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Date: Fri, 14 Dec 2018 20:48:39 +1000
From: Anthony Towns <aj@erisian.com.au>
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Subject: [bitcoin-dev] Schnorr and taproot (etc) upgrade
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Hi *,

(All the following is heavily informed by talking with other smart people,
and while probably all the clever ideas are theirs, any nonsense and
mistakes are certainly my own. I guess I'll pretend there were Chatham
House rules or something to avoid any blame/responsibility accidently
landing on their shoulders? Anyway, I hope discussing this in public
turns out more useful and productive than disastrous and bikesheddy :)


Rusty wrote "Without a concrete taproot proposal it's hard to make
assertions". I'm not going to offer a completely concrete proposal,
but fwiw, here's my thoughts on what should be included in the segwit v1
proposal, which I think might be concrete enough for discussion purposes:

 - introduce 33-byte v1 witness addresses should encode a secp256k1 ECC
   point (P), spendable either by:

    - a direct schnorr signature (s,R) on that point
      (s*G = R + H(R,P,txdigest)*P), with the 1-byte sighash per the
      other thread indicating exactly what goes into the tx digest, etc

    - a script (s), the witness data for the script (wit(s)),
      with a taproot/merkle path to the script (P,path(S,s)),
      satisfying the taproot condition (Q = P + H(P,S)*G)

 - the taproot scripts should get a version, and since you have to
   provide P anyway in order to spend by a script, you've got 7-bits spare
   in the byte that encodes the evenness/oddness of P, so that gives you
   v1.0 to v1.127 for free. So if we define script version 0 initially,
   and just automatically accept any script with a later version, we
   can soft-fork arbitrary script upgrades without bumping the segwit
   (major) version.

 - we should replace the ECDSA CHECKSIG/CHECKMULTISIG ops with new
   Schnorr ops. A name that's been suggested for the new ops is "CHECKDLS"
   for discrete-log-signature; I'm using that.

   Rather than CHECKMULTISIG, a simple, more general approach seems to
   be "CHECKDLSADD" which takes a signature, a number, and a pubkey,
   and increments the number if the signature is valid, and leaves it
   untouched if not. So "2 of 3 multisig" becomes "0 <p> CHECKDLSADD
   <q> CHECKDLSADD <r> CHECKDLSADD 2 EQ", eg. That means replacing the
   current four CHECK(multi)SIG(verify) opcodes, with three opcodes:
   CHECKDLS, CHECKDLSVERIFY and CHECKDLSADD.

   To make batch verifiability of signatures work, the only acceptable
   invalid signature for CHECKDLS or CHECKDLSADD needs to be an empty
   vector; anything else should fail the script/transaction/block.

 - adding OP_MASK to support script masking via sighash per the other
   thread; note this only matters for the new CHECKDLS opcodes, since for
   direct signatures on the scriptPubKey, there is no script to mask.
   This means it's completely changeable with new script versions,
   if desired.

 - making (almost) all the currently invalid opcodes upgradeable
   with what I'm calling "OP_SUCCESS" semantics [0], so that we have more
   flexibility than OP_NOP gives us. An approach for those semantics
   that seems fairly easy to analyse is to treat script processing as
   going in phases:

      1. tokenise; check push sizes and overall script size
      2. if any OP_SUCCESS appeared; succeed
      3. if banned opcodes appeared; fail (OP_VERIF, OP_VERNOTIF?)
      4. otherwise, run the script; fail if there's an error
      5. if there's exactly one, non-zero item on the stack; succeed
      6. otherwise; fail

   (Obviously an implementation can do these in parallel if that's more
   efficient)

   That way any of the "OP_SUCCESS" opcodes can be replaced by any
   normal opcode (eg addition, a different sort of signature checking,
   push tx or blockchain data to the stack) in a soft-fork; and you
   can easily be sure that the new functionality is a soft-fork (as
   long as you're not trying to change how pushes work)

   [1]

   This even means you could use an OP_SUCCESS opcode to signal an
   upgrade of other opcodes, eg an OP_ARITH64BIT that upgrades OP_ADD
   etc to support arithmetic on 64 bit inputs.

 - and that's it.

I think this is a fairly modest collection of changes:

 signature/address stuff:
   - schnorr
   - new sighash (including "noinput")
   - taproot
   - merkelized-scripts
   - avoid weird CHECKMULTISIG behaviour
 upgradeability:
   - script minor versions
   - OP_SUCCESS

I think there's a good reason to bundle all those together: the signature
stuff go together with a new address version, and the upgradeability
stuff helps reduce the need to do more new address versions.

Well, it's modest at least compared to what's conceivable: there are a
*lot* of other neat ideas that could theoretically be done in the same
soft-fork, but IMHO are better left for later, eg:

 - graftroot, g'root, cross-input signature aggregation
 - non-interactive half-signature aggregation
 - re-enabling opcodes (CAT, MUL, XOR, etc)
 - check-sig-of-msg-on-stack, push txdata, other covenant-y things
 - different cryptosystems (eg, 384 bit curves for better protection
   against future quantum computing advances; conceivably pairing curves?)
 - "EVAL" and similar language features
 - [etc]

As far as how those things could get done in future, this collection of
features leaves four ways to make further improvements:

 - new segwit version (v2-v16)
   (needed for graftroot, signature aggregation, different signature
    systems)

 - different length segwit v1 pubkey
   (could be used to provide a hash instead of the actual taproot point,
    or use a larger ECC curve)

 - new segwit v1 script version (v1.0-v1.127)
   (needed for big redesigns/simplifications of script)

 - additional opcodes (OP_SUCCESS replacement)
   (can be used to re-enable disabled opcodes like MUL/CAT/XOR/etc;
    can be used to add more complicated things like CHECKSTACKDLS,
    or PUSHTXDATA; can be used to try out different signature
    schemes)

I think its worth noting that OP_SUCCESS upgrades could be
developed/deployed in parallel, since you just need to choose an opcode to
take over and (presumably) a versionbit to signal when the new behaviour
gets activated. The other methods require agreeing on everything that's
going to go in the new version, which needs a bit more coordination.

[2] 



Anyway, to get back to the intro sentence, and to give an example of how I
think v1 addresses will work, here's my take on Eltoo in a taproot world:

  Funding tx:
    inputs: <whatever>
    outputs:
      ...
      i. pay to Q = P+H(P,S)G
         P = muSig(A,B)
         S = "MASK <500M> CLTV <P> CHECKDLSVERIFY"
      ...

  Update tx n:
    nlocktime = 500M + n
    inputs:
      1. Funding tx, or Update tx m, m<n; 
           witness: P, (S or Sm),
             sig(P, sighash=in_scriptmask:"MASK VERIF CLTV <P> CHECKDLSVERIFY")
    outputs:
      1. pay to Qn = P+H(P,Sn)G
         Sn = "MASK <500M+n+1> CLTV <P> CHECKDLSVERIFY

  Settlement tx n:
    inputs:
      1. Update tx n (unknown txid); 
	   witness: sig(Qn, sighash=in_scriptpubkey)
           nseq = csv delay
           (note: Qn != Qm unless n=m, because Sn != Sm)
    outputs:
      1: pay A's balance to A
      2: pay B's balance to B
      3..n: HTLC paying to B: see below

  Cooperative close:
    inputs:
      Funding tx, sig(Q, sighash=in_all+out_all)
    outputs:
      1..n: as agreed

(I'm assuming you create "Update tx 0" and "Settlement tx 0" to pay
yourself back if setup fails, prior to publishing the funding tx. The
eltoo paper has a "trigger" phase for that purpose instead, aiui. Also,
these two txs don't actually need to use NOINPUT, because they directly
spend from the funding tx)

As far as the HTLC outputs go... For SHA256 preimages, you prepare
a taproot address Q=P+H(P,SH), where SH is the merkle root for the
tree of two scripts, "<t> CLTV <A> CHECKDLSVERIFY" and "HASH160 <h>
EQUAL <B> CHECKDLSVERIFY". For secp256k1 preimages, your address is
P'=muSig(A,B,n*G) for some value n that just ensures you have different
keys for each htlc, and you prepare two pre-signed transactions, spending
the settlement output (whose txid is unknown), both signed with sighash
committing to the scriptPubKey and a single output. One pays A and has
a partial signature from B and nTimeLock set to the timeout; so A can
complete the signature and claim after the timeout; the other pays B
and has a conditional partial signature from A, which B can complete
upon finding out the preimage.

The settlement and pre-signed-HTLC-spend transactions all make use of
the NOINPUT-commit-to-scriptPubKey varaint in this arrangement; so it
does seem like it's probably useful in practice; scriptless scripts make
the direct-signature path pretty useful.

Cheers,
aj

[0] aka OP_RETURNTRUE https://bitcointalk.org/index.php?topic=1106586.0
    aka OP_RETURNVALID https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2018-March/015838.html

[1] The "drawback" to this approach is that it means that you can't
    partially verify a script if you think you know what the first few
    opcodes mean; so if a script upgrade has happened but your node hasn't
    upgraded, even if you see a transaction in a block with what you
    think is "<p> OP_CHECKDLS OP_SUCCESS", you don't check the signature.

[2] One thing that could be feasible would be to have some simple
    OP_SUCCESS upgrades (like enabling CAT/XOR/etc or adding
    CHECKSTACKDLS) specced, implemented, and tested, and have them
    activate at the same time as schnorr/taproot/etc, while keeping them
    as an independent feature at the BIP/concept/implementation levels.

    The idea there is that if it turns out they're not ready in time,
    schnorr/taproot/etc don't need to get delayed, and the others can
    just be enabled when they're ready later using a separate version bit.
    I'm not sure if there's anyone who's interested in shepherding/doing
    the spec/implementation for any of the more straight-forward features
    like that, though.