[bitcoin-dev] Taproot (and graftroot) complexity (reflowed)

Bryan Bishop kanzure at gmail.com
Sun Feb 9 20:47:29 UTC 2020

Apologies for my previous attempt at relaying the message- it looks like
the emails got mangled on the archive. I am re-sending them in this
combined email with what I hope will be better formatting. Again this is
from some nym that had trouble posting to this mailing list; I didn't see
any emails in the queue so I couldn't help to publish this sooner.

SUBJECT: Taproot (and Graftroot) Complexity

This email is the first of a collection of sentiments from a group of
developers who in aggregate prefer to remain anonymous. These emails have
been sent under a pseudonym so as to keep the focus of discussion on the
merits of the technical issues, rather than miring the discussion in
personal politics.  Our goal isn't to cause a schism, but rather to help
figure out what the path forward is with Taproot. To that end, we:

1) Discuss the merits of Taproot's design versus simpler alternatives (see
thread subject, "Taproot (and Graftroot) Complexity").

2) Propose an alternative path to deploying the technologies described in
BIP-340, BIP-341, and BIP-342 (see thread subject, "An Alternative
Deployment Path for Taproot Technologies").

3) Suggest a modification to Taproot to reduce some of the overhead (see
thread subject, "Taproot Public NUMS Optimization").

Now that the BIP has moved to draft we felt that now was the time to
prioritize review to make sure it was an acceptable change for our
activities. As a group, we're excited about the totality of what Taproot
has to offer. However, after our review, we're left perplexed about the
development of Taproot (and Graftroot, to a lesser extent).

We also want to convey that we have nothing but respect for the developers
and community who have poured their heart and soul into preparing Taproot.
Self evidently, it is an impressive synthesis of ideas. We believe that the
highest form of respect to pay such a synthesis of ideas is a detailed and
critical review, as it's pertinent to closely consider changes to Bitcoin.

In essence, Taproot is fundamentally the same as doing
https://github.com/bitcoin/bips/blob/master/bip-0114.mediawiki and Schnorr
signatures separately.

The main reason for putting them together -- as mentioned in the BIP -- is
a gain in efficiency. But this efficiency pre-supposes a specific use case
and probability distribution of use cases.


Suppose a MAST for {a,b,c,d,e,f,g,h} spending conditions it looks something
like this:

     /  \
    /    \
   /      \
  /\      /\
 /  \    /  \
/\  /\  /\  /\
a b c d e f g h

If we want this to be functionally equivalent to Taproot, we add a new path:

      /\ {<pk> schnorr_checksig}
     /  \
    /    \
   /      \
  /\      /\
 /  \    /  \
/\  /\  /\  /\
a b c d e f g h

Now, to spend from this MBV you have to reveal 32 bytes on the stack for
the not taken branch, and 35 bytes for the <pk> schnorr_checksig (1 byte
push, 33 bytes PK, 1 byte checksig).

This is 67 bytes more than Taproot would require for the same spending

However, suppose we wanted to use one of the script paths instead. We still
need to have one extra hash for the {<pk> schnorr_checksig} (depending on
if we put the key in this position or not--see below). But now we can spend
with just a logarithmic control program path.

However, if we do the same script via taproot, we now need to provide the
base public key (33 bytes) as well as the root hash (32 bytes) and path and
then the actual scripts. With the need for 2 push bytes, this ends up being
back at 67 bytes extra.

Is Taproot just a probability assumption about the frequency and likelihood
of the signature case over the script case? Is this a good assumption?  The
BIP only goes as far as to claim that the advantage is apparent if the
outputs *could be spent* as an N of N, but doesn't make representations
about how likely that N of N case would be in practice compared to the
script paths. Perhaps among use cases, more than half of the ones we expect
people to be doing could be spent as an N of N. But how frequently would
that path get used? Further, while the *use cases* might skew toward things
with N of N opt-out, we might end up in a power law case where it's the one
case that doesn't use an N of N opt out at all (or at a de minimis level)
that becomes very popular, thereby making Taproot more costly then

Further, if you don't want to use a Taproot top-level key (e.g., you need
to be able to audit that no one can spend outside of one of the script
conditions), then you need to use a NUMS (nothing up my sleeve) point. This
forces users who don't want Taproot to pay the expense, when if they just
had a MAST based witness type they would be cheaper. So if this use case is
at all common, Taproot leaves them worse off in terms of fees. Given that
script paths are usually done in the case where there is some contested
close, it's actually in the interest of protocol developers that the
contested script path be as efficient as possible so that the fees paid
maximally increase the feerate. We think this can be fixed simply in
Taproot though, as noted below.

On privacy, we're also a bit confused as to the goal of Taproot over MAST
and Schnorr. Earlier, we presented a design with MAST which is very close
to Taproot.  However, it'd also be possible to just add {<pk>
schnorr_checksig} to the set {a,b,c,d,e,f,g,h}, shuffle them, and compute
some MAST structure (perhaps probability encoded) on them. This has the
effect of not having much additional fees for adding the extra Schnorr path
at redeem time (only 1 extra branch on 2/8 script paths), e.g.

     /  \
    /    \
   /      \
  /\      /\
 /  \    /  \
/\  /\  /\  /\
a b c d e f/\ {<pk> schnorr_checksig}
          g  h

We could argue that this is more private than Taproot, because we don't
distinguish between the Schnorr key case and other cases by default, so
chain analyzers can't tell if the signature came from the Taproot case or
from one of the Script paths. There's also no NUMS point required, which
means chain analyzers can't tell when you spend that there was no top level
key if the NUMS point is not per-output indistinguishable. By using a
semi-randomized MAST structure, chain analyzers also can't tell exactly how
big your spend condition MAST was. In particular, you care more about
privacy when you are contesting a close of a channel or other script path
because then the miners could be more likely to extract a rent from you as
"ransom" for properly closing your channel (or in other words, in a
contested close the value of the closing transaction is larger than usual).

It would also be possible to do something really simple which is to allow
the witness type to be either a MAST hash OR a schnorr key (but not a
Taproot). This allows you to not completely fracture the anonymity set
between people who want plain Schnorr and people who want MAST (at least
until they go to spend). This fix can also be used in Taproot in place of a
NUMS point, to decrease extra fees. It's unclear if this plays negatively
with any future batch validation mechanism though, but the contextual
checks to exclude a witness program from the batch are relatively simple.
See thread subject, "Taproot Public NUMS Optimization".

The considerations around Graftroot, a proposed delegation mechanism, is a
bit similar. Delegation is a mechanism by which a UTXO with script S can
sign a script R which can then be executed in addition to S without
requiring a transaction. This allows an output to monotonically and
dynamically increase the number of conditions under which it can be spent.
As noted by Pieter Wiulle here:
delegation was originally possible in Bitcoin, but got broken during an
emergency fork to split the scriptSig and scriptpubkey separation. Rather
than adding some fancy delegation mechanism in Bitcoin, why not just have a
P2SH-like semantic which allows a delegated script to be evaluated? See
BIP-117 https://github.com/bitcoin/bips/blob/master/bip-0117.mediawiki.
This way we aren't special casing where delegation can occur, and we can
allow taproot nested spending conditions (i.e., with timelocks) to generate
their own delegations. As I've seen Graftroot discussed thus far, it is as
a top-level witness program version like Taproot and non-recursive. Similar
to the above discussion, top-level is more efficient if you suspect that
delegation will be most likely occurring at the top level, but it's not
clear that's a good assumption as it may be common to want to allow
different scripts to delegate.

Overall, we are left with concerns both about the merit of doing Taproot
versus alternatives, as well as the process through which we got to be here.

1) Is Taproot actually more private than bare MAST and Schnorr separately?
What are the actual anonymity set benefits compared to doing the separately?

2) Is Taproot actually cheaper than bare MAST and Schnorr separately? What
evidence do we have that the assumption it will be more common to use
Taproot with a key will outweigh Script cases?

3) Is Taproot riskier than bare MAST and Schnorr separately given the new
crypto? How well reviewed is the actual crypto parts? None of us personally
feel comfortable reviewing the crypto in Schnorr -- what's the set of
people who have thoroughly reviewed the crypto and aren't just ACKing
because they trust other developers to have looked at it close enough?

4) Design wise, couldn't we forego the NUMS point requirement and be able
to check if it's a hash root directly? This would encumber users who don't
need the key path a cheaper spend path. See thread subject, "Taproot Public
NUMS Optimization".

5) Is the development model of trying to jam a bunch of features into
Bitcoin all at once good for Bitcoin development? Would we be better off if
we embraced incremental improvements that can work together (e.g., MAST and
then Schnorr)?  Although the BIP raises some points about anonymity sets
being why to do them all at once, it's not clear to me this argument holds
water (same goes for businesses not upgrading). If we can take things as
smaller steps, we are not only more secure, but we also have more time to
dedicate review to each change independently. We also end up co-mingling
changes that people end up accepting only because they want one and they're
bundled (e.g., MAST and Schnorr, MAST seems like a much less risky addition
versus Schnorr). See thread subject, "An Alternative Deployment Path for
Taproot Technologies".

Our provocation with this email is primarily that we think we should more
carefully consider the benefits of Taproot over simpler primitives that are
not only easier to review, but could have been made available much sooner
rather than waiting on putting everything all together for an unclear
aggregate benefit.

We do think that most of the developers have been honest about the benefits
of Taproot, but that on closer look we feel the general ecosystem has
oversold Taproot as being the key enabler for a collection of techniques
that we could do with much simpler building blocks.

At the end of the day, we do not strongly advocate not deploying Taproot at
this point in the review cycle. We think the Taproot Public NUMS
Optimization may be a good idea, worth considering if it's not insecure, as
it cuts through the case where you would otherwise need a NUMS point.
Things like TapScript and its MAST mechanisms are well designed and offer
exciting new deployment paths, and would be something we would use even if
we opted for MAST instead of Taproot. However, we also believe it is our
duty to raise these concerns and suggestions, and we look forward to
listening to the responses of the community.

Great thanks,

The Group


SUBJECT: An Alternative Deployment Path for Taproot Technologies

This email is the second of a collection of sentiments from a group of
developers who in aggregate prefer to remain anonymous. These emails have
been sent under a pseudonym so as to keep the focus of discussion on the
merits of the technical issues, rather than miring the discussion in
personal politics. Our goal isn't to cause a schism, but rather to help
figure out what the path forward is with Taproot. To that end, we: [clip

As a follow up to our prior message, we propose a different path forward
for the Taproot family of changes:

1) A separate soft-fork for Merkle Branch Witnesses based on Taproot;

2) A separate soft-fork for Schnorr Signatures

3) A separate follow up soft-fork which enables Taproot and Graftroot

We think that the first 2 forks can be offered at the same time or one at a

Taproot, as a follow up to changes 1 and 2, can be enabled as a soft-fork
on the existing semantics, but requiring a new witness version. With the
Public NUMS Optimization, wallets could upgrade by just changing one
version byte to be in the same anonymity set as Taproot.

It's not clear to us that the time to prepare a BIP and implementation for
1 and 2 at this point would be any less than the time to do Taproot as
currently proposed. However, we believe that such a deployment plan is a
reasonable option as it is more conservative, as Merkle Branch witnesses
are relatively simple and users only have to use Schnorr signing if they
want to, and can otherwise continue to use ECDSA. A further benefit of
waiting on 3 is that we get to collect real world protocol engineering
experience to see how frequently the Taproot frequency of use assumption
holds, and if it is worth doing or not.

Great thanks,

The Group


SUBJECT: Taproot Public NUMS Optimization

This email is the third of a collection of sentiments from a group of
developers who in aggregate prefer to remain anonymous. These emails have
been sent under a pseudonym so as to keep the focus of discussion on the
merits of the technical issues, rather than miring the discussion in
personal politics. Our goal isn't to cause a schism, but rather to help
figure out what the path forward is with Taproot. To that end, we: [clipped

We propose to modify Taproot's specification in BIP-341 by adding the rule:

If there is one element on the witness stack:

1) Attempt hashing it to see if it's equal to  the witness program. The
first byte is the control byte for leaf versioning.

2) If it's not the witness program, and it's 65 bytes, try signature

If there is more than one element on the witness stack:

If the control block is even, treat it as a non-Taproot MAST and get the
leaf version as the last byte of the script (so you can pop it off before

If greater anonymity is required, a NUMS point can still be used in
Taproot, at the expense of the additional data. However, if NUMS points are
just a couple well known constants this could actually decrease privacy as
then the NUMS points could differ from application to application
fingerprinting wallets.  Instead, the NUMS point should only be used when a
single use nonce can be sent, so that NUMS cannot be distinguished from a
normal Taproot to a third party who doesn't know the setup (e.g., that the
NUMS is H(X) for known X).

Great thanks,

The Group

- Bryan
1 512 203 0507
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