[bitcoin-dev] Private Collaborative Custody with FROST

[Nick Farrow <nicholas.w.farrow@gmail.com>]

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Hello all,

Some thoughts on private collaborative custody services for Bitcoin.

With multiparty computation multisignatures like FROST [0], it is possible
to build a collaborative custodian service that is extremely private for
users.

Today's collaborative custodians can see your entire wallet history even if
you never require them to help sign a transaction, and they have full
liberty to censor any signature requests they deem inappropriate or are
coerced into censoring.

With FROST, a private collaborative custodian can hold a key to a multisig
while remaining unaware of the public key (and wallet) which they help
control. By hiding this public key, we solve the issue of existing
collaborative custodians who learn of all wallet transactions even if you
never use them.

Further, in the scenario that we do call upon a private collaborative
custodian to help sign a transaction, this transaction could be signed
**blindly**. Being blind to the transaction request itself and unknowing of
past onchain behavior, these custodians have no practical information to
enact censorship requests or non-cooperation. A stark contrast to today's
non-private collaborative custodians who could very easily be coerced into
not collaborating with users.


Enrolling a Private Collaborative Custodian

Each signer in a FROST multisig controls a point belonging to a joint
polynomial at some participant index.

Participants in an existing multisig can collaborate in an enrollment
protocol (Section 4.1.3 of [1], [2]) to securely generate a new point on
this shared polynomial and verifiably communicate it to a new participant,
in this case a collaborative custodian.

The newly enrolled custodian should end by sharing their own *public* point
so that all other parties can verify it does in-fact lie on the image of
the joint polynomial at their index (i.e. belong to the FROST key). (The
custodian themselves is unable to verify this, since we want to hide our
public key we do not share the image of our joint polynomial with them).


Blind Collaborative Signing

Once the collaborative custodian controls a point belonging to this FROST
key, we can now get their help to sign messages.

We believe it to be possible for a signing server to follow a scheme
similar to that of regular blind Schnorr signatures, while making the
produced signature compatible with the partial signatures from other FROST
participants.

We can achieve this compatibility by having the server sign under a single
nonce (not a binding nonce-pair like usual FROST), which is later blinded
by the nonce contributions from other signers. The challenge also can be
blinded with a factor that includes the necessary Lagrange coefficient so
that this partial signature correctly combines with the other FROST
signatures from the signing quorum.

As an overview, we give a 3rd party a secret share belonging to our FROST
key. When we need their help to sign something, we ask them to send us
(FROST coordinator) a public nonce, then we create a challenge for them to
sign with a blind Schnorr scheme. They sign this challenge, send it back,
and we then combine it with the other partial signatures from FROST to form
a complete Schnorr signature that is valid under the multisignature's
public key.

During this process the collaborative custodian has been unknowing of our
public key, and unknowing as to the contents of the challenge which we have
requested them to sign. The collaborative signer doesn't even need to know
that they are participating in FROST whatsoever.


Unknowing Signing Isn't So Scary

A server that signs arbitrary challenges sounds scary, but each secret
share is unique to a particular FROST key. The collaborative custodian
should protect this service well with some policy, e.g. user
authentication, perhaps involving cooperation from a number of other
parties (< threshold) within the multisig. This could help prevent parties
from abusing the service to "get another vote" towards the multisig
threshold.

Unknowingly collaborating in the signing of bitcoin transactions could be a
legal gray area, but it also places you in a realm of extreme privacy that
may alleviate you from regulatory and legal demands that are now impossible
for you to enforce (like seen with Mullvad VPN [3]). Censorship requests
made from past onchain behavior such as coinjoins becomes impossible, as
does the enforcement of address or UTXO blocklists.

By having the collaborative custodian sign under some form of blind
Schnorr, the server is not contributing any nonce with binding value for
the aggregate nonce. Naively this could open up some form of Drijvers
attacks which may allow for forgeries (see FROST paper [0]), but I think we
can eliminate given the right approach.

Blind Schnorr schemes also introduce attack vectors with
multiple concurrent signing requests [4], one idea to prevent this is to
disallow simultaneous signing operations at the collaborative custodian.
Even though Bitcoin transactions can require multiple signatures, these
signatures could be made sequentially with a rejection of any signature
request that uses anything other than the latest nonce.

Risks may differ depending on whether the service is emergency-only or for
whether it is frequently a participant in signing operations.

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Thanks to @LLFOURN for ongoing thoughts, awareness of enrollment protocols,
and observation that this can all fall back into a standard Schnorr
signature.

Curious for any thoughts, flaws or expansions upon this idea,

Gist of this post, which I may keep updated and add equations:
https://gist.github.com/nickfarrow/4be776782bce0c12cca523cbc203fb9d/

Nick

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References

* [0] FROST: https://eprint.iacr.org/2020/852.pdf
* [1] A Survey and Refinement of Repairable Threshold Schemes (Enrollment:
Section 4.3): https://eprint.iacr.org/2017/1155.pdf
* [2] Modifying FROST Threshold and Signers:
https://gist.github.com/nickfarrow/64c2e65191cde6a1a47bbd4572bf8cf8/
* [3] Mullvad VPN was subject to a search warrant. Customer data not
compromised:
https://mullvad.net/en/blog/2023/4/20/mullvad-vpn-was-subject-to-a-search-warrant-customer-data-not-compromised/
* [4] Blind Schnorr Signatures and Signed ElGamal Encryption in the
Algebraic Group Model: https://eprint.iacr.org/2019/877.pdf
* [5] FROST in secp256kfun:
https://docs.rs/schnorr_fun/latest/schnorr_fun/frost/index.html

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