6.1 Hashpower attack resistance
The main thrust of this paper surrounds two-way peg using SPV proofs, which are forgeable by a 51%-majority and blockable by however much hashpower is needed to build a sufficiently-long proof during the transfer’s contest period. (There is a tradeoff on this latter point — if 33% hashpower can block a proof, then 67% is needed to successfully use a false one, and so on.)
This is the bit that I don't really agree with (or don't understand properly). The hashpower to block a proof and the hashpower to successfully use a false one will only add up to 100% if the bitcoin client knows the current greatest proof of work on the side chain.
The parent chain won't be monitoring all nodes of all side chains because this would be too burdensome on the bitcoin nodes so it won't always know the longest proof of work chain on the side chain. This will reduce the percentage of hashpower needed to double spend.
Say I try to double spend a coin on the side chain by redeeming it to the parent chain and spending it on the side chain. A block is found with my transaction redeeming it to the parent chain so I produce this to the parent chain with an spv proof and the contest period begins.
Now this block is orphaned and my other transaction, spending on the side chain is valid.
Somebody supplies the block chain with details of the re-org and it now invalidates my transaction redeeming to the parent chain. Now my question is do I have from now until the end of the contest period to try and better this re-org proof? If so I am not trying to better the length of proof of work on the side chain at the end of the contest period, I am trying to better the length of the sidechain proof of work at the time the re-org proof is submitted. I have the whole of the contest period to work away building a proof of work that includes my transaction redeeming the coin to the parent chain but I don't have to beat the longest side chain proof of work I only have to beat the proof of work when the re-org was submitted. Then just before the contest period ends I submit my re-org and validate the transaction redeeming the coin on the parent chain that has been spent on the side chain.
Or does the redemption transaction have to be re-submittted to the parent chain if a re-org is submitted and the contest period starts again? (but then maybe bad actors could submit false re-orgs to cancel redemptions because the parent chain doesn't know the current longest side chain pow)
I'm also concerned that checking the re-org proofs for all side chains would be an extra burden on the parent chain nodes.
Anyway I realise that many of these details might still be being worked out by the designers or have been considered and aren't an issue.
Also I might be completely misunderstanding it.
I don't think that any of these problems could not be overcome and I think side chains are a great idea, I'm just trying to analyse where weak points might be (because this will definitely get analysed by people trying to beat the system anyway) and improve my understanding.