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From: Nagaev Boris <bnagaev@gmail.com>
Date: Fri, 22 Dec 2023 13:36:56 -0300
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To: jlspc <jlspc@protonmail.com>, 
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 <lightning-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] Scaling Lightning Safely With Feerate-Dependent
	Timelocks
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Hi John!

I have two questions regarding the window, which are related.

1. Why is the window aligned? IIUC, this means that the blocks mined
since the latest block whose height is divisible by window_size do not
affect transaction's validity. So a recent change of fees does not
reflect if a transaction can be confirmed.

2. Does it make sense to have a global window_size? This would save
space in FDT (=3D in transaction) and simplify verification, especially
for a non-aligned window case (see 1). An array of integers of size
window_size would be sufficient to give answer to a question if there
were at least x blocks among window_size latest blocks with median fee
rate <=3D y, using O(1) time per query.

Moving on to another topic, what are the implications for light
clients? A light client can validate current timelocks without
downloading whole blocks, because they depend on timestamps and block
height only, the information from block headers. To validate a
transaction with FDT or to choose FDT parameters for its own
transaction, a light client would have to determine the median fee
rate of the recent blocks. To do that without involving trust, it has
to download the blocks. What do you think about including median
feerate as a required OP_RETURN output in coinbase transaction? A
block without it would be invalid (new consensus rule). A light client
can rely on median feerate value from coinbase transaction,
downloading only one tx instead of the whole block.

On Fri, Dec 15, 2023 at 6:20=E2=80=AFAM jlspc via bitcoin-dev
<bitcoin-dev@lists.linuxfoundation.org> wrote:
>
> TL;DR
> =3D=3D=3D=3D=3D
> * All known Lightning channel and factory protocols are susceptible to fo=
rced expiration spam attacks, in which an attacker floods the blockchain wi=
th transactions in order to prevent honest users from putting their transac=
tions onchain before timelocks expire.
> * Feerate-Dependent Timelocks (FDTs) are timelocks that automatically ext=
end 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, feerate=
s increase and FDTs are extended, thus penalizing the attacker by keeping t=
heir capital timelocked for longer.
>   - FDTs are tunable and can be made to be highly resistant to attacks fr=
om dishonest miners.
> * Of separate interest, an exact analysis of the risk of double spend att=
acks is presented that corrects an error in the original Bitcoin whitepaper=
.
>
> Overview
> =3D=3D=3D=3D=3D=3D=3D=3D
>
> Because the Lightning protocol relies on timelocks to establish the corre=
ct 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 Ne=
twork" 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 "spam=
ming the blockchain to encourage transactions to timeout" is "imperative" [=
1].
>
> Channel factories that create multiple Lightning channels with a single o=
nchain transaction [2][3][4][5] increase this risk in two ways.
> First, factories allow more channels to be created, thus increasing the p=
otential for many channels to require onchain transactions at the same time=
.
> Second, channel factories themselves use timelocks, and thus are vulnerab=
le 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 or=
dinals) can cause a sudden spike in congestion at any time.
> As a result, timelocks that were set when congestion was low can be too s=
hort 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 the=
ir channels onchain due to the heightened risk.
>
> One way to reduce the risk of a forced expiration spam attack is to use l=
onger timelocks that give honest users more time to put their transactions =
onchain.
> However, long timelocks limit the ability to dynamically reassign the cha=
nnel's (or factory's) funds, thus creating a tradeoff between capital effic=
iency and safety [6].
> While long timelocks could maintain safety for small numbers of channels,=
 supporting billions (or tens of billions) of channels while maintaining sa=
fety 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 ve=
rsion of the two-party eltoo protocol [8], the fully-factory-optimized prot=
ocol [9], and the tunable-penalty channel protocol [10] include such penalt=
ies.
> 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 sc=
alability, as they depend on getting large numbers of casual users to coord=
inate and co-sign transactions [11][5].
>
> In contrast, the timeout-tree protocol [5] scales via simple covenants (e=
nabled 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 o=
ne 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 alre=
ady "imperative" for the original Lightning channel protocol [1], the use o=
f 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 tra=
nsactions onchain.
> Such Feerate-Dependent Timelocks (FDTs) can be used to make the above cha=
nnel and factory protocols resistant to sudden spikes in blockchain congest=
ion.
> In the normal case, when there's no spike in congestion, FDTs don't exten=
d 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 tim=
elocks and thus penalize the owner of the timelocked capital by reducing it=
s efficiency.
> Therefore, FDTs can be viewed as creating a penalty for spamming the bloc=
kchain, 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 unexpe=
ctedly high fees during a congestion spike, improving the accuracy of fee-p=
enalties [5] and reducing the risk of one-shot receives [12].
>
> Of separate interest, the analysis of FDTs given here leads to an exact a=
nalysis of the risk of double spend attacks that corrects an error in the o=
riginal Bitcoin whitepaper [13].
>
> A more complete description and analysis of FDTs is given in a paper [14]=
.
>
> Feerate-Dependent Timelock (FDT) Proposal
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
>
> 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 relati=
ve timelock encoded in the same nSequence field, if present) has been satis=
fied, and
>   2) the prevailing feerate has fallen below the FDT's feerate upper boun=
d.
> As a result, FDTs are automatically extended when the feerate for putting=
 transactions onchain spikes (such as would occur during a forced expiratio=
n 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 occas=
ionally mine a block with an artificially low feerate.
> As a result, it isn't safe to wait for one block (or some other fixed num=
ber of blocks) with a low feerate in order to guarantee that honest users h=
ave had an opportunity to put their transactions onchain.
>
> Instead, an FDT requires that some maximum number of blocks within an ali=
gned 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_val=
ue.
> 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 tr=
ansaction's absolute timelock (and corresponding relative timelock, if pres=
ent) is satisfied.
>
> In addition, the CheckSequenceVerify (CSV) operator is extended to enforc=
e the desired feerate_value, window_size and block_count.
> The details are given in the paper [14].
>
> Safe Lightning Channels And Factories
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
>
> In order to protect a channel or factory protocol against forced expirati=
on 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 fe=
erate) 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 diffe=
rent FDTs (with later timelocks allowing higher feerates) in order to avoid=
 timelocks that will never expire if feerates remain high permanently.
>
> Other Uses
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
>
> FDTs have uses in addition to protecting channel and factory protocols fr=
om forced expiration spam attacks.
>
> For example, FDTs can protect users that are racing against timelocks fro=
m having to pay an unexpectedly high feerate due to temporary feerate fluct=
uations [14].
> In addition, FDTs can be used to improve the accuracy of fee-penalties th=
at 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 sudde=
n spike in feerates, thus reducing the risk of one-shot receives [14][12].
>
> Analysis
> =3D=3D=3D=3D=3D=3D=3D=3D
>
> FDT Implementation Cost
> -----------------------
> In order to verify an FDT, nodes have to determine whether or not there i=
s an aligned window with a sufficient number of low-feerate blocks after th=
e 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 timelo=
cks to verify the FDT.
> Because the FDT parameters can be expressed using 14 bits, nodes only hav=
e to keep track of the starting block for 2^14 =3D 16k different low-feerat=
e windows.
> The starting block for each such window can be stored in 4 bytes, so 16k =
* 4B =3D 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 numb=
er of computations, suffice to verify an FDT.
>
> FDT Dishonest Miner Attacks
> ---------------------------
> The window_size and block_count parameters can be selected to balance bet=
ween:
>   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 bl=
ock_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_si=
ze can be set to 16k and block_count can be set to 1024, in which case dish=
onest 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 p=
rior 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 dishone=
st miner attacks can also be used to analyze the risk of double spend attac=
ks.
>
> The original Bitcoin whitepaper [13] includes an analysis of the probabil=
ity of a double spend attack in which a dishonest party colludes with disho=
nest miners in order to undo a bitcoin transaction and steal the goods purc=
hased 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 pre=
viously.
>
> Exact formulas for the risk of double spend attacks, including pre-mining=
, are given in the paper [14] and programs that implement those formulas ar=
e available on GitHub [16].
>
> The effect of including pre-mining only becomes apparent when a large fra=
ction of the miners are dishonest.
> For example, Nakamoto estimates the required value of z to guarantee at m=
ost a 0.1% chance of a successful double spend, and Grunspan and Perez-Marc=
o 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]
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D  =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D  =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D  =3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
>          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 guarantee=
d to succeed given any value of z, but the expected time required to perfor=
m the attack grows exponentially with z [14].
>
> Conclusions
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
>
> Securing Lightning channels and channel factories against forced expirati=
on 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 e=
fficiency vs. safety tradeoff.
> Furthermore, a dishonest user who tries to use a forced expiration spam a=
ttack to steal funds is penalized by having their funds timelocked for a lo=
nger 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 cal=
culation of fee-penalties.
>
> While implementing FDTs requires some additional DRAM and computation, th=
e costs are extremely small.
> Given these advantages and their low costs, it's hoped that the Bitcoin c=
onsensus rules will be changed to support FDTs.
>
> Regards,
> John
>
> [1] Poon and Dryja, The Bitcoin Lightning Network, https://lightning.netw=
ork/lightning-network-paper.pdf
> [2] Burchert, Decker and Wattenhofer, "Scalable Funding of Bitcoin Microp=
ayment Channel Networks", http://dx.doi.org/10.1098/rsos.180089
> [3] Decker, Russell and Osuntokun. "eltoo: A Simple Layer2 Protocol for B=
itcoin", 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/Jo=
hnLaw2/ln-scaling-covenants
> [6] Towns, "Re: Scaling Lightning With Simple Covenants", https://lists.l=
inuxfoundation.org/pipermail/bitcoin-dev/2023-September/021943.html
> [7] Law, "Re: Scaling Lightning With Simple Covenants", https://lists.lin=
uxfoundation.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://git=
hub.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 u=
pdate of Taproot leaves", https://lists.linuxfoundation.org/pipermail/bitco=
in-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://b=
itcoin.org/bitcoin.pdf
> [14] Law, "Scaling Lightning Safely With Feerate-Dependent Timelocks", ht=
tps://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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--=20
Best regards,
Boris Nagaev