Re: [bitcoin-dev] Statechain implementations

[Bob McElrath <bob@mcelrath.org>]

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Big picture, it seems to me this idea is workable and very interesting. I see
three likely enhancements that will be necessary or desirable:
    1. Atomic swap of multiple UTXOs, and binary decomposition of value in lots
    2. Key exchange ("addresses") to facilitate a secure comms path from 
        sender -> receiver
    3. (Optional) single-use seals to close old state

(1) It's unlikely that a party sending a UTXO to another party will have a UTXO
of exactly the right size that's needed, already locked into the statechain. If
he has to create the UTXO first and then lock it into the statechain, the
statechain solution is no better than an on-chain send. And once the receiver
has the UTXO, it's unlikely that he will want to send exactly that same amount
to another receiver later. This isn't a problem in Lightning where amounts can
be arbitrarily updated. As a consequence, I think Lightning is more valuable for
small-value payments, and statechains will be more valuable for larger values.

The natural solution is to decompose your outputs in a binary decomposition,
having e.g. UTXOs with 1048576 satoshis, another with 2097152 satoshis, and so
on. Then when I want to send, I select the appropriate UTXOs as a binary
decomposition of the value I want to send, with a "lot size" of 1048576
satoshis, or the dust limit. The notion of "lots" like this is common in
traditional markets...many stocks are bought and sold in lots of 100, and forex
is traded in lots of $100,000. Users of a statechain therefore need log(V)
available UTXOs locked into the statechain, where V is their value in BTC.
Having fixed lot sizes like this also makes coinjoin-type uses more viable. The
statechain could also assist in dividing a UTXO into two utxos of the next lot
size down, so that I have the right UTXOs to hit the value I want to send.

This means that the statechain now has to *atomically* swap multiple UTXOs. In
principle, it should be possible for a statechain to circumvent the
Pagnia-Gärtner theorem[1] as it is a trusted third party, but guaranteed output
delivery will still be a problem. If a statechain can do this, it is also
capable of performing such swaps across two blockchains, creating the
execution/clearing element (but not order book) for a DEX. This same mechanism
can also be used to pay the SE for its service through a different UTXO than the
one being transferred.

Second (2), the steps in Tom's protocol presuppose a secure communications path
from the sender's wallet to the receiver's. This is probably not practical for a
myriad of reasons, but this data can be relayed through the SE if it is
encrypted for the target. This implies a new kind of "address" or "payment
request" that identifies the IP of the SE in use, pubkey of the
sender/recipient, and amount. If sender and receiver have each other's pubkeys
through another channel, as addresses/lightning payment requests are used today,
they can perform a Diffie-Hellman round mediated by the SE to establish a secure
communications path for the rounds of the protocol. Piggybacking on the
Lightning p2p network might be another option.

Third (3), a logical enhancement would be to use some kind of single-use seal,
which is "opened" when the UTXO is created or transferred, and "closed" when it
is transferred again. Thus a receiver can ensure that the sender is the holder
of current state and not some old state.  It's a good idea from Peter Todd, and
Tom's Mainstay[2] may be a way to do it. The SE itself can maintain a rolling
single-use seal Merkle root, periodically timestamped into Bitcoin for faster
time resolution than Bitcoin, if you trust the SE but not your counterparty
(which is the trust assumption present in the first place). Getting Bitcoin
itself to reject backout transactions from closed seals is another problem...but
having a single-use seal implementation involved is a start.

.. [1] https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.7863

.. [2] https://mainstay.xyz

Tom Trevethan via bitcoin-dev [bitcoin-dev@lists.linuxfoundation.org] wrote:
> Hi all,
> 
> We are starting to work on an implementation of the statechains concept (https:
> //medium.com/@RubenSomsen/
> statechains-non-custodial-off-chain-bitcoin-transfer-1ae4845a4a39), with
> particular interest in using the protocol enable the change of ownership
> (novation) of an individual position in an active discreet log contract (DLC)
> without an on-chain transaction, and without needing the cooperation of the
> counterparty. The protocol as outlined by Ruben requires features not currently
> available in Bitcoin (like SIGHASH_NOINPUT), and it is uncertain when (or even
> if) this will be added. So we are looking at variants that would work with
> current Bitcoin functionality, and it would be good to get some feedback on
> them.
> 
> There are two main modifications we are looking at:
> 1. Instead of an eltoo-based backup/refund transaction (enabling the current
> owner to claim the UTXO in case the statechain entity disappears) we propose
> using a decrementing nLocktime for backup transactions as the output changes
> hands. Here, the first owner gets a backup transaction with an nLocktime at
> some future height (h0), then the next owner gets a backup transaction with
> nLocktime (h0-c) where c is a confirmation window. This approach has the
> downside of limiting the lifetime of the UTXO, but it also doesn't require the
> current owner to be always online.
> 
> 2. Replacing the 2-of-2 multisig output (paying to statechain entity SE key and
> transitory key) with a single P2(W)PKH output where the public key shared
> between the SE and the current owner. The SE and the current owner can then
> sign with a 2-of-2 ECDSA MPC. This enables each owner to generate their own
> private key share, and the SE changes their key share at each change of
> ownership (with the shared public key remaining the same). This works as
> follows (.G is EC point multiplication, * is scalar multiplication):
> 
> KeyGen:
> 
> a. Owner 1 generates private key share o1 then calculates the corresponding
> public key of the share O1 and sends it to the SE: O1 = o1.G
> b. The SE then generates a private key: s1 (the SE private key share),
> calculates the corresponding public key and sends it to Owner 1: S1 = s1.G
> c. Both SE and Owner 1 then multiply the public keys they receive by their own
> private key shares to obtain the same shared public key P (which corresponds to
> a shared private key of p = o1*s1): P = o1.(s1.G) = s1.(o1.G)
> d. Owner 1 creates a funding transaction (Tx0) to pay an amount A to the
> address corresponding to P (but doesn't sign it).
> e. Once Owner 1 and SE cooperatively sign the first backup transaction, Owner 1
> then signs and broadcasts the deposit transaction Tx0.
> 
> Transfer from Owner 1 to Owner 2:
> 
> a. Owner 2 generates two private keys: o2 (the new owner UTXO private key
> share) and b2 (the new owner refund private key).
> b. The SE generates a temporary blinding nonce x and calculates the value x*s1
> and sends this securely to Owner 2.
> c. Owner 2 then multiplies this received value by the modular inverse of o2
> (o2_inv) and then sends this value (x*s1*o2_inv), to Owner 1.
> d. Owner 1 then multiplies this received value by the key share o1 and sends
> the resulting value (x*s1*o2_inv*o1) to the SE.
> e. The SE then multiplies this received value by the modular inverse of the
> temporary nonce (x_inv) to obtain x*s1*o2_inv*o1*x_inv. This cancels the
> blinding nonce x to give s1*o2_inv*o1. This value, when multiplied by the new
> owner key share o2 equals the original shared private key s1*o1.
> f. The SE then sets this value equal to s2 = s1*o2_inv*o1 and deletes s1. s2
> and o2 are now the key shares of `P` and can be used to colaboritively sign
> (with 2P ECDSA). So long as the SE delets s1, the old owner key share (o1) is
> of no use in deriving or co-signing with the full shared private key, and is
> invalidated.
> g. The shared public key P remains unchanged, but the corresponding private key
> (which no individual party ever has knowledge of or can derive) can only be
> determined from the key shares of the SE and Owner 2 (i.e. P = s2*o2.G).
> h. Owner 2 then calculates their backup public key (B2 = b2.G) and sends it to
> the SE.
> i. The SE creates a backup transaction (Tx2) that pays the output of Tx0 to the
> address corresponding to B2 , with `nLockTime` set to a block height h0 - c0,
> where c0, is a confirmation time sufficient to guarantee that Tx2 can be
> confirmed in the blockchain before Tx1 (therefore making Tx1 invalid).
> j. Owner 2 and the SE then cooperate to sign Tx2 with shared key (P) using the
> 2P ECDSA protocol, which Owner 2 then saves.
> 
> The principle of the logic of the key transfer is that the two separate key
> shares are updated, but the full shared private key (which no-one knows)
> remains the same. The new owner chooses a new secret value for their private
> key share, and this (along with the private key share of the previous owner) is
> utilized by the SE to update their share. The use of the nonce (x) prevents any
> of the participants from determining any information about each others secret
> keys. In this way Owner 2 cannot determine s1 from x*s1, Owner 1 cannot
> determine s1 or o2 from x*s1*o2_inv and the SE cannot determine o1 or o2 from
> x*s1*o2_inv*o1.
> 
> This transfer protocol can be repeated to transfer the ownership to new owners.
> Each time the SE key share sX is updated, the previous key shares become
> invalid and are of no use even if the current key share is subsequently
> revealed. The SE still needs to be trusted to delete the old key share, but
> this protocol removes the risk the the SE can be hacked by a previous owner to
> steal the funds.
> 
> Any comments on the above would be greatly appreciated.
> 
> Tom
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--
Cheers, Bob McElrath

"For every complex problem, there is a solution that is simple, neat, and wrong."
    -- H. L. Mencken 


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