Hi dlc-dev and bitcoin-dev,
tl;dr OP_CTV simplifies and improves performance of DLCs by a factor of *a lot*.
## Introduction
Dryja introduced the idea of Discreet Log Contracts (DLC) in his
breakthrough work[1].
Since then (DLC) has become an umbrella term for Bitcoin protocols
that map oracle secret revelation to an on-chain transaction which
apportions coins accordingly.
The key property that each protocol iteration preserves is that the
oracle is an *oblivious trusted party* -- they do not interact with
the blockchain and it is not possible to tell which event or which
oracle the two parties were betting on with blockchain data alone.
`OP_CHECKTEMPLATEVERIFY` (CTV) a.k.a. BIP119 [2] is a proposed
upgrade to Bitcoin which is being actively discussed.
CTV makes possible an optimized protocol which improves DLC
performance so dramatically that it solves several user experience
concerns and engineering difficulties.
To me this is the most compelling and practical application of CTV so
I thought it's about time to share it!
## Present state of DLC specification
The DLC specifications[3] use adaptor signatures to condition each
possible payout.
The protocol works roughly like this:
1. Oracle(s) announce events along with a nonce `R` for each event.
Let's say each event has `N` outcomes.
2. Two users who wish to make a bet take the `R` from the oracle
announcement and construct a set of attestation points `S` and their
corresponding payouts.
3. Each attestation point for each of the `N` outcomes is calculated
like `S_i = R + H(R || X || outcome_i) * X` where `X` is the oracle's
static key.
4. The users combine the attestation points into *contract execution
transaction* (CET) points e.g `CET_i = S1_i + S2_i + S3_i`.
Here `CET_i` is the conjunction (`AND`) between the event outcomes
represented by `S1_i, S2_i, S3_i`.
5. The oracle(s) reveals the attestation `s_i` where `s_i * G = S_i`
if the `i`th is the outcome transpired.
6. Either of the parties takes the `s_i`s from each of the
attestations and combines them e.g. `cet_i = s1_i + s2_i + s3_i` and
uses `cet_i` to decrypt the CET adaptor signature encrypted by `CET_i`
and broadcast the transaction.
## Performance issues with DLCs
In the current DLC protocol both parties compute:
- `E * N` attestation points where `E` is the number of events you
are combining and `N` is the number of outcomes per event. (1 mul)
- `C >= E * N` CET adaptor signatures and verify them. (2 mul -- or
with MuSig2, 3 muls).
Note that the number of CETs can be much greater than the number of
attestation points. For example,
if an oracle decomposes the price of BTC/USD into 20 binary digits
e.g. 0..(2^20 -1), you could have
`E=20,N=2,C=2^20`. So the biggest concern for worst case performance
is the adaptor signatures multiplications.
If we take a multiplication as roughly 50 microseconds computing
MuSig2 adaptor signatures for ~6000 CETs would take around a second of
cpu time (each) or so.
6000 CETs is by no means sufficient if you wanted, for example, to bet
on the BTC/USD price per dollar.
Note there may be various ways of precomputing multiplications and
using fast linear combination algorithms and so on but I hope this
provides an idea of the scale of the issue.
Then consider that you may want to use a threshold of oracles which
will combinatorially increase this number (e.g. 3/5 threshold would
10x this).
You also would end up sending data on the order of megabytes to each other.
## committing to each CET in a tapleaf with CHECKTEMPLATEVERIFY
What can we do with OP_CTV + Taproot to improve this?
Instead of creating an adaptor signature for every CET, commit to the
CET with OP_CTV in a tapleaf:
```
CHECKTEMPLATEVERIFY CHECKSIG
```
When the oracle(s) reveals their attestations either party can combine
them to get the secret key
corresponding to `CET_i` and spend the coins to the CET (whose CTV
hash is `CET-hash`) which
distributes the funds according to the contract.
This replaces all the multiplications needed for the adaptor signature
with a few hashes!
You will still need to compute the `CET_i` which will involve a point
normalisation but it still brings the computational cost per CET down
from hundreds of microseconds to around 5 (per party).
There will be a bit more data on chain (and a small privacy loss) in
the uncooperative case but even with tens of thousands of outcomes
it's only going to roughly double the virtual size of the transaction.
Keep in mind the uncooperative case should hopefully be rare too esp
when we are doing this in channels.
The amount of data that the parties need to exchange is also reduced
to a small constant size.
## getting rid of combinatorial complexity of oracle thresholds
Now that we're using script it's very easy to do a threshold along
with the script. e.g. a 2/3:
```
CHECKTEMPLATEVERIFY
CHECKSIG
CHECKSIGADD
CHECKSIGADD
2 EQUAL
```
The improvement here is that the amount of computation and
communication does n
