Subject: [bitcoin-dev] Fwd: [Lightning-dev] Post-Schnorr lightning txes

From: Bryan Bishop <[email-masked]>
Date: Tue, 20 Feb 2018 16:42:19 -0600

---------- Forwarded message ----------
From: Anthony Towns <[email-masked]>
Date: Mon, Feb 19, 2018 at 4:59 PM
Subject: [Lightning-dev] Post-Schnorr lightning txes
To: [email-masked]

Hi *,

My understanding of lightning may be out of date, so please forgive
(or at least correct :) any errors on my behalf.

I was thinking about whether Greg Maxwell's graftroot might solve the
channel monitoring problem (spoiler: not really) and ended up with maybe
an interesting take on Schnorr. I don't think I've seen any specific
writeup of what that might look like, so hopefully at least some of this
is novel!

I'm assuming familiarity with current thinking on Schnorr sigs -- but all
you should need to know is the quick summary at footnote [0].

So I think there's four main scenarios for closing a lightning channel:

 - both parties are happy to close, do so cooperatively, and can
   sign a new unconditional transaction that they agree on. already fine.
   (should happen almost all of the time, call it 80%)

 - communications failure: one side has to close, but the other side
   is happy to cooperate as far as they're able but can only do so via
   the blockchain and maybe with some delay (maybe 15% of the time)

 - disappearance, uncooperative: one side effectively completely
   disappears so the other side has to fully close the channel on their
   own (5% of the time)

 - misbehaviour: one side tries publishing an old channel state due to
   error or maliciousness, and the other collects the entire balance as
   penalty (0% of the time)

With "graftroot" in mind, I was thinking that optimising for the last
case might be interesting -- despite expecting it to be vanishingly
rare. That would have to look something like:

   (0) funding tx
   (1) ...which is spent by a misbehaving commitment tx
   (2) ...which is spent by a penalty tx

You do need 3 txes for that case, but you really only need 1 output
for each: so (0) is 2-in-1-out, (1) is 1-in-1-out, (2) is 1-in-1-out;
which could all be relatively cheap. (And (2) could be batched with other
txes making it 1 input in a potentially large tx)

For concreteness, I'm going to treat A as the one doing the penalising,
and B (Bad?) as the one that's misbehaving.

If you treat each of those txes as a muSig Schnorr pay-to-pubkey, the
output addresses would be:

   (0) funding tx pays to [A,B]
   (1) commitment tx pays to [A(i),Revocation(B,i)]
   (2) pays to A

(where i is a commitment id / counter for the channel state)

If B misbehaves by posting the commitment tx after revealing the
revocation secret, A can calculate A(i) and Revocation(B,i) and claim
all the funds immediately.

As far as the other cases go:

  - In a cooperative close, you don't publish any commitment txes, you
    just spend the funding to each party's preferred destinations
    directly; so this is already great.

  - Otherwise, you need to be able to actually commit to how the funds
    get distributed.

But committing to distributing funds is easy: just jointly sign
a transaction with [A(i),Revocation(B,i)]. Since B is the one we're
worrying about misbehaving, it needs to hold a transaction with the
appropriate outputs that is:

  - timelocked to `to_self_delay` blocks/seconds in advance via nSequence
  - signed by A(i)

That ensures A has `to_self_delay` blocks/seconds to penalise misehaviour,
and that when closing properly, B can complete the signature using the
current revocation secret.

This means the "appropriate outputs" no longer need the OP_CSV step, which
should simplify the scripts a bit.

Having B have a distribution transaction isn't enough -- B could vanish
between publishing the commitment transaction and the distribution
transaction, leaving A without access to any funds. So A needs a
corresponding distribution transaction. But because that transaction can
only be published if B signs and publishes the corresponding commitment
transaction, the fact that it's published indicates both A and B are
happy with the channel close -- so this is a semi-cooperative close and
no delay is needed. So A should hold a partially signed transaction with
the same outputs:

  - without any timelock
  - signed by Revocation(B,i), waiting for signature by A(i)

Thus, if B does a non-cooperative close, either:

  - A proves misbehaviour and claims all the funds immediately
  - A agrees that the channel state is correct, signs and publishes
    the un-timelocked distribution transaction, then claims A's outputs;
    B can then immediately claim its outputs
  - A does nothing, and B waits for the `to_self_delay` period, signs
    and publishes its transaction, then claims B's outputs; A can eventually
    claim its own outputs

In that case all of the transactions except the in-flight HTLCs just look
like simple pay-to-pubkey transactions.

Further, other than the historical secrets no old information needs
to be retained: misbehaviour can be dealt with (and can only be dealt
with) by creating a new transaction signed by your own secrets and the
revocation information.

None of that actually relies on Schnorr-multisig, I think -- it could
be done today with normal 2-of-2 multisig as far as I can see.

I'm not 100% sure how this approach works compared to the current one
for the CSV/CLTV overlap problem. I think any case you could solve by
obtaining a HTLC-Timeout or HTLC-Success transaction currently, you could
solve in the above scenario by just updating the channel state to remove
the HTLC.

So I believe the above lets you completely forget info about old HTLCs,
while still enforcing correct behavior, and also makes enforcing correct
behaviour cheaper because it's just two extremely simple transactions
to post. If I haven't missed any corner cases, it also seems to simplify
the scripts a fair bit.

Does this make sense? It seems to to me...

So for completeness, it would make sense to do HTLCs via Schnorr --
at least to make them reveal elliptic curve private keys, and ideally
to make them mostly indistinguishable from regular transactions as a
"scriptless script" [1] or "discreet log contract" [2]. (I think, at
least for HTLCs, these end up being the same?)

The idea then is to have the HTLC payment hash be R=r*G, where r is the
secret/payment receipt.

Supposing your current commitment has n HTLCs in-flight, some paying A
if the HTLC succeeds and "r" is revealed, others paying B. We'll focus
on one paying A.

So you succeed by A completing a signature that reveals r to B,
and which simultaneously allows collection of the funds on chain. A
needs to be able to do this knowing nothing other than r (and their own
private keys). So agree to sign to muSig 2-of-2 multisig [A,B]. A and B
generate random values i and j respectively and reveal I=i*G and J=j*G,
and each calculates Q=I+J+R, and they generate partial signatures of a
transaction paying A:

    I, i + H(X,Q,m)*H(L,A)*a
    J, j + H(X,Q,m)*H(L,B)*b

where L = H(A,B) and X = H(L,A)*A + H(L,B)*B as usual. Once A knows r,
A can construct a full signature by adding R, r to the above values,
and B can then determine r by subtracting the above values from signature
A generated.

To ensure B gets paid if the HTLC timesout, they should also sign a
timelocked transaction paying B directly, that B can hold onto until
the channel state gets updated.

And once you're doing payment hashes via ECC, you can of course change
them at each hop to make it harder to correlate steps in a payment route.

I think that when combined with the above method of handling CSV delays
and revocation, this covers all the needed cases with a straightforward
pay-to-pubkey(hash) output, no script info needed at all. It does mean
each HTLC needs a signature every time the channel state updates (B needs
to sign a tx allowing A to claim the output once A knows the secret,
A needs to sign a tx allowing B to claim the output on timeout).

For channel monitoring this is pretty good, I think. You need to
keep track of the revocation info and your secret keys -- but that's
essentially a constant amount of data.

If you're happy to have the data grow by 64 bytes every time the channel
state updates, you can outsource channel monitoring: arrange a formula
for constructing a penalty tx based on the channel commitment tx --
eg, 95% of the balance goes to me, 4% goes to the monitor's address, 1%
goes to fees, there's a relative locktime of to_self_delay/3 to allow me
to directly claim 100% of the funds if I happen to be paying attention;
then do a partial signature with A(i), and then allow the monitoring
service to catch fraudulent transactions, work out the appropriate
revocation secret, and finish the signature.

If your channel updates 100 times a second for an entire year, that's
200GB of data, which seems pretty feasible. (You can't just regenerate
that data though, unless you keep each commitment tx) And it's pretty
easy to work out which bit of data you need to access: the funding
tx that's being spent tells you which channel, and the channel state
index is encoded in the locktime and sequence, so you should only need
small/logarithmic overhead even for frequently updated channels rather
than any serious indexes.

I don't think you can do better than that without serious changes to
bitcoin: if you let the monitoring agency sign on its own, you'd need some
sort of covenant opcode to ensure it sends any money to you; and with
segwit outputs, there's no way to provide a signature for a transaction
without committing to exactly which transaction you're signing.

I was hoping covenants and graftroot would be enough, but I don't
think they are. The idea would be that since the transaction spends to
A(i)+Rev(B,i), you'd sign an output script with A that uses covenant
opcodes to ensure the transaction only pays the appropriate monitoring
reward, and the monitor could then work out A(i)-A and Rev(B,i) and finish
the signature. But the signature by "A" would need to know A(i)+Rev(B,i)
when calculating the hash, and that's different for every commitment
transaction, so as far as I can see, it just doesn't work. You can't
drop the muSig-style construction because you need to be protect yourself
against potential malicious choice of the revocation secret [3].

Summary:

 - Funding txes as 2-of-2 multisig is still great. Convert to
   Schnorr/muSig when available of course.

 - Generate 6+8*n transactions everytime the channel state is updated,
   (n = number of HTLCs in-flight)

   1. Channel state commitment tx, held by A, spends funding tx,
      payable to Schnorr muSig address [A(i),Rev(B,i)], signed by B
   2. Channel fund distribution tx, held by A (CSV), spends (1),
      signed by Rev(B,i)
   3. Channel fund distribution tx, held by B (no CSV), spends (1),
      signed by A(i)
   4. Channel state commitment tx, held by B, spends funding tx
      payable to Schnorr muSig address [B(i),Rev(A,i)], signed by A
   5. Channel fund distribution tx, held by B (CSV), spends (4),
      signed by Rev(A,i)
   6. Channel fund distribution tx, held by A (no CSV), spends (4),
      signed by B(i)

   The fund distribution txs all pay the same collection of addresses:
     - channel balance for A directly to A's preferred address
     - channel balance for B directly to B's preferred address
     - HTLC balance to muSig address for [A,B] for each in-flight HTLC
       paying A on success
     - HTLC balance to muSig address for [B,A] for each in-flight HTLC
       paying B on success
     - (probably makes sense to bump the HTLC addresses by some random
       value to make it harder for third parties to tell which addresses
       were balances versus HTLCs)

   Both (1) and (4) include obscured channel state ids as per current
   standard.

   For each HTLC that pays X on timeout and Y on success:
     a. Timeout tx, held by X, signed by Y, spends from (2)
     b. Timeout tx, held by X, signed by Y, spends from (3)
     c. Timeout tx, held by X, signed by Y, spends from (5)
     d. Timeout tx, held by X, signed by Y, spends from (6)

     e. Success tx, held by Y, signed by X, spends from (2)
     f. Success tx, held by Y, signed by X, spends from (3)
     g. Success tx, held by Y, signed by X, spends from (5)
     h. Success tx, held by Y, signed by X, spends from (6)

     (these should all be able to be SIGHASH_SINGLE, ANYONECANPAY
      to allow some level of aggregation)

 - Fund distribution tx outputs can all be pay2pubkey(hash): HTLCs work
   by pre-signed timelocked transactions and scriptless
   scripts/discreet-log contracts to reveal the secret; balances work
   directly; CSV and revocations are already handled by that point

 - You can discard all old transaction info and HTLC parameters once
   they're not relevant to the current channel state

 - Channel monitoring can be outsourced pretty efficiently -- as little as
   a signature per state could be made to works as far as I can see,
   which doesn't add up too fast.

 - There's still no plausible way of doing constant space outsourced
   channel monitoring without some sort of SIGHASH_NOINPUT, at least
   that I can see

Thoughts?

[4]

Cheers,
aj, very sad that this didn't turn out to be a potential use case for
    graftroot :(

[0] In particular, I'm assuming that:

    - Schnorr sigs in bitcoin will look something like:
        R, r + H(X,R,m)*x

      (where m is the message being signed by private key x, r is a
      random per-sig nonce, R and X are public keys corresponding to r,x;
      H is the secure hash function)

    - muSig is a secure way for untrusting parties to construct an n-of-n
      combined signature; for public keys A and B, it produces a combined
      public key:
        X = H(L,A)*A + H(L,B)*B
      with L = H(A,B)

   See https://blockstream.com/2018/01/23/musig-key-aggregation-
schnorr-signatures.html

[1] https://scalingbitcoin.org/stanford2017/Day2/Using-the-
Chain-for-what-Chains-are-Good-For.pdf
    http://diyhpl.us/wiki/transcripts/scalingbitcoin/
stanford-2017/using-the-chain-for-what-chains-are-good-for/

[2] https://adiabat.github.io/dlc.pdf
    https://diyhpl.us/wiki/transcripts/discreet-log-contracts/

[3] Well, maybe you could request a zero-knowledge proof to ensure a new
    revocation hash conforms to the standard for generating revocation
    secrets without revealing the secret, and have the public key be
    a(i)*G + r(B,i)*G without using the muSig construct, but that would
    probably be obnoxious to have to generate every time you update
    the channel state.

[4] As an aside -- this could make it feasible and interesting to penalise
    disappearance as well as misbehaviour. If you add a transaction
    the B pre-signs, spending the commitment tx A holds, giving all the
    channel funds to A but only after a very large CSV timeout, perhaps
    `to_self_delay`*50, then the scenarios are:

    If A is present:

      - B publishes an old commitment: A immediately steals all the
        funds if active or outsourced misbehaviour monitoring. Whoops!

      - B publishes the current commitment: A publishes its distribution
        transaction and collects its funds immediately, allowing B to
        do likewise

    If A has disappeared:

      - B publises the current commitment and waits a modest amount
        of time, publishes its distribution transaction claiming its
        rightful funds, and allowing A to collect its funds if it ever
        does reappear and still knows its secrets

      - B publishes the current commitment, waits a fair while,
        A reappears and publishes its distribution transactions, both
        parties get their rightful funds

      - B publishes the current commitment, waits an extended period
        of time, and claims the entire channel's funds. If B is
        particularly reputable, and A can prove its identity (but not
        recover all its secrets) maybe B even refunds A some/all of its
        rightful balance

    Perhaps that provides too much of an incentive to try blocking
    someone from having access to the blockchain though.

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