Thanks Greg!

I'd be hesitant to deploy a MAST proposal without this clever application of pay-to-contract-hash now! Looks like the overhead over a more-naive MAST construction is rather trivial, too!

Matt

On January 23, 2018 12:30:06 AM UTC, Gregory Maxwell via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> 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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