Subject: [bitcoin-dev] Scaling Lightning Safely With Feerate-Dependent Timelocks

From: jlspc <[email-masked]>
Date: Thu, 14 Dec 2023 17:07:40 +0000

TL;DR
=====
* All known Lightning channel and factory protocols are susceptible to forced expiration spam attacks, in which an attacker floods the blockchain with transactions in order to prevent honest users from putting their transactions onchain before timelocks expire.
* Feerate-Dependent Timelocks (FDTs) are timelocks that automatically extend when blockchain feerates spike.
  - In the normal case, there's no spike in feerates and thus no tradeoff between capital efficiency and safety.
  - If a dishonest user attempts a forced expiration spam attack, feerates increase and FDTs are extended, thus penalizing the attacker by keeping their capital timelocked for longer.
  - FDTs are tunable and can be made to be highly resistant to attacks from dishonest miners.
* Of separate interest, an exact analysis of the risk of double spend attacks is presented that corrects an error in the original Bitcoin whitepaper.

Overview
========

Because the Lightning protocol relies on timelocks to establish the correct channel state, Lightning users could lose their funds if they're unable to put their transactions onchain quickly enough.
The original Lightning paper [1] states that "[f]orced expiration of many transactions may be the greatest systemic risk when using the Lightning Network" and it uses the term "forced expiration spam" for an attack in which a malicious party "creates many channels and forces them all to expire at once", thus allowing timelocked transactions to become valid.
That paper also says that the creation of a credible threat against "spamming the blockchain to encourage transactions to timeout" is "imperative" [1].

Channel factories that create multiple Lightning channels with a single onchain transaction [2][3][4][5] increase this risk in two ways.
First, factories allow more channels to be created, thus increasing the potential for many channels to require onchain transactions at the same time.
Second, channel factories themselves use timelocks, and thus are vulnerable to a "forced expiration spam" attack.

In fact, the timelocks in Lightning channels and factories are risky even without an attack from a malicious party.
Blockchain congestion is highly variable and new applications (such as ordinals) can cause a sudden spike in congestion at any time.
As a result, timelocks that were set when congestion was low can be too short when congestion spikes.
Even worse, a spike in congestion could be self-reinforcing if it causes malicious parties to attack opportunistically and honest parties to put their channels onchain due to the heightened risk.

One way to reduce the risk of a forced expiration spam attack is to use longer timelocks that give honest users more time to put their transactions onchain.
However, long timelocks limit the ability to dynamically reassign the channel's (or factory's) funds, thus creating a tradeoff between capital efficiency and safety [6].
While long timelocks could maintain safety for small numbers of channels, supporting billions (or tens of billions) of channels while maintaining safety is probably impossible [7].

Another way to reduce risk is to impose a penalty on an attacker.
Some channel protocols, such as the original Lightning protocol [1], a version of the two-party eltoo protocol [8], the fully-factory-optimized protocol [9], and the tunable-penalty channel protocol [10] include such penalties.
In addition, the tunable-penalty and single-commitment factory protocols [4] support penalties.
However, as was noted in the original Lightning paper [1], penalties don't eliminate the risk of a forced expiration spam attack.
Furthermore, existing penalty-based factory protocols [4] have limited scalability, as they depend on getting large numbers of casual users to coordinate and co-sign transactions [11][5].

In contrast, the timeout-tree protocol [5] scales via simple covenants (enabled by support for CheckTemplateVerify, AnyPrevOut, or a similar change to the Bitcoin consensus rules).
As a result, a single timeout-tree can support millions of channels and one small transaction per block can fund timeout-trees with tens of billions of offchain channels [5].
However, timeout-trees don't support penalties, and like all other known factory protocols [2][3][4], timeout-trees rely on timelocks.

Therefore, if the need to protect against forced expiration spam was already "imperative" for the original Lightning channel protocol [1], the use of scalable channel factories will make such protection indispensable.

This post proposes a change to Bitcoin's consensus rules that allows the length of a timelock to depend on the feerate being charged for putting transactions onchain.
Such Feerate-Dependent Timelocks (FDTs) can be used to make the above channel and factory protocols resistant to sudden spikes in blockchain congestion.
In the normal case, when there's no spike in congestion, FDTs don't extend the lengths of timelocks and thus don't create a tradeoff between capital efficiency and safety.
On the other hand, when congestion spikes, FDTs extend the lengths of timelocks and thus penalize the owner of the timelocked capital by reducing its efficiency.
Therefore, FDTs can be viewed as creating a penalty for spamming the blockchain, thus reducing the likelihood of such an attack even if the channel (or factory) protocol being used doesn't have an explicit penalty mechanism.

FDTs have other uses, including reducing the risk of having to pay unexpectedly high fees during a congestion spike, improving the accuracy of fee-penalties [5] and reducing the risk of one-shot receives [12].

Of separate interest, the analysis of FDTs given here leads to an exact analysis of the risk of double spend attacks that corrects an error in the original Bitcoin whitepaper [13].

A more complete description and analysis of FDTs is given in a paper [14].

Feerate-Dependent Timelock (FDT) Proposal
=========================================

A Feerate-Dependent Timelock (FDT) is created by encoding a feerate upper bound in a transaction's nSequence field.
A transaction with an FDT cannot be put onchain until:
  1) its absolute timelock encoded in its nLocktime field (and its relative timelock encoded in the same nSequence field, if present) has been satisfied, and
  2) the prevailing feerate has fallen below the FDT's feerate upper bound.
As a result, FDTs are automatically extended when the feerate for putting transactions onchain spikes (such as would occur during a forced expiration spam attack).

In order to determine the prevailing feerate, the median feerate of each block is calculated as the feerate (in satoshis/vbyte) that is paid for at least half of the block's vbytes.

If all miners were honest, a single block with a low median feerate would be enough to guarantee that congestion is low.
However, even a small fraction of dishonest miners would be able to occasionally mine a block with an artificially low feerate.
As a result, it isn't safe to wait for one block (or some other fixed number of blocks) with a low feerate in order to guarantee that honest users have had an opportunity to put their transactions onchain.

Instead, an FDT requires that some maximum number of blocks within an aligned window of consecutive blocks have a high median feerate.
The FDT proposal uses 14 currently masked-off bits in the nSequence field to express the FDT's three parameters:
  * feerate_value,
  * window_size, and
  * block_count.
An aligned window of window_size blocks satisfies the FDT's parameters if it has fewer than block_count blocks with median feerate above feerate_value.
A transaction with an FDT can only be put onchain after an aligned window that satisfies the FDT's parameters and starts no earlier than when the transaction's absolute timelock (and corresponding relative timelock, if present) is satisfied.

In addition, the CheckSequenceVerify (CSV) operator is extended to enforce the desired feerate_value, window_size and block_count.
The details are given in the paper [14].

Safe Lightning Channels And Factories
=====================================

In order to protect a channel or factory protocol against forced expiration spam attacks, the protocol's timelocks are made to be feerate-dependent.
This is done by selecting a feerate_value (such as 4 times the current feerate) that would be caused by a forced expiration spam attack, along with the desired window_size and block_count parameters.

It's also possible to create multiple conflicting transactions with different FDTs (with later timelocks allowing higher feerates) in order to avoid timelocks that will never expire if feerates remain high permanently.

Other Uses
==========

FDTs have uses in addition to protecting channel and factory protocols from forced expiration spam attacks.

For example, FDTs can protect users that are racing against timelocks from having to pay an unexpectedly high feerate due to temporary feerate fluctuations [14].
In addition, FDTs can be used to improve the accuracy of fee-penalties that are assessed when a casual user puts their timeout-tree leaf onchain [14](Section 4.10 of [5]).
Finally, FDTs can be used to allow a casual user to submit a transaction to the blockchain without having to then monitor the blockchain for a sudden spike in feerates, thus reducing the risk of one-shot receives [14][12].

Analysis
========

FDT Implementation Cost
-----------------------
In order to verify an FDT, nodes have to determine whether or not there is an aligned window with a sufficient number of low-feerate blocks after the FDT's absolute timelock (and corresponding relative timelock, if present) is satisfied.
Therefore, if a node knows the starting block of the most recent aligned window that satisfies the FDT's feerate_value, window_size, and block_count parameters, the node can compare that starting block with the FDT's timelocks to verify the FDT.
Because the FDT parameters can be expressed using 14 bits, nodes only have to keep track of the starting block for 2^14 = 16k different low-feerate windows.
The starting block for each such window can be stored in 4 bytes, so 16k * 4B = 64kB of memory allows a node to verify an FDT in constant time.
(In practice, slightly more memory could be used in order to accommodate a reordering of the most recent 1k blocks.)
Therefore, DRAM that costs less than one cent, plus a small constant number of computations, suffice to verify an FDT.

FDT Dishonest Miner Attacks
---------------------------
The window_size and block_count parameters can be selected to balance between:
  1) latency,
  2) the feerate paid by honest users, and
  3) security against dishonest miners.
At one extreme, if dishonest miners are of no concern, window_size and block_count can be set to 1, so the FDT can be satisfied when the first block with a sufficiently low feerate is mined.
At the other extreme, if dishonest miners are of great concern, window_size can be set to 16k and block_count can be set to 1024, in which case dishonest miners with 45% of the hashpower would have less than a 10^-33 chance of dishonestly mining enough blocks in a given window to satisfy the FDT prior to the honest users being able to get their transactions onchain [14].

Double Spend Attacks
--------------------
While it's unrelated to FDTs, the analysis of FDTs' resistance to dishonest miner attacks can also be used to analyze the risk of double spend attacks.

The original Bitcoin whitepaper [13] includes an analysis of the probability of a double spend attack in which a dishonest party colludes with dishonest miners in order to undo a bitcoin transaction and steal the goods purchased with that transaction.
That analysis correctly shows that the probability of success of a double spend attack falls exponentially with z, the depth of the transaction that's being double spent.
However, there are two problems with that analysis:
  1) it is approximate, and
  2) it ignores the possibility of the dishonest miners using pre-mining.

The first problem was addressed by Grunspan and Perez-Marco [15].
However, it doesn't appear that the second problem has been addressed previously.

Exact formulas for the risk of double spend attacks, including pre-mining, are given in the paper [14] and programs that implement those formulas are available on GitHub [16].

The effect of including pre-mining only becomes apparent when a large fraction of the miners are dishonest.
For example, Nakamoto estimates the required value of z to guarantee at most a 0.1% chance of a successful double spend, and Grunspan and Perez-Marco give exact values assuming no pre-mining.
Those results, plus exact results with pre-mining, are as follows:

% dishonest  Estimated z w/o      Exact z w/o       Exact z w/
     miners  pre-mining [13]  pre-mining [15]  pre-mining [14]
===========  ===============  ===============  ===============
         10                5                6                6
         15                8                9                9
         20               11               13               13
         25               15               20               20
         30               24               32               33
         35               41               58               62
         40               89              133              144
         45              340              539              589

It's important to note that the above results with pre-mining assume that the time of the double spend attack is not selected by the attacker.
If the attacker can select when to perform the attack, they are guaranteed to succeed given any value of z, but the expected time required to perform the attack grows exponentially with z [14].

Conclusions
===========

Securing Lightning channels and channel factories against forced expiration spam attacks is imperative.

Feerate-Dependent Timelocks (FDTs) provide this security without forcing the timelocks to be extended in the typical case, thus avoiding a capital efficiency vs. safety tradeoff.
Furthermore, a dishonest user who tries to use a forced expiration spam attack to steal funds is penalized by having their funds timelocked for a longer period, thus discouraging such attacks.
Finally, FDTs can be made to be highly resistant to attacks by dishonest miners.

FDTs have other uses, including the reduction of feerate risk and the calculation of fee-penalties.

While implementing FDTs requires some additional DRAM and computation, the costs are extremely small.
Given these advantages and their low costs, it's hoped that the Bitcoin consensus rules will be changed to support FDTs.

Regards,
John

[1] Poon and Dryja, The Bitcoin Lightning Network, https://lightning.network/lightning-network-paper.pdf
[2] Burchert, Decker and Wattenhofer, "Scalable Funding of Bitcoin Micropayment Channel Networks", http://dx.doi.org/10.1098/rsos.180089
[3] Decker, Russell and Osuntokun. "eltoo: A Simple Layer2 Protocol for Bitcoin", https://blockstream.com/eltoo.pdf
[4] Law, "Efficient Factories For Lightning Channels", https://github.com/JohnLaw2/ln-efficient-factories
[5] Law, "Scaling Lightning With Simple Covenants", https://github.com/JohnLaw2/ln-scaling-covenants
[6] Towns, "Re: Scaling Lightning With Simple Covenants", https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2023-September/021943.html
[7] Law, "Re: Scaling Lightning With Simple Covenants", https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2023-November/022175.html
[8] Towns, "Two-party eltoo w/ punishment", https://lists.linuxfoundation.org/pipermail/lightning-dev/2022-December/003788.html
[9] Law, "Factory-Optimized Channel Protocols For Lightning", https://github.com/JohnLaw2/ln-factory-optimized
[10] Law, "Lightning Channels With Tunable Penalties", https://github.com/JohnLaw2/ln-tunable-penalties
[11] Riard, "Solving CoinPool high-interactivity issue with cut-through update of Taproot leaves", https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2023-September/021969.html
[12] Law, "Watchtower-Free Lightning Channels For Casual Users", https://github.com/JohnLaw2/ln-watchtower-free
[13] Nakamoto. "Bitcoin: A Peer-to-Peer Electronic Cash System", http://bitcoin.org/bitcoin.pdf
[14] Law, "Scaling Lightning Safely With Feerate-Dependent Timelocks", https://github.com/JohnLaw2/ln-fdts
[15] Grunspan and Perez-Marco, "Double Spend Races", CoRR, vol. abs/1702.02867, http://arxiv.org/abs/1702.02867v3
[16] Law, https://github.com/JohnLaw2/ln-fdts

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