only build the chain on blocks which are valid according to the agreed-uponsoft-cap. This permits miners to agree on raising the block size limit without requiring frequent hard-forks from clients, so long as the amount raisedby miners does not go over the clients’ hard limit. This mitigates the riskof mass expiry of transactions at once. All transactions which are not redeemed via Exercise Settlement (ES) may have a very high fee attached, andminers may use a consensus rule whereby those transactions are exemptedfrom the soft-cap, making it very likely the correct transactions will enter
the blockchain.
When transactions are viewed as circuits and contracts instead oftransaction packets, the consensus risks can be measured by the amount oftime available to cover the UTXO set controlled by hostile parties. In effect,
the upper bound of the UTXO size is determined by transaction fees andthe standard minimum transaction output value. If the bitcoin miners havea deterministic mempool which prioritizes transactions respecting a “weak”
local time order of transactions, it could become extremely unprofitable andunlikely for an attack to succeed. Any transaction spam time attack by
broadcasting the incorrect Commitment Transaction is extremely high risk
for the attacker, as it requires an immense amount of bitcoin and all funds
committed in those transactions will be lost if the attacker fails.
53

11

Use Cases

In addition to helping bitcoin scale, there are many uses for transactions on
the Lightning Network:• Instant Transactions. Using Lightning, Bitcoin transactions are now
nearly instant with any party. It is possible to pay for a cup of coffeewith direct non-revocable payment in milliseconds to seconds.
• Exchange Arbitrage. There is presently incentive to hold funds on
exchanges to be ready for large market moves due to 3-6 block confirmation times. It is possible for the exchange to participate in thisnetwork and for clients to move their funds on and off the exchange
for orders nearly instantly. If the exchange does not have deep market
depth and commits to only permitting limit orders close to the top of
the order book, then the risk of coin theft becomes much lower. The
exchange, in effect, would no longer have any need for a cold storage
wallet. This may substantially reduce thefts and the need for trusted
third party custodians.
• Micropayments. Bitcoin blockchain fees are far too high to accept
micropayments, especially with the smallest of values. With this system, near-instant micropayments using Bitcoin without a 3rd party
custodian would be possible. It would enable, for example, paying
per-megabyte for internet service or per-article to read a newspaper.
• Financial Smart Contracts and Escrow. Financial contracts are especially time-sensitive and have higher demands on blockchain computation. By moving the overwhelming majority of trustless transactions
off-chain, it is possible to have highly complex transaction contract
terms without ever hitting the blockchain.
• Cross-Chain Payments. So long as there are similar hash-functions
across chains, it’s possible for transactions to be routed over multiple chains with different consensus rules. The sender does not haveto trust or even know about the other chains – even the destination
chain. Simiarly, the receiver does not have to know anything about
the sender’s chain or any other chain. All the receiver cares about
is a conditional payment upon knowledge of a secret on their chain.
54

Payment can be routed by participants in both chains in the hop. E.g.
Alice is on Bitcoin, Bob is on both Bitcoin and X-Coin and Carol is
on a hypothetical X-Coin, Alice can pay Carol without understanding
the X-Coin consensus rules.

12

Conclusion

Creating a network of micropayment channels enables bitcoin scalability,
micropayments down to the satoshi, and near-instant transactions. Thesechannels represent real Bitcoin transactions, using the Bitcoin scripting opcodes to enable the transfer of funds without risk of counterparty theft,
especially with long-term miner risk mitigations.
If all transactions using Bitcoin were on the blockchain, to enable
7 billion people to make two transactions per day, it would require 24GB
blocks every ten minutes at best (presuming 250 bytes per transaction and144 blocks per day). Conducting all global payment transactions on theblockchain today implies miners will need to do an incredible amount ofcomputation, severely limiting bitcoin scalability and full nodes to a few
centralized processors.
If all transactions using Bitcoin were conducted inside a network of
micropayment channels, to enable 7 billion people to make two channels
per year with unlimited transactions inside the channel, it would require
133 MB blocks (presuming 500 bytes per transaction and 52560 blocks peryear). Current generation desktop computers will be able to run a full nodewith old blocks pruned out on 2TB of storage.
With a network of instantly confirmed micropayment channels whose
payments are encumbered by timelocks and hashlock outputs, Bitcoin canscale to billions of users without custodial risk or blockchain centralization
when transactions are conducted securely off-chain using bitcoin scripting,with enforcement of non-cooperation by broadcasting signed multisignaturetransactions on the blockchain.

13

Acknowledgements

Micropayment channels have been developed by many parties, and has been
discussed on bitcointalk, the bitcoin mailing list, and IRC. The amount of
55

contributors to this idea are immense and much thought have been put into
this ability. Effort has been placed into citing and finding similar ideas,
however it is absolutely not near complete. In particular, there are many
similarities to a proposal by Alex Akselrod by using hashlocking as a methodof encumbering a hub-and-spoke payment channel.
Thanks to Peter Todd for correcting a significant error in the HTLC
script, as well as optimizing the opcode size.
Thanks to Elizabeth Stark for reviewing and corrections.
Thanks to Rusty Russell for reviewing this document and suggestions
for making the concept more digestible, as well as working on a construction
which may provide a stop-gap solution before a long-term malleability fix(to be described in a future version).

Appendix A

Resolving Malleability

In order to create these contracts in Bitcoin without a third party trusted
service, Bitcoin must fix the transaction malleability problem. If transactions can be mutated, then signatures can be invalidated, thereby making
refund transactions and commitment bonds invalidated. This creates anopportunity for hostile actors to use it as an opportunity for a negotiatingtactic to steal coins, in effect, a hostage scenario.
To mitigate malleability, it is necessary to make a soft-fork change tobitcoin. Older clients would still work, but miners would need to update.
Bitcoin has had several soft forks in the past, including pay-to-script-hash(P2SH).
To mitigate malleability, it requires changing which contents are
signed by the participants. This is achieved by creating new sighash types.
In order to accommodate this new behavior, a new P2SH type or new
OP CHECKSIG is necessary to make it a soft-fork rather than a hard-fork.
If a new P2SH was defined, it would use a different output script
such as:OP DUP OP HASH160 <20-byte hash> OP EQUALVERIFY

Since this will always resolve to true provided a valid redeemScript,
56

all existing clients will return true. This allows the scripting system toconstruct new rules, including new signature validation rules. At least one
new sighash would need to exist.
SIGHASH NOINPUT would neither sign any input transactions IDs
nor sign the index. By using SIGHASH NOINPUT, one can be assured thatone’s counterparty cannot invalidate entire trees of chained transactions ofpotential contract states which were previously agreed upon, using transaction ID mutation. With the new sighash flags, it is possible to spend froma parent transaction even though the transaction ID has changed, so longas the script evaluates as true (i.e. a valid signature).
SIGHASH NOINPUT implies significant risk with address reuse, as
it can work with any transaction in which the sigScript returns as valid, so
multiple transactions with the same outputs are redeemable (provided theoutput values are less).
Further, and just as importantly, SIGHASH NOINPUT permits participants to sign spends of transactions without knowing the signatures of
the transaction being spent. By solving malleability in the above manner,
two parties may build contracts and spend transactions without either party
having the ability to broadcast that original transaction on the blockchain
until both parties agree. With the new sighash type, participants may build
potential contract states and potential payout conditions and agree upon
all terms, before the contract may be paid, broadcast, and executed upon
without the need for a trusted third party.
Without SIGHASH NOINPUT, one cannot build outputs before thetransaction can be funded. It is as if one cannot make any agreements
without committing funds without knowing what one is committing to.
SIGHASH NOINPUT allows one to build redemption for transactions which
do not yet exist. In other words, one can form agreements before funding
the transaction if the output is a 2-of-2 multisignature transaction.
To use SIGHASH NOINPUT, one builds a Funding Transaction,and does not yet sign it. This Funding Transaction does not need to use
SIGHASH NOINPUT if it is spending from a transaction which has alreadybeen entered into the blockchain. To spend from a Funding Transaction
with a 2-of-2 multisignature output which has not yet been signed andbroadcast, however, requires using SIGHASH NOINPUT.
A further stop-gap solution using OP CHECKSEQUENCEVERIFY57

or a less-optimal use of OP CHECKLOCKTIMEVERIFY will be describedin a future paper by Rusty Russell. An updated version of this paper will
also include these constructions.

References[1] Satoshi Nakamoto. Bitcoin: A Peer-to-peer Electronic Cash System.
https://bitcoin.org/bitcoin.pdf, Oct 2008.
[2] Manny
Trillo.
Stress
Test
Prepares
VisaNet
for
the
Most
Wonderful
Time
of
the
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