Currently Bitcoin Core implements a Replace-by-Fee (RBF) policy, where transactions are not replaced unless the new transaction pays at least a higher total fee than the replaced transaction, regardless of fee-rate.

When RBF was first implemented over 8 years ago this was a reasonable, conservative, default. However, since then we’ve found that strictly requiring a higher absolute fee creates the potential for transaction pinning attacks in contracting protocols such as Lightning; replacing transactions based on fee-rate would make it possible¹ to eliminate these attacks by eliminating BIP-125 Rule #3 pinning.

Here we will propose an incentive compatible solution, One-Shot Replace-By-Fee-Rate, that mitigates prior concerns over replace-by-fee-rate policies by allowing the replacement to only happen when it would immediately bring a transaction close enough to the top of the mempool to be mined in the next block or so. Finally, we will show that both one-shot and pure replace-by-fee-rate policies sufficiently resist bandwidth exhaustion attacks to be implementable.

Thanks goes to Fulgur Ventures for sponsoring this research. They had no editorial control over the contents of this post and did not review it prior to publication.

Background

The Expected Return of an Unconfirmed Transaction

Suppose there exists a transaction that pays a fee of \(F\) at a fee-rate \(r\). What is the expected return \(E\) of that transaction to miners as a whole? If the transaction pays a fee-rate high enough to definitely get mined in the next block, the answer seems obvious: \(E = F\). The transaction will be mined, and miners as a whole will earn the entire \(F\) fee.

But what if that transaction pays a lower fee-rate? For example, as I write this, mempool.space reports that their mempool contains \(535\mathrm{MvB}\) of transactions, enough that a typical Bitcoin Core node with its typical \(300\mathrm{MB}\) mempool size limit would reject transactions paying less than \(22.9\frac{\mathrm{sat}}{\mathrm{vB}}\).

If a transaction has a fee-rate of \(23\frac{\mathrm{sat}}{\mathrm{vB}}\), just barely enough to get into a default mempool, what is that transaction worth to miners? How do we even answer this question?

Intuitively it seems obvious that the low fee-rate transaction should be worth less than the high fee-rate transaction, because the low fee-rate transaction probably won’t be mined for days, or even weeks, if ever. Certainly, in a shorter time frame, a transaction at the bottom of the mempool does not directly represent income to the miner.

We can think about this a bit more rigorously by observing that because block finding is a Poisson Process, even if we ignore the supply of new transactions, the probability that a transaction \(n\) blocks deep is mined in a time interval \(t\) is the probability that \(N \ge n\) blocks are found in the time interval \(t\). That probability rapidly diminishes as \(n\) increases, because it’s less and less likely for so many blocks to be found in a short period of time.

Unconfirmed Transactions are Honest Signals

Do low fee-rate transactions have a value? Yes!

Assuming your node is well connected, unconfirmed transactions in your mempool are honest signals: because unconfirmed transactions could be mined, they’re clear evidence that if you wish your transaction to be mined sooner, you need to offer an even higher fee-rate. There’s a constant supply of people with high time preference who want their transactions mined in a short period of time. So low fee-rate transactions indirectly increase the revenue of miners in the short term, because they force higher time preference transactors to outbid them.

Note how I said a higher fee-rate, not fee: because it maximizes revenue to mine transactions in fee-rate order, fee-rate is what matters in terms of priority.

Expected Return vs Fee-Rate

Suppose we now have two different conflicting transactions, \(a\) and \(b\). Suppose that the total size of \(a\) is \(100000\mathrm{vB}\), and pays \(23\frac{\mathrm{sat}}{\mathrm{vB}}\), for a total fee of \(2300000\mathrm{sat}\). Meanwhile \(b\) has a size of just \(150\mathrm{vB}\), and pays \(15000\frac{\mathrm{sat}}{\mathrm{vB}}\), for a total fee of \(2250000\mathrm{sat}\).

It seems intuitive that transaction \(b\) is the one the miner should accept to maximize revenue. It pays a far higher fee-rate, almost certainly high enough to be mined in the next block. \(a\) might never get mined, in part because another miner might mine \(b\) first². Yet currently, Bitcoin Core will reject \(b\), because BIP-125 Rule #3 requires a transaction to pay a higher total fees than the replacement!

Conversely if transaction \(b\) was broadcast first, transaction \(a\) would not be accepted even though it pays a higher total fee: Bitcoin Core does not allow a transaction to be replaced unless the replacement pays a higher fee-rate.

One-Shot Replace-by-Fee-Rate

We can mitigate Rule #3 transaction pinning in a miner-incentive compatible way by replacing transactions (or alternatively, transaction packages) that do not qualify for replacement based on the existing rules, if they qualify under these alternative rules:

1. The new transaction (package) has a fee-rate more than \(r\) times higher than the fee-rate of the transactions it replaces.
2. The new transaction (package) has a sufficiently high fee-rate to place it into the upper \(N\) blocks worth of the mempool.
3. The highest mineable replaced fee-rate is not high enough to place the replaced transactions in the upper \(N\) blocks of the mempool. Highest mineable replaced fee-rate in this context refers to the fee-rate a miner can obtain by mining one or more of the replaced transactions, taking unconfirmed parents³ into account.

Setting \(r = 1.25\) and \(N = 1\) would be reasonable.

Provided that a small \(N\) is chosen, this alternative Replace-by-Fee-Rate mechanism solves BIP-125 Rule #3 transaction pinning for contracting protocols such as Lightning because:

1. If the one-shot RBFr replacement conditions are met, the higher fee-rate intended transaction replaces the pin, and will be mined in the near future.
2. If the replacement conditions are not met, the pin must already have a sufficiently high fee-rate to be mined “soon”, allowing the protocol to make forward progress anyway.

This works because contracting protocols are not secure if they absolutely depend on the highest fee/fee-rate transaction being mined. Mempools don’t have consensus, so it’s impossible to guarantee that a particular transaction gets mined when more than one transaction is possible. But, contracting protocols do require forward progress to be made, defined as transactions getting mined. So as long as we can ensure that a transaction is mined, the protocol can make progress.

For miners, these one-shot RBFr rules are reasonably incentive compatible because:

1. In the typical case where fees are reasonably steady, there is a constant supply of new transactions created by people who want those transactions to be mined in the near future.
2. The old transaction did not have a high enough fee-rate to be mined soon. Thus the value to the miner of that transaction was not the fees themselves. But rather, the fee-rate, which new, high time preference, bidders have to outbid.
3. The new transaction does have a high enough fee-rate to be mined soon. Which means other high time preference transactors will have to outbid it, or alternatively, the transactions it pushed further down the mempool.
4. Contracting protocols, in particular Lightning-like protocols, are profitable to miners because they allow many layer 2 transactions to pay for the transaction fees of a single layer 1 transaction. Adopting rules that allow these protocols to work better will, in the long run, increase miner revenue.
5. It is sufficient for only a subset of miners to run replace-by-fee-rate policies, as well-designed contracting protocols only need to make forward progress eventually, prior to deadlines being reached.

Remember that we are not claiming that one-shot RBFr is always perfectly incentive compatible; no one set of rules could ever be perfectly incentive compatible in all possible scenarios. We are simply claiming that on average, in the situations where these rules are active, miners make more money.

Finally node runners should adopt these rules because:

1. If we assume node runners are donating their bandwidth to be used for the good of Bitcoin users and miners, all the above arguments apply.
2. These rules are usually a strict increase in the number of transactions that nodes propagate to miners; replace-by-fee-rate policies propagate transactions that otherwise would not have been propagated.

Denial of Service Attacks

The Status Quo

The amount of bandwidth transactors can consume by broadcasting Bitcoin transactions must be limited. But even without transaction replacement, the exact way these limits work is non-obvious.

You might think that the minimum relay fee implements a direct cost that must be paid to use up bandwidth, if you assume that any transaction will eventually be mined. But in fact this is not true! There are a variety of ways that a previously broadcast transaction might become impossible to mine due to a double spend of one of the inputs, by a transaction that did not pay the full cost of the minimum relay fee for that transaction.

For example, an attacker could broadcast a large, \(400{\small,}000\mathrm{byte}\), low fee-rate transaction that violates Ocean mining pool’s restrictions on data carrying transactions. Almost all relay nodes will relay this transaction, using up relay bandwidth. But at some point in the future, the attacker can give Ocean a much smaller transaction spending one of that large, low fee-rate, transaction’s inputs. It will eventually be mined, creating a conflict that invalidates the large transaction, at a much lower cost than the total fees the large transaction was supposed to pay.

Similarly, an attacker could broadcast a large, low fee-rate, transaction while simultaneously sending a small double-spend directly to a mining pool. With good timing, the super-majority of nodes will waste bandwidth broadcasting the large transaction, which is eventually removed from mempools when the small transaction is mined at low cost.

How much is such an attacker paying? Interestingly, the worst case is made a bit worse worse if the ephemeral anchors proposal is implemented. So for the purpose of conservatively analyzing a worst case situation, we will assume the attacker makes use of the most efficient possible version of ephemeral anchors, a bare scriptPubKey spent by an OP_True. If ephemeral anchors is not implemented, all of the steps below can be done nearly as efficiently via P2SH outputs with the spending script OP_True.

1. Attacker creates \(N\) ephemeral anchor outputs.⁴
2. Attacker broadcasts \(N\), \(404{\small,}000\mathrm{byte}\) transaction packages⁵ with fee-rate low enough to not be mined any time soon, in such a way that the transactions is not accepted by some hash power. Each transaction spends an ephemeral anchor output.
3. Attacker spends those \(N\) ephemeral anchor outputs in a transaction paying market fee-rates rates.

Spending each ephemeral output requires an additional \(41\mathrm{vB}\) per output spent, and creating an ephemeral output, an additional \(9\mathrm{vB}\). Thus the attacker has broadcast \(404{\small,}000\mathrm{bytes}\) while paying for just \(50\mathrm{vB}\), a \(\frac{1}{8080}\) cost reduction⁶ over the intended minimum relay fee.

Remember, we are not analyzing replace-by-fee-rate here! We’re just looking at what is already possible with Bitcoin Core. Or at least, almost already possible, as OP_True P2SH outputs cost only a bit more.

So why isn’t this attack happening? Let’s work out how much it costs, using the current Bitcoin price and current lower-bound mining fees:

\[\frac{50\mathrm{vB}}{404{\small,}000\mathrm{B}} \times \frac{30\mathrm{sat}}{\mathrm{vB}} \times \frac{40{\small,}000 \mathrm{USD}}{100{\small,}000{\small,}000\mathrm{sats}} \approx \frac{1485 \mathrm{USD}}{\mathrm{GB}}\]

Even Digital Ocean charges just \(0.01\frac{\mathrm{USD}}{\mathrm{GB}}\)⁷. So if you wanted to DoS attack all ~20,000 publicly reachable nodes, you’d be spending only \(200\frac{\mathrm{USD}}{\mathrm{GB}}\). This isn’t an entirely fair comparison, as relaying transactions also uses up bandwidth on non-public nodes. But it is an indication that there are probably cheaper and more effective ways to attack Bitcoin.

Conflicting Versions

Attackers can further multiply the bandwidth usage of their attack by simultaneously broadcasting multiple conflicting versions of the large transaction to different nodes, where each conflict pays the same fee/fee-rate. At the points in the node network graph where the conflicts “meet”, nodes will end up downloading multiple versions from their peers, again increasing bandwidth usage by the number of conflicts each node sees.

Analyzing this case is more difficult, as the impact depends on network topology, and the attacker has to use more of their own bandwidth broadcasting the conflicting transactions. But in a perfectly executed attack, a node might receive one conflicting version per peer; public nodes have, by default, up to 125 connections, and non-public nodes have, by default, 8 outgoing transaction relaying peers.

Even in the 125x public node case it would probably be cheaper to try to DoS attack all publicly accessible nodes via an unsophisticated packet flood.

Re-using Third Party Outputs

An attacker can make use of others’ transactions rather than creating their own transaction outputs to reduce cost. This of course is a transaction pinning attack! Doing this is possible against unsigned anchor outputs, as well as transactions signed with SIGHASH_ANYONECANPAY. However for the purpose of using up relay bandwidth this attack strategy is inherently limited by two factors:

1. There usually aren’t that many suitable victim transactions being broadcast, limiting the total bandwidth that can be consumed.
2. The attacker has to intercept the victim transactions prior to them being widely broadcast, and somehow get their “bloated” versions of those transactions widely broadcast first.

Fill and Dump Attack

In addition to using up bandwidth an attacker could also use transaction invalidation to fill, and then empty, mempools at less cost than the full fees required to broadcast the “fill” transactions. In fact, any attack that tries to use up a significant amount of relay bandwidth by mining conflicting transactions will have this effect by default, as conflicts can only invalidate transactions when blocks are mined.

Filling mempools requires access to large amounts of capital. Bitcoin Core implements the mempool size limit in terms of RAM usage, not serialized bytes, so exactly what the default \(300\mathrm{MB}\) limit means depends on CPU architecture. But for sake of argument, let’s say that the limit works out to approximately \(75\mathrm{MvB}\) worth of transactions, and the attacker is “filling” \(70\mathrm{MvB}\) worth, to avoid getting their transactions actually mined. Even at \(10\frac{\mathrm{sat}}{\mathrm{vB}}\) the attacker needs:

\[70\mathrm{MvB} \times \frac{10\mathrm{sat}}{\mathrm{vB}} \times \frac{40{\small,}000 \mathrm{USD}}{100{\small,}000{\small,}000\mathrm{sats}} = 280{\small,}000 \mathrm{USD}\]

An obvious question is, what exactly does this attack accomplish? Transactions that are outbid can simply be rebroadcast by anyone once mempools have space again; while the transactions are in mempools the attacker is legitimately outbidding those transactions, and they could hypothetically be mined. Arguably the transactions are driving up fees overall. But unless the attacker wants to bid high enough that their “fill” transactions actually get mined, the attacker isn’t having any direct impact on the higher fee part of mempools that is actually getting mined.

Is One Shot Replace-By-Fee-Rate Similar To The Status Quo?

Yes.

As we have shown above, an attacker can already broadcast large transactions that are invalidated by smaller transactions that pay less total fees. With one-shot replace-by-fee-rate the attack becomes a little less challenging to pull off, as it can be done generically, rather than with a target mining pool. But either way, the real limiting factor to the attack is that it is still a very expensive way to use up bandwidth.

With regard to the fill-and-dump attack, again the attacker is able to do fill-and-dump cycles more frequently than once per block with one-shot replace-by-fee-rate. But again, we have to ask what does the attacker get out of this other than bandwidth consumption, and possibly confusing some badly written fee estimation code?

Pure Replace-By-Fee-Rate

What if we don’t have the one-shot condition? Is a pure replace-by-fee-rate policy viable from a DoS attack perspective? This is an important question because:

1. An initial prototype is easier to implement without the one-shot feature, and compatible with nodes/miners who choose to do something more sophisticated.
2. Pure replace-by-fee-rate is simpler for users to understand.
3. In a rising fee-rate environment, the one-shot policy may degrade to pure replace-by-fee-rate.

Provided that the minimum fee-rate ratio, \(r\) is sufficiently high the total number of plausible replacements is limited. For example, even starting at just \(1\frac{\mathrm{sat}}{\mathrm{vB}}\), \(r = 1.25\) results in:

\[1\frac{\mathrm{sat}}{\mathrm{vB}} \times 1.25^{30} \approx 808\frac{\mathrm{sat}}{\mathrm{vB}}\]

That’s sufficient to get into the next block at any point in time in Bitcoin’s history, for a mere 30x theoretical increase in bandwidth, by an attacker who is going to have to tie up thousands of dollars worth of BTC just to broadcast a few megabytes worth of transactions. And that example is unrealistic, as minimum relay fees were never actually that low during Bitcoin’s high fee events.

It’s probably worth trying out pure replace-by-fee-rate in a Bitcoin Core fork, especially if \(r\) is set to a more conservative value, e.g. \(r=2\).

Impact on Coinjoins

Replace-by-fee-rate does introduce a new way to double-spend low fee-rate coinjoin transactions at lower cost than outbidding the entire fee paid by the coinjoin. This is most relevant to Wasabi, which typically creates coinjoin transactions with hundreds of inputs and outputs; other coinjoin implementations create much smaller transactions.

However, double-spending is not a new attack. There are already other cheap ways to cause coin-join rounds to fail, including other types of double-spend attacks, and cheapest of all, simply failing to complete the coinjoin protocol by failing to provide a signature where required. Wasabi deals with this by imposing a cost on the attacker, by blacklisting UTXO’s that fail to complete a coinjoin round for a period of time; the majority of Wasabi coinjoin rounds fail due to one of the parties failing to sign in time.

Simply failing to sign is generally a cheaper attack than double-spending, as any type of double-spend requires fees to be paid per round disrupted. Thus replace-by-fee-rate is unlikely to pose a significant threat to coinjoin protocols.

Footnotes