Good morning Itay, Ittay, and Matan,
I believe an unstated assumption in Bitcoin is that miners are short-sighted.
The reasoning for this assumption is:
* Deployment of new mining hardware controlled by others may occur at any time you do not control.
* Thus, any transactions you leave on the table are potentially taken by somebody else and not by you.
* Sudden changes in hashpower distribution may reduce your expected future earnings, so any future theoretical earnings should be discounted (*in addition to* expected return-on-investment on getting money you can invest *now*).
Our analysis assumes constant difficulty, i.e., no significant changes of the miners set. Indeed, hash-rate changes typically occur at a much larger granularity than your average HTLC timeout. For instance, we noticed plenty of lightning nodes use timeouts of a day. So, we do not consider optimization at infinity, just a day ahead, and within this time frame all the factors you mentioned are not expected to dramatically change.
That being said, it would be interesting to analyze the effect of miners joining during the HTLC duration. Intuitively, this shouldn’t affect the results, as those new miners have the same incentive to wait for the higher-paying tx.
It also strikes me that, in a world with RBF and CPFP, the same endpoint (i.e. miners earn the entire fund of the HTLC) is achieved by existing HTLCs, without the additional branch and script opcodes needed by MAD-HTLC.
For example, if an HTLC is confirmed but the hashlock-claiming transaction is not being confirmed (because miners are holding it up because Bob is offering a much higher fee in the future for the timelock-claiming transaction), then Alice can, regardless of the reason why it is not being confirmed, bump up the fee with RBF or CPFP.
If the fee bump offered by Alice is sufficiently large, then miners will start re-preferring the Alice hashlock transaction.
To counter this, Bob has to bid up its version higher.
As the timeout approaches, Alice can bump up its fee until it is just 1 satoshi short of the total fund.
It is rational for Alice to do so since at timeout, it can expect to lose the entire fund.
In order for Bob to win, it has to beat that fee, at which point it equals or exceeds the total fund, and miners get the total fund (or more).
Knowing this end-point, rational Bob will not even begin this game.
I think this research considers these two endpoints to be distinct:
* Bob misbehaves and the entire fund is punished by miners, leaving miners with the fund and Alice and Bob without money (MAD-HTLC).
* Bob misbehaves, Alice counters, and the ensuing fee war leads to fees approaching the fund value, leaving miners with the fund and Alice and Bob without money (standard HTLC).
But in practice I think both endpoints are essentially equivalent.
These are not the same scenario, since in HTLC there is a race between Alice and Bob. Alice might not wish to pay the full HTLC amount once she sees Bob is trying to cheat. She could wait until close to the timeout so as to reduce the time Bob can respond. Of course Bob would do the same. So this is an actual race, and Bob takes no risk since his payment is all from the HTLC amount. Mutual destruction is only assured under certain assumptions in HTLC. MAD-HTLC achieves security without relying on such assumptions.
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What MAD-HTLC can do would be to make different claims:
* Inputs:
* Bob 1 BTC - HTLC amount
* Bob 1 BTC - Bob fidelity bond
* Cases:
* Alice reveals hashlock at any time:
* 1 BTC goes to Alice
* 1 BTC goes to Bob (fidelity bond refund)
* Bob reveals bob-hashlock after time L:
* 2 BTC goes to Bob (HTLC refund + fidelity bond refund)
* Bob cheated, anybody reveals both hashlock and bob-hashlock:
* 2 BTC goes to miner
This is an actual improvement over HTLC: Bob misbehavior leads to loss of the fidelity bond.
The above cases can be assured by requiring both Alice and Bob to sign in the alice-hashlock branch, so that the splitting of the fund is enforced, and SegWit signing so that the dependent transaction is signed before the HTLC-funding transaction is.
It can also be implemented with `OP_CHECKTEMPLATEVERIFY`.
The cases you present are exactly how MAD-HTLC works. It comprises two contracts (UTXOs):
* Deposit (holding the intended HTLC tokens), with three redeem paths:
- Alice (signature), with preimage "A", no timeout
- Bob (signature), with preimage "B", timeout T
- Any entity (miner), with both preimages "A" and "B", no timeout
* Collateral (the fidelity bond, doesn't have to be of the same amount)
- Bob (signature), no preimage, timeout T
- Any entity (miner), with both preimages "A" and "B", timeout T
Only Bob initially knows preimage "B", and is required to reveal it if he wishes to get the Deposit tokens.
Consider first the case where Alice publishes preimage "A": Bob can safely publish preimage "B" and get both the Deposit and Collateral tokens after the timeout.
Now, consider the case where Alice does not publish preimage "A": If Bob publishes preimage "B" he gets nothing (and so does Alice - this is the mutual assured destruction), and if he doesn't, he gets the Collateral tokens.
Best,