Date: Wed, 04 Mar 2020 23:29:09 +0000
To: Lloyd Fournier <lloyd.fourn@gmail.com>,
 Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
From: ZmnSCPxj <ZmnSCPxj@protonmail.com>
Reply-To: ZmnSCPxj <ZmnSCPxj@protonmail.com>
Message-ID: <tXbP-9UVzs4Je3MdjTYAbm0ZWVMctlhY15v6_G8CCRnaWJjo8VU8h2WDfUSiqnWl8rQa0zbrsupNRNtss0gDFjMiqwNil_ahiqSraICAP9Q=@protonmail.com>
In-Reply-To: <CAH5Bsr2m3+kN67h0Dd+60-i3WCnCRXr_ywzub5_OV=UxxzN3hQ@mail.gmail.com>
References: <CAH5Bsr2m3+kN67h0Dd+60-i3WCnCRXr_ywzub5_OV=UxxzN3hQ@mail.gmail.com>
Feedback-ID: el4j0RWPRERue64lIQeq9Y2FP-mdB86tFqjmrJyEPR9VAtMovPEo9tvgA0CrTsSHJeeyPXqnoAu6DN-R04uJUg==:Ext:ProtonMail
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: quoted-printable
Subject: Re: [bitcoin-dev] Hash function requirements for Taproot
Precedence: list

Good morning LL,

Thank you very much for this work, it seems quite interesting.

> 5. You can completely circumvent this result by using coin-tossing rather=
 than MuSig for the key generation protocol. In most cases this doesn't eve=
n add any extra rounds of communication since you are doing 3-round coin to=
ssing to choose the R values for the signatures that spend from the joint o=
utput anyway. You can just toss your public keys in parallel.

I am uncertain what you mean here by "coin-tossing".
From the comparison to MuSig, I imagine it is an interactive key generation=
 protocol like this:

* Everybody generates fresh keypairs.
* Everybody sends the hash of their pubkey to everyone else.
* After receiving a hash of pubkey from everyone else, everybody sends thei=
r pubkey to everyone else.
* They add all their pubkeys to generate the aggregate key (and if using Ta=
proot, use it as the internal key).

Is that correct?

In any case, the comparison to MuSig signing appears to imply interactive k=
ey generation.
The advantage of MuSig is that it requires no interactivity for key generat=
ion of n-of-n (I am told it requires interactivity to generate k-of-n).

However, it can generally be pointed out that, before you put anything into=
 an n-of-n, you would damn well sure want to have *some* assurance that you=
 can get it out later.
So in general you would need coordination and interaction anyway to arrange=
 getting into an n-of-n in the first place.

On the other hand, it would be best to have at least some minimum of privac=
y by always interacting over Tor and having a Tor .onion address, which has=
 absolutely horrid latency because human beings cry when peeling onions.
So in general reducing the latency by reducing communication rounds is bett=
er in general.
Counter to this, assuming you use an n-of-n in an offchain protocol of some=
 sort, the number of communication rounds to generate the aggregate key may=
 be dwarfed by the total number of communication rounds to create signature=
s to update the offchain protocol.
Counter counter to this is that one plan for reducing communications rounds=
 for creating signatures during offchain operation is to (haha) use a Tapro=
ot with an n-of-n internal key and a tapscript that has n `OP_CHECKSIG` ope=
rations, so that for normal operation you just toss individual signatures a=
t each other but at termination of the offchain protocol you can do the hea=
vy MuSig-style signing with the n-of-n aggregate key.

Regards,
ZmnSCPxj