Subject: [bitcoin-dev] Design approaches for Signature Aggregation

From: "Russell O'Connor" <[email-masked]>
Date: Tue, 30 Jan 2018 14:12:31 -0500

On Sat, Jan 27, 2018 at 12:23 PM, Matt Corallo <[email-masked]>
wrote:

> Gah, please no. I see no material reason why cross-input signature
> aggregation shouldn't have the signatures in the first n-1 inputs replaced
> with something like a single-byte push where a signature is required to
> indicate aggregation, and the combined signature in the last input at
> whatever position the signature is required.
>

That would be the expedient approach.

I want to preface what I'm about to write by first stating that I think the
cross-input signature aggregation is the most important forthcoming
development for Bitcoin and I would be very happy to have any solution for
it deployed in any workable form.  Also, it is difficult to discuss pros
and cons of various designs without concrete proposals, but perhaps we can
try to say some things about various design approaches while still saying
something useful.

I think there are some issues with the expedient proposal for signature
aggregation.  The problems begin with the arbitrary choice of which input
witness will be the canonical choice for holding the aggregated signature.
We want to strictly define which input is the canonical choice for holding
the aggregated signature because we wish to avoid introducing new witness
malleability vectors.  However, the definition of the canonical input is
somewhat complicated.  Because not all inputs are necessarily participating
the aggregation, the canonical choice of input necessarily depends on the
run-time behavior of all the other input Scripts in the transaction.  This
complicates the specification and makes the implementation somewhat
error-prone.

Furthermore designing the canonical choice of input for the aggregated
signature to support future extensions of new script versions or new
opcodes that may want to participate in signature aggregation (for example,
adding CHECKSIGFROMSTACK later) is going to be extraordinarily difficult, I
think.  I don't know how it could even be done.

On the other hand, the extended-transaction approach supports a clean model
of script semantics whereby the signature aggregation is supported via a
new writer (aka logging) side-effect for Script[1].  In this model, rather
than the semantics of Script returning only failure or success, Script
instead results in either failure or conditional success plus a log of
additional constraints that need to be satisfied for the transaction to be
valid.  In the case of signature aggregation, these constraints are of the
form "I require cryptographic evidence that there is a signature on message
M from public key P".  The aggregated signature in the extension of the
transaction provides a witness that demonstrates all the constraints
emitted by all the scripts are satisfied.

Even in the extended-transaction approach, supporting future extensions of
new script versions or new opcodes that may want to participate in
signature aggregation is going to be very difficult.  However, I do have
some half-baked ideas (that you will probably like even less) on how we
could support new script versions and new opcodes based on this idea of a
writer side-effect model of Script semantics.  I hope that designing
support for extendable signature aggregation isn't infeasible.

I think that the cleaner semantic model of the extended-transaction
approach is by itself enough reason to prefer it over the expedient
approach, but reasonable people can disagree about this.  However, there
are even larger issues lurking which appear when we start looking for
unintended semantic consequences of the expedient design.  This is a common
problem with expedient approaches.  It is hard enough to come up with a
design that enables a new feature, but it is even harder to come up with a
design that enables a new feature without enabling other, unintended
"features".  I worry that people do not pay enough attention to the later,
after achieving the former. This sort of thing happened with OP_EVAL in bip
12.  In that situation, the goal was to create a design that enabled pay to
script hash, and OP_EVAL does achieve that in a very straightforward way.
However, the unintended semantic consequences was that bip 12 also enable
unbounded recursion[2] and extended the class of functions definable by
script all the way to the entire class of all computable functions.

We can find unintended semantic consequences of the expedient approach to
signature aggregation by looking at the ways it fails to fit into the
writer side-effect model for signature aggregation.

A. Firstly, we notice that scripts can determine whether or not they are in
canonical position or not by checking the length of their signature data.
This is an effect that goes beyond the abilities of just allowing signature
aggregation.  We can build scripts that can only be redeemed when they are,
or aren't the ones holding the aggregated signature.

B. In the presence of sufficient computation power[3], I expect that
scripts can recover the public keys and signed message data of the
aggregated data, using the same methods used in Enchancing Bitcoin
Transactions with Covenants
<http://fc17.ifca.ai/bitcoin/papers/bitcoin17-final28.pdf>. With this
ability, the script in canonical position can determine what messages are
being signed by other inputs, and which public keys they have chosen to
use.  Perhaps a script could enforce a whitelist or blacklist of
approved/disapproved public keys that it is willing or unwilling to be
aggregated with, etc.

C. Scripts can subvert the use the public keys being aggregated themselves
for the purpose of communicate arbitrary data to other script inputs.  With
aggregated CHECKSIGFROMSTACK, scripts can directly use signed messages for
this communication.

I'm not trying to say that the above are good or bad things, after all
signature aggregation is an interactive process so it is expected that
users could decide which keys they are willing to aggregate with.  What I'm
trying to say is that the expedient proposal has a host of unintended
semantic consequences and the above list is only the ones that I can think
of off the top of my head.  I do not even know the full extent of what we
will be enabling with this design but it seems to include adding a
subversive unidirectional cross-input communication channel for Script. Is
that really a feature we want to be bundling with a signature aggregation
proposal?

I believe that the extended-transaction design is the conservative design.
I conjecture that one can build a reduction from scripts supporting
signature aggregation in the extended-transaction design to scripts that
don't support signature aggregation, while preserving the same security
properties. (The proposed reduction would "simply" replace every aggregated
signature call with a non-aggregated signature call.)  If this conjecture
holds, that means we can prove that the extended-transaction design is only
an optimization and doesn't have any further unintended semantic
consequences.  In particular, we see that the expedient approach doesn't
have such a reduction proof because scripts that are using the expedient
design for cross-input communication cannot be modeled by scripts that
don't have the signature aggregation ability.

I would be disappointed if we end up taking the expedient approach to
signature aggregation (but still very happy that we get signature
aggregation), and there are probably other designs for signature
aggregation beyond the two designs I'm discussing here.

-- 
Russell

[1]For those familiar with using monads to model side-effects, we can model
the output of Script as a (M Bool) value where M is a writer monad over the
monoid of a set of formal constraints, or some other small variant of this
model.  I know that the word monad makes some people's eyes glaze over, but
I'm not trying to use jargon here to exclude people; I'm trying to use
jargon here to be precise about what it means to formally model
computational side-effects for those who are familiar how to do that sort
of thing.

[2]Due to an attempt at a gas limit, OP_EVAL wasn't not intended to enable
unbounded computation in practice.  However when talking about the formal
expressiveness of a programming language we usually discard these sorts of
limits, such as stack size limits, gas limits etc.  Those limits are there
to prevent denial of service attacks against Bitcoin consensus.  The limits
are not designed to enforce language and security properties through the
restriction of computational expressiveness.

[3]Here sufficient computation power means that we have access to functions
like CHECKSIGFROMSTACK and/or basic operations on elliptic curves and hash
functions.  These are all pure functions that can be defined by logical
gates. Since bitcoin script has boolean logic operations, they technically
fall into scope of what is ostensibly definable by script.  Nevertheless,
these sorts of functions could reasonably appear in a Bitcoin Script 2.0 as
they would make a host of new protocols practical.