Re: [bitcoin-dev] Taproot: Privacy preserving switchable scripting

[Chris Belcher <belcher@riseup.net>]

This sounds like a useful idea for improving the privacy of coinswap.
Traditionally coinswap mixing had an anonymity set related to the number
of multisig transactions being used on the blockchain. With the new tech
of Schnorr, MAST and now this Taproot, with sufficient adoption
coinswap's anonymity set could be much higher, potentially including
almost every other on-chain transaction.

[1] https://bitcointalk.org/index.php?topic=321228.0
[2] https://github.com/AdamISZ/CoinSwapCS

On 23/01/18 00:30, Gregory Maxwell via bitcoin-dev wrote:
> Interest in merkelized scriptPubKeys (e.g. MAST) is driven by two main
> areas: efficiency and privacy. Efficiency because unexecuted forks of
> a script can avoid ever hitting the chain, and privacy because hiding
> unexecuted code leaves scripts indistinguishable to the extent that
> their only differences are in the unexecuted parts.
> 
> As Mark Friedenbach and others have pointed out before it is almost
> always the case that interesting scripts have a logical top level
> branch which allows satisfaction of the contract with nothing other
> than a signature by all parties.  Other branches would only be used
> where some participant is failing to cooperate. More strongly stated,
> I believe that _any_ contract with a fixed finite participant set
> upfront can be and should be represented as an OR between an N-of-N
> and whatever more complex contract you might want to represent.
> 
> One point that comes up while talking about merkelized scripts is can
> we go about making fancier contract use cases as indistinguishable as
> possible from the most common and boring payments. Otherwise, if the
> anonymity set of fancy usage is only other fancy usage it may not be
> very large in practice. One suggestion has been that ordinary
> checksig-only scripts should include a dummy branch for the rest of
> the tree (e.g. a random value hash), making it look like there are
> potentially alternative rules when there aren't really.  The negative
> side of this is an additional 32-byte overhead for the overwhelmingly
> common case which doesn't need it.  I think the privacy gains are
> worth doing such a thing, but different people reason differently
> about these trade-offs.
> 
> It turns out, however, that there is no need to make a trade-off.  The
> special case of a top level "threshold-signature OR
> arbitrary-conditions" can be made indistinguishable from a normal
> one-party signature, with no overhead at all, with a special
> delegating CHECKSIG which I call Taproot.
> 
> Let's say we want to create a coin that can be redeemed by either
> Alice && Bob   or by CSV-timelock && Bob.
> 
> Alice has public A, Bob has pubkey B.
> 
> We compute the 2-of-2 aggregate key C = A + B.  (Simplified; to
> protect against rogue key attacks you may want to use the MuSig key
> aggregation function [1])
> 
> We form our timelock script S =  "<timeout> OP_CSV OP_DROP B OP_CHECKSIGVERIFY"
> 
> Now we tweak C to produce P which is the key we'll publish: P = C + H(C||S)G.
> 
> (This is the attack hardened pay-to-contract construction described in [2])
> 
> Then we pay to a scriptPubKey of [Taproot supporting version] [EC point P].
> 
> Now Alice and Bob-- assuming they are both online and agree about the
> resolution of their contract-- can jointly form a 2 of 2 signature for
> P, and spend as if it were a payment to a single party (one of them
> just needs to add H(C||S) to their private key).
> 
> Alternatively, the Taproot consensus rules would allow this script to
> be satisfied by someone who provides the network with C (the original
> combined pubkey), S, and does whatever S requires-- e.g. passes the
> CSV check and provides Bob's signature. With this information the
> network can verify that C + H(C||S) == P.
> 
> So in the all-sign case there is zero overhead; and no one can tell
> that the contract alternative exists. In the alternative redemption
> branch the only overhead is revealing the original combined pubkey
> and, of course, the existence of the contract is made public.
> 
> This composes just fine with whatever other merkelized script system
> we might care to use, as the S can be whatever kind of data we want,
> including the root of some tree.
> 
> My example shows 2-of-2 but it works the same for any number of
> participants (and with setup interaction any threshold of
> participants, so long as you don't mind an inability to tell which
> members signed off).
> 
> The verification computational complexity of signature path is
> obviously the same as any other plain signature (since its
> indistinguishable). Verification of the branch redemption requires a
> hash and a multiplication with a constant point which is strictly more
> efficient than a signature verification and could be efficiently fused
> into batch signature validation.
> 
> The nearest competitor to this idea that I can come up with would
> supporting a simple delegation where the output can be spent by the
> named key, or a spending transaction could provide a script along with
> a signature of that script by the named key, delegating control to the
> signed script. Before paying into that escrow Alice/Bob would
> construct this signature. This idea is equally efficient in the common
> case, but larger and slower to verify in the alternative spend case.
> Setting up the signature requires additional interaction between
> participants and the resulting signature must be durably stored and
> couldn't just be recomputed using single-party information.
> 
> I believe this construction will allow the largest possible anonymity
> set for fixed party smart contracts by making them look like the
> simplest possible payments. It accomplishes this without any overhead
> in the common case, invoking any sketchy or impractical techniques,
> requiring extra rounds of interaction between contract participants,
> and without requiring the durable storage of other data.
> 
> 
> [1] https://eprint.iacr.org/2018/068
> [2] https://blockstream.com/sidechains.pdf Appendix A
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