Good morning,

> The tricky question is what happens when X arrives on its own and it
> might be that no one ever sends a replacement for B,C,D)

It feels ok to me, but this is definitely arguable.

It covers the fact that B,C,D could have been fake transactions whose
sole purpose was to do a pinning attack: in that case the attacker would
have found a way to ensure these transactions don't confirm anyway (or
pay minimal/negligible fees).

If these transactions were legitimate, I believe that their owners would
remake them at some point (because these transactions reflect a business
relationship that needed to happen, so it should very likely still
happen). It's probably hard to verify because the new corresponding
transactions may have nothing in common with the first, but I think the
simplifications it offers for wallets is worth it (which is just my
opinion and needs more scrutiny/feedback).

> But if your backlog's feerate does drop off, *and* that matters, then
> I don't think you can ignore the impact of the descendent transactions
> that you might not get a replacement for.

That is because you're only taking into account the current backlog, and
not taking into account the fact that new items will be added to it soon
to replace the evicted descendants. But I agree that this is a bet: we
can't predict the future and guarantee these replacements will come.

It is really a trade-off, ignoring descendents provides a much simpler
contract that doesn't vary from one mempool to another, but when your
backlog isn't full enough, you may lose some future profits if
transactions don't come in later.

> I think "Y% higher" rather than just "higher" is only useful for
> rate-limiting, not incentive compatibility. (Though maybe it helps
> stabilise a greedy algorithm in some cases?)

That's true. I claimed these policies only address incentives, but using
a percentage increase addresses rate-limiting a bit as well (I couldn't
resist trying to do at least something for it!). I find it a very easy
mechanism to implement, while choosing an absolute value is hard (it's
always easier to think in relatives than absolutes).

> This is why I think it is important to understand the rationales for introducing the rules in the first place

I completely agree. As you mentioned, we are still in brainstorming
phase, once (if?) we start to converge on what could be better policies,
we do need to clearly explain each policy's expected goal. That will let
future Bastien writing code in 2030 clearly highlight why the 2022 rules
don't make sense anymore!

Cheers,
Bastien

Le sam. 5 févr. 2022 à 14:22, Michael Folkson <michaelfolkson@protonmail.com> a écrit :
Thanks for this Bastien (and Gloria for initially posting about this).

I sympathetically skimmed the eclair PR (https://github.com/ACINQ/eclair/pull/2113) dealing with replaceable transactions fee bumping.

There will continue to be a (hopefully) friendly tug of war on this probably for the rest of Bitcoin's existence. I am sure people like Luke, Prayank etc will (rightfully) continue to raise that Lightning and other second layer protocols shouldn't demand that policy rules be changed if there is a reason (e.g. DoS vector) for those rules on the base network. But if there are rules that have no upside, introduce unnecessary complexity for no reason and make Lightning implementers like Bastien's life miserable attempting to deal with them I really hope we can make progress on removing or simplifying them. 

This is why I think it is important to understand the rationales for introducing the rules in the first place (and why it is safe to remove them if indeed it is) and being as rigorous as possible on the rationales for introducing additional rules. It sounds like from Gloria's initial post we are still at a brainstorming phase (which is fine) but knowing what we know today I really hope we can learn from the mistakes of the original BIP 125, namely the Core implementation not matching the BIP and the sparse rationales for the rules. As Bastien says this is not criticizing the original BIP 125 authors, 7 years is a long time especially in Bitcoin world and they probably weren't thinking about Bastien sitting down to write an eclair PR in late 2021 (and reviewers of that PR) when they wrote the BIP in 2015.

--
Michael Folkson
Email: michaelfolkson at
protonmail.com
Keybase: michaelfolkson
PGP: 43ED C999 9F85 1D40 EAF4 9835 92D6 0159 214C FEE3



------- Original Message -------
On Monday, January 31st, 2022 at 3:57 PM, Bastien TEINTURIER via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:
Hi Gloria,

Many thanks for raising awareness on these issues and constantly pushing
towards finding a better model. This work will highly improve the
security of any multi-party contract trying to build on top of bitcoin
(because most multi-party contracts will need to have timeout conditions
and participants will need to make some transactions confirm before a
timeout happens - otherwise they may lose funds).

For starters, let me quickly explain why the current rules are hard to
work with in the context of lightning (but I believe most L2 protocols
will have the same issues). Feel free to skip this part if you are
already convinced.

## Motivation

The biggest pain point is BIP 125 rule 2.
If I need to increase the fees of a time-sensitive transaction because
the feerate has been rising since I broadcast it, I may need to also pay
high fees just to produce a confirmed utxo that I can use. I'm actually
paying a high fee twice instead of once (and needlessly using on-chain
space, our scarcest asset, because we could have avoided that additional
transaction!).

It also has some annoying "non-determinism".
Imagine that my transaction has been evicted from my mempool because its
feerate was too low. I could think "Great, that means I don't have to
apply BIP 125 restrictions, I can just fund this transaction as if it
were a new one!". But actually I do, because my transaction could still
be in miner's mempools and I have no way of knowing it...this means that
whenever I have broadcast a transaction, I must assume that I will
always need to abide by whatever replacement rules the network applies.

Fortunately, as far as I understand it, this rule only exists because of
a previous implementation detail of bitcoin core, so there's simply no
good reason to keep it.

The second biggest pain point is rule 3. It prevents me from efficiently
using my capital while it's unconfirmed. Whenever I'm using a big utxo
to fund a transaction, I will get a big change output, and it would
really be a waste to be unable to use that change output to fund other
transactions. In order to be capital-efficient, I will end up creating
descendant trees for my time-sensitive transactions. But as Gloria
explained, replacing all my children will cost me an absurdly large
amount of fees. So what I'm actually planning to do instead is to RBF
one of the descendants high enough to get the whole tree confirmed.
But if those descendants' timeouts were far in the future, that's a
waste, I paid a lot more fees for them than I should have. I'd like to
just replace my transaction and republish the invalidated children
independently.

Rule 4 doesn't hurt as much as the two previous ones, I don't have too
much to say about it.

To be fair to the BIP 125 authors, all of these scenarios were very hard
to forecast at the time this BIP was created. We needed years to build
on those rules to get a better understanding of their limitations and if
the rationale behind them made sense in the long term.

## Proposals

I believe that now is a good time to re-think those, and I really like
Gloria's categorization of the design constraints.

I'd like to propose a different way of looking at descendants that makes
it easier to design the new rules. The way I understand it, limiting the
impact on descendant transactions is only important for DoS protection,
not for incentive compatibility. I would argue that after evictions,
descendant transactions will be submitted again (because they represent
transactions that people actually want to make), so evicting them does
not have a negative impact on mining incentives (in a world where blocks
are full most of the time).

I'm curious to hear other people's thoughts on that. If it makes sense,
I would propose the following very simple rules:

1. The transaction's ancestor absolute fees must be X% higher than the
previous transaction's ancestor fees
2. The transaction's ancestor feerate must be Y% higher than the
previous transaction's ancestor feerate

I believe it's completely ok to require increasing both the fees and
feerate if we don't take descendants into account, because you control
your ancestor set - whereas the descendant set may be completely out of
your control.

This is very easy to use by wallets, because the ancestor set is easy to
obtain. And an important point is that the ancestor set is the same in
every mempool, whereas the descendant set is not (your mempool may have
rejected the last descendants, while other people's mempools may still
contain them).

Because of that reason, I'd like to avoid having a rule that relies on
some size of the replaced descendant set: it may be valid in your
mempool but invalid in someone else's, which makes it exploitable for
pinning attacks.

I believe these rules are incentive compatible (again, if you accept
the fact that the descendants will be re-submitted and mined as well,
so their fees aren't lost).

Can we choose X and Y so that these two rules are also DoS-resistant?
Unfortunately I'm not sure, so maybe we'll need to add a third rule to
address that. But before we do, can someone detail what it costs for a
node to evict a descendant tree? Given that bitcoin core doesn't allow
chains of more than 25 transactions, the maximum number of transactions
being replaced will be bounded by 25 * N (where N is the number of
outputs of the transaction being replaced). If it's just O(n) pruning of
a graph, maybe that's ok? Or maybe we make X or Y depend on the number
of outputs of the transaction being replaced (this would need very
careful thoughts)?

If you made it this far, thanks for reading!
A couple of comments on the previous messages:

> Currently, if we see a transaction
> that has the same txid as one in the mempool, we reject it as a
> duplicate, even if the feerate is much higher. It's unclear to me if
> we have a very strong reason to change this, but noting it as a
> limitation of our current replacement policy.

I don't see a strong reason from an L2 protocol's point of view yet, but
there are many unkown unknowns. But from a miner incentive's point of
view, we should keep the transaction with the higher feerate, shouldn't
we? In that case it's also a more efficient use of on-chain space, which
is a win, right?

> We might have a more-or-less long transition period during which we support both...

Yes, this is a long term thing.
Even if bitcoin core releases a new version with updated RBF rules, as a
wallet you'll need to keep using the old rules for a long time if you
want to be safe.

But it's all the more reason to try to ship this as soon as possible,
this way maybe our grand-children will be able to benefit from it ;)
(just kidding on the timespan obviously).

Cheers,
Bastien

Le lun. 31 janv. 2022 à 00:11, Antoine Riard via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> a écrit :
Hi Gloria,

Thanks for this RBF sum up. Few thoughts and more context comments if it can help other readers.

> For starters, the absolute fee pinning attack is especially
> problematic if we apply the same rules (i.e. Rule #3 and #4) in
> Package RBF. Imagine that Alice (honest) and Bob (adversary) share a
> LN channel. The mempool is rather full, so their pre-negotiated
> commitment transactions' feerates would not be considered high
> priority by miners. Bob broadcasts his commitment transaction and
> attaches a very large child (100KvB with 100,000sat in fees) to his
> anchor output. Alice broadcasts her commitment transaction with a
> fee-bumping child (200vB with 50,000sat fees which is a generous
> 250sat/vB), but this does not meet the absolute fee requirement. She
> would need to add another 50,000sat to replace Bob's commitment
> transaction.

Solving LN pinning attacks, what we're aiming for is enabling a fair feerate bid between the counterparties, thus either forcing the adversary to overbid or to disengage from the confirmation competition. If the replace-by-feerate rule is adopted, there shouldn't be an incentive for Bob to
pick up the first option. Though if he does, that's a winning outcome for Alice, as one of the commitment transactions confirms and her time-sensitive second-stage HTLC can be subsequently confirmed.

> It's unclear to me if
> we have a very strong reason to change this, but noting it as a
> limitation of our current replacement policy. See [#24007][12].

Deployment of Taproot opens interesting possibilities in the vaults/payment channels design space, where the tapscripts can commit to different set of timelocks/quorum of keys. Even if the pre-signed states stay symmetric, whoever is the publisher, the feerate cost to spend can fluctuate.

> While this isn't completely broken, and the user interface is
> secondary to the safety of the mempool policy

I think with L2s transaction broadcast backend, the stability and clarity of the RBF user interface is primary. What we could be worried about is a too-much complex interface easing the way for an attacker to trigger your L2 node to issue policy-invalid chain of transactions. Especially, when we consider that an attacker might have leverage on chain of transactions composition ("force broadcast of commitment A then commitment B, knowing they will share a CPFP") or even transactions size ("overload commitment A with HTLCs").

> * If the original transaction is in the top {0.75MvB, 1MvB} of the
> mempool, apply the current rules (absolute fees must increase and
> pay for the replacement transaction's new bandwidth). Otherwise, use a
> feerate-only rule.

How this new replacement rule would behave if you have a parent in the "replace-by-feerate" half but the child is in the "replace-by-fee" one ?

If we allow the replacement of the parent based on the feerate, we might decrease the top block absolute fees.

If we block the replacement of the parent based on the feerate because the replacement absolute fees aren't above the replaced package, we still preclude a pinning vector. The child might be low-feerate junk and even attached to a low ancestor-score branch.

If I'm correct on this limitation, maybe we could turn off the "replace-by-fee" behavior as soon as the mempool is fulfilled with a few blocks ?

> * Rate-limit how many replacements we allow per prevout.

Depending on how it is implemented, though I would be concerned it introduces a new pinning vector in the context of shared-utxo. If it's a hardcoded constant, it could be exhausted by an adversary starting at the lowest acceptable feerate then slowly increasing while still not reaching
the top of the mempool. Same if it's time-based or block-based, no guarantee the replacement slot is honestly used by your counterparty.

Further, an above-the-average replacement frequency might just be the reflection of your confirmation strategy reacting to block schedule or mempools historical data. As long as the feerate penalty is paid, I lean to allow replacement.

(One solution could be to associate per-user "tag" to the LN transactions, where each "tag" would have its own replacement slots, but privacy?)

> * Rate-limit transaction validation in general, per peer.

I think we could improve on the Core's new transaction requester logic. Maybe we could bind the peer announced flow based on the feerate score (modulo validation time) of the previously validated transactions from that peer ? That said, while related to RBF, it sounds to me that enhancing Core's rate-limiting transaction strategy is a whole discussion in itself [0]. Especially ensuring it's tolerant to the specific requirements of LN & consorts.

> What should they be? We can do some arithmetic to see what happens if
> you start with the biggest/lowest feerate transaction and do a bunch
> of replacements. Maybe we end up with values that are high enough to
> prevent abuse and make sense for applications/users that do RBF.

That's a good question.

One observation is that the attacker can always renew the set of DoSy utxos to pursue the attack. So maybe we could pick up constants scaled on the block size ? That way an attacker would have to burn fees, thus deterring them from launching an attack. Even if the attackers are miners, they have to renounce their income to acquire new DoSy utxos. If a low-fee period, we could scale up the constants ?


Overall, I think there is the deployment issue to warn of. Moving to a new set of RBF rules implies for a lot of Bitcoin applications to rewrite their RBF logics. We might have a more-or-less long transition period during which we support both...

Cheers,
Antoine

[0] https://github.com/bitcoin/bitcoin/pull/21224

Le jeu. 27 janv. 2022 à 09:10, Gloria Zhao via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> a écrit :
Hi everyone,

This post discusses limitations of current Bitcoin Core RBF policy and
attempts to start a conversation about how we can improve it,
summarizing some ideas that have been discussed. Please reply if you
have any new input on issues to be solved and ideas for improvement!

Just in case I've screwed up the text wrapping again, another copy can be
found here: https://gist.github.com/glozow/25d9662c52453bd08b4b4b1d3783b9ff

## Background

Please feel free to skip this section if you are already familiar
with RBF.

Nodes may receive *conflicting* unconfirmed transactions, aka
"double spends" of the same inputs. Instead of always keeping the
first transaction, since v0.12, Bitcoin Core mempool policy has
included a set of Replace-by-Fee (RBF) criteria that allows the second
transaction to replace the first one and any descendants it may have.

Bitcoin Core RBF policy was previously documented as BIP 125.
The current RBF policy is documented [here][1]. In summary:

1. The directly conflicting transactions all signal replaceability
explicitly.

2. The replacement transaction only includes an unconfirmed input if
that input was included in one of the directly conflicting
transactions.

3. The replacement transaction pays an absolute fee of at least the
sum paid by the original transactions.

4. The additional fees pays for the replacement transaction's
bandwidth at or above the rate set by the node's *incremental relay
feerate*.

5. The sum of all directly conflicting transactions' descendant counts
(number of transactions inclusive of itself and its descendants)
does not exceed 100.

We can split these rules into 3 categories/goals:

- **Allow Opting Out**: Some applications/businesses are unable to
handle transactions that are replaceable (e.g. merchants that use
zero-confirmation transactions). We (try to) help these businesses by
honoring BIP125 signaling; we won't replace transactions that have not
opted in.

- **Incentive Compatibility**: Ensure that our RBF policy would not
accept replacement transactions which would decrease fee profits
of a miner. In general, if our mempool policy deviates from what is
economically rational, it's likely that the transactions in our
mempool will not match the ones in miners' mempools, making our
fee estimation, compact block relay, and other mempool-dependent
functions unreliable. Incentive-incompatible policy may also
encourage transaction submission through routes other than the p2p
network, harming censorship-resistance and privacy of Bitcoin payments.

- **DoS Protection**: Limit two types of DoS attacks on the node's
mempool: (1) the number of times a transaction can be replaced and
(2) the volume of transactions that can be evicted during a
replacement.

Even more abstract: our goal is to make a replacement policy that
results in a useful interface for users and safe policy for
node operators.

## Motivation

There are a number of known problems with the current RBF policy.
Many of these shortcomings exist due to mempool limitations at the
time RBF was implemented or result from new types of Bitcoin usage;
they are not criticisms of the original design.

### Pinning Attacks

The most pressing concern is that attackers may take advantage of
limitations in RBF policy to prevent other users' transactions from
being mined or getting accepted as a replacement.

#### SIGHASH_ANYONECANPAY Pinning

BIP125#2 can be bypassed by creating intermediary transactions to be
replaced together. Anyone can simply split a 1-input 1-output
transaction off from the replacement transaction, then broadcast the
transaction as is. This can always be done, and quite cheaply. More
details in [this comment][2].

In general, if a transaction is signed with SIGHASH\_ANYONECANPAY,
anybody can just attach a low feerate parent to this transaction and
lower its ancestor feerate. Even if you require SIGHASH\_ALL which
prevents an attacker from changing any outputs, the input can be a
very low amount (e.g. just above the dust limit) from a low-fee
ancestor and still bring down the ancestor feerate of the transaction.

TLDR: if your transaction is signed with SIGHASH\_ANYONECANPAY and
signals replaceability, regardless of the feerate you broadcast at, an
attacker can lower its mining priority by adding an ancestor.

#### Absolute Fee

The restriction of requiring replacement transactions to increase the
absolute fee of the mempool has been described as "bonkers." If the
original transaction has a very large descendant that pays a large
amount of fees, even if it has a low feerate, the replacement
transaction must now pay those fees in order to meet Rule #3.

#### Package RBF

There are a number of reasons why, in order to enable Package RBF, we
cannot use the same criteria.

For starters, the absolute fee pinning attack is especially
problematic if we apply the same rules (i.e. Rule #3 and #4) in
Package RBF. Imagine that Alice (honest) and Bob (adversary) share a
LN channel. The mempool is rather full, so their pre-negotiated
commitment transactions' feerates would not be considered high
priority by miners. Bob broadcasts his commitment transaction and
attaches a very large child (100KvB with 100,000sat in fees) to his
anchor output. Alice broadcasts her commitment transaction with a
fee-bumping child (200vB with 50,000sat fees which is a generous
250sat/vB), but this does not meet the absolute fee requirement. She
would need to add another 50,000sat to replace Bob's commitment
transaction.

Disallowing new unconfirmed inputs (Rule #2) in Package RBF would be
broken for packages containing transactions already in the mempool,
explained [here][7].

Note: I originally [proposed][6] Package RBF using the same Rule #3
and #4 before I realized how significant this pinning attack is. I'm
retracting that proposal, and a new set of Package RBF rules would
follow from whatever the new individual RBF rules end up being.

#### Same Txid Different Witness

Two transactions with the same non-witness data but different
witnesses have the same txid but different wtxid, and the same fee but
not necessarily the same feerate. Currently, if we see a transaction
that has the same txid as one in the mempool, we reject it as a
duplicate, even if the feerate is much higher. It's unclear to me if
we have a very strong reason to change this, but noting it as a
limitation of our current replacement policy. See [#24007][12].

### User Interface

#### Using Unconfirmed UTXOs to Fund Replacements

The restriction of only allowing confirmed UTXOs for funding a
fee-bump (Rule #2) can hurt users trying to fee-bump their
transactions and complicate wallet implementations. If the original
transaction's output value isn't sufficient to fund a fee-bump and/or
all of the user's other UTXOs are unconfirmed, they might not be able
to fund a replacement transaction. Wallet developers also need to
treat self-owned unconfirmed UTXOs as unusable for fee-bumping, which
adds complexity to wallet logic. For example, see BDK issues [#144][4]
and [#414][5].

#### Interface Not Suitable for Coin Selection

Currently, a user cannot simply create a replacement transaction
targeting a specific feerate or meeting a minimum fee amount and
expect to meet the RBF criteria. The fee amount depends on the size of
the replacement transaction, and feerate is almost irrelevant.

Bitcoin Core's `bumpfee` doesn't use the RBF rules when funding the
replacement. It [estimates][13] a feerate which is "wallet incremental
relay fee" (a conservative overestimation of the node's incremental
relay fee) higher than the original transaction, selects coins for
that feerate, and hopes that it meets the RBF rules. It never fails
Rule #3 and #4 because it uses all original inputs and refuses to
bump a transaction with mempool descendants.

This is suboptimal, but is designed to work with the coin selection
engine: select a feerate first, and then add fees to cover it.
Following the exact RBF rules would require working the other way
around: based on how much fees we've added to the transaction and its
current size, calculate the feerate to see if we meet Rule #4.

While this isn't completely broken, and the user interface is
secondary to the safety of the mempool policy, we can do much better.
A much more user-friendly interface would depend *only* on the
fee and size of the original transactions.

### Updates to Mempool and Mining

Since RBF was first implemented, a number of improvements have been
made to mempool and mining logic. For example, we now use ancestor
feerates in mining (allowing CPFP), and keep track of ancestor
packages in the mempool.

## Ideas for Improvements

### Goals

To summarize, these seem to be desired changes, in order of priority:

1. Remove Rule #3. The replacement should not be *required* to pay
higher absolute fees.

2. Make it impossible for a replacement transaction to have a lower
mining score than the original transaction(s). This would eliminate
the `SIGHASH\_ANYONECANPAY` pinning attack.

3. Remove Rule #2. Adding new unconfirmed inputs should be allowed.

4. Create a more helpful interface that helps wallet fund replacement
transactions that aim for a feerate and fee.

### A Different Model for Fees

For incentive compatibility, I believe there are different
formulations we should consider. Most importantly, if we want to get
rid of the absolute fee rule, we can no longer think of it as "the
transaction needs to pay for its own bandwidth," since we won't always
be getting additional fees. That means we need a new method of
rate-limiting replacements that doesn't require additional fees every
time.

While it makes sense to think about monetary costs when launching a
specific type of attack, given that the fees are paid to the miner and
not to the mempool operators, maybe it doesn't make much sense to
think about "paying for bandwidth". Maybe we should implement
transaction validation rate-limiting differently, e.g. building it
into the P2P layer instead of the mempool policy layer.

Recently, Suhas gave a [formulation][8] for incentive compatibility
that made sense to me: "are the fees expected to be paid in the next
(N?) blocks higher or lower if we process this transaction?"

I started by thinking about this where N=1 or `1 + p`.
Here, a rational miner is looking at what fees they would
collect in the next block, and then some proportion `p` of the rest of
the blocks based on their hashrate. We're assuming `p` isn't *so high*
that they would be okay with lower absolute fees in the next 1 block.
We're also assuming `p` isn't *so low* that the miner doesn't care
about what's left of the mempool after this block.

A tweak to this formulation is "if we process this transaction, would
the fees in the next 1 block higher or lower, and is the feerate
density of the rest of the mempool higher or lower?" This is pretty
similar, where N=1, but we consider the rest of the mempool by feerate
rather than fees.

### Mining Score of a Mempool Transaction

We are often interested in finding out what
the "mining score" of a transaction in the mempool is. That is, when
the transaction is considered in block template building, what is the
feerate it is considered at?

Obviously, it's not the transaction's individual feerate. Bitcoin Core
[mining code sorts][14] transactions by their ancestor feerate and
includes them packages at a time, keeping track of how this affects the
package feerates of remaining transactions in the mempool.

*ancestor feerate*: Ancestor feerate is easily accessible information,
but it's not accurate either, because it doesn't take into account the
fact that subsets of a transaction's ancestor set can be included
without it. For example, ancestors may have high feerates on their own
or we may have [high feerate siblings][8].

TLDR: *Looking at the current ancestor feerate of a transaction is
insufficient to tell us what feerate it will be considered at when
building a block template in the future.*

*min(individual feerate, ancestor feerate)*: Another
heuristic that is simple to calculate based on current mempool tooling
is to use the [minimum of a transaction's individual score and its
ancestor score][10] as a conservative measure. But this can
overestimate as well (see the example below).

*min ancestor feerate(tx + possible ancestor subsets)* We can also
take the minimum of every possible ancestor subset, but this can be
computationally expensive since there can be lots and lots of ancestor
subsets.

*max ancestor feerate(tx + possible descendant subsets)*: Another idea
is to use the [maximum ancestor score of the transaction + each of its
descendants][9]. This doesn't work either; it has the same blindspot
of ancestor subsets being mined on their own.

#### Mining Score Example

Here's an example illustrating why mining score is tricky to
efficiently calculate for mempool transactions:

Let's say you have same-size transactions A (21sat/vB), B (1sat/vB),
C(9sat/vB), D(5sat/vB).
The layout is: grandparent A, parent B, and two children C and D.

```
A
^
B
^ ^
C D
```

A miner using ancestor packages to build block templates will first
include A with a mining score of 21. Next, the miner will include B and
C with a mining score of 6. This leaves D, with a mining score of 5.

Note: in this case, mining by ancestor feerate results in the most
rational decisions, but [a candidate set-based approach][10] which
makes ancestor feerate much less relevant could
be more advantageous in other situations.

Here is a chart showing the "true" mining score alongside the values
calculating using imperfect heuristics described above. All of them
can overestimate or underestimate.

```
A B C D
mining score | 21 | 6 | 6 | 5 |
ancestor feerate | 21 | 11 | 10.3 | 9 |
min(individual, ancestor) | 21 | 1 | 9 | 5 |
min(tx + ancestor subsets) | 21 | 1 | 5 | 3 |
max(tx + descendants subsets) | 21 | 9 | 9 | 5 |

```

Possibly the best solution for finding the "mining score" of a
transaction is to build a block template, see what feerate each
package is included at. Perhaps at some cutoff, remaining mempool
transactions can be estimated using some heuristic that leans
{overestimating, underestimating} depending on the situation.

Mining score seems to be relevant in multiple places: Murch and I
recently [found][3] that it would be very important in
"ancestor-aware" funding of transactions (the wallet doesn't
incorporate ancestor fees when using unconfirmed transactions in coin
selection, which is a bug we want to fix).

In general, it would be nice to know the exact mining priority of
one's unconfirmed transaction is. I can think of a few block/mempool
explorers who might want to display this information for users.

### RBF Improvement Proposals

After speaking to quite a few people, here are some suggestions
for improvements that I have heard:

* The ancestor score of the replacement must be {5, 10, N}% higher
than that of every original transaction.

* The ancestor score of the replacement must be 1sat/vB higher than
that of every original transaction.

* If the original transaction is in the top {0.75MvB, 1MvB} of the
mempool, apply the current rules (absolute fees must increase and
pay for the replacement transaction's new bandwidth). Otherwise, use a
feerate-only rule.

* If fees don't increase, the size of the replacement transaction must
decrease by at least N%.

* Rate-limit how many replacements we allow per prevout.

* Rate-limit transaction validation in general, per peer.

Perhaps some others on the mailing list can chime in to throw other
ideas into the ring and/or combine some of these rules into a sensible
policy.

#### Replace by Feerate Only

I don't think there's going to be a single-line feerate-based
rule that can incorporate everything we need.
On one hand, a feerate-only approach helps eliminate the issues
associated with Rule #3. On the other hand, I believe the main concern
with a feerate-only approach is how to rate limit replacements. We
don't want to enable an attack such as:

1. Attacker broadcasts large, low-feerate transaction, and attaches a
chain of descendants.

2. The attacker replaces the transaction with a smaller but higher
feerate transaction, attaching a new chain of descendants.

3. Repeat 1000 times.

#### Fees in Next Block and Feerate for the Rest of the Mempool

Perhaps we can look at replacements like this:

1. Calculate the directly conflicting transactions and, with their
descendants, the original transactions. Check signaling. Limit the
total volume (e.g. can't be more than 100 total or 1MvB or something).

2. Find which original transactions would be in the next ~1 block. The
replacement must pay at least this amount + X% in absolute fees. This
guarantees that the fees of the next block doesn't decrease.

3. Find which transactions would be left in the mempool after that ~1
block. The replacement's feerate must be Y% higher than the maximum
mining score of these transactions. This guarantees that you now have
only *better* candidates in your after-this-block mempool than you did
before, even if the size and fees the transactions decrease.

4. Now you have two numbers: a minimum absolute fee amount and a
minimum feerate. Check to see if the replacement(s) meet these
minimums. Also, a wallet would be able to ask the node "What fee and
feerate would I need to put on a transaction replacing this?" and use
this information to fund a replacement transaction, without needing to
guess or overshoot.

Obviously, there are some magic numbers missing here. X and Y are
TBD constants to ensure we have some kind of rate limiting for the
number of replacements allowed using some set of fees.

What should they be? We can do some arithmetic to see what happens if
you start with the biggest/lowest feerate transaction and do a bunch
of replacements. Maybe we end up with values that are high enough to
prevent abuse and make sense for applications/users that do RBF.

### Mempool Changes Need for Implementation

As described in the mining score section above,
we may want additional tooling to more accurately assess
the economic gain of replacing transactions in our mempool.

A few options have been discussed:

* Calculate block templates on the fly when we need to consider a
replacement. However, since replacements are [quite common][11]
and the information might be useful for other things as well,
it may be worth it to cache a block template.

* Keep a persistent block template so that we know what transactions
we would put in the next block. We need to remember the feerate
at which each transaction was included in the template, because an
ancestor package may be included in the same block template in
multiple subsets. Transactions included earlier alter the ancestor
feerate of the remaining transactions in the package. We also need
to keep track of the new feerates of transactions left over.

* Divide the mempool into two layers, "high feerate" and "low
feerate." The high feerate layer contains ~1 block of packages with
the highest ancestor feerates, and the low feerate layer contains
everything else. At the edge of a block, we have a Knapsacky problem
where the next highest ancestor feerate package might not fit, so we
would probably want the high feerate layer ~2MvB or something to avoid
underestimating the fees.

## Acknowledgements

Thank you to everyone whose RBF-related suggestions, grievances,
criticisms and ideas were incorporated in this document:
Andrew Chow, Matt Corallo, Suhas Daftuar, Christian Decker,
Mark Erhardt, Lloyd Fournier, Lisa Neigut, John Newbery,
Antoine Poinsot, Antoine Riard, Larry Ruane,
S3RK and Bastien Teinturier.

Thanks for reading!

Best,
Gloria

[1]: https://github.com/bitcoin/bitcoin/blob/master/doc/policy/mempool-replacements.md
[2]: https://github.com/bitcoin/bitcoin/pull/23121#issuecomment-929475999
[3]: https://github.com/Xekyo/bitcoin/commit/d754b0242ec69d42c570418aebf9c1335af0b8ea
[4]: https://github.com/bitcoindevkit/bdk/issues/144
[5]: https://github.com/bitcoindevkit/bdk/issues/414
[6]: https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2021-September/019464.html
[7]: https://gist.github.com/glozow/dc4e9d5c5b14ade7cdfac40f43adb18a#new-unconfirmed-inputs-rule-2
[8]: https://github.com/bitcoin/bitcoin/pull/23121#discussion_r777131366
[9]: https://github.com/bitcoin/bitcoin/pull/22290#issuecomment-865887922
[10]: https://gist.github.com/Xekyo/5cb413fe9f26dbce57abfd344ebbfaf2#file-candidate-set-based-block-building-md
[11]: https://github.com/bitcoin/bitcoin/pull/22539#issuecomment-885763670
[12]: https://github.com/bitcoin/bitcoin/pull/24007
[13]: https://github.com/bitcoin/bitcoin/blob/1a369f006fd0bec373b95001ed84b480e852f191/src/wallet/feebumper.cpp#L114
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