With federated peg there is a real side-chain, including mining, consensus rules etc and then the federated peg servers act as a protocol adaptor - the peg servers are full nodes on the side-chain, and pegged coins are paid to their multisig address (eg 10 of 15) and the side-chain fullnodes and miners watch the multisig address on the bitcoin network, and coins arriving there count as a peg to put coins into the side-chain; and when the side-chain hashrate majority approves a return peg to reanimate a coin, the federated pegs are watching the side-chain as they are full nodes so they release the funds to the address the return peg tells them to.
Now obviously the limitation is if >= 10 of the federated peg servers are hostile or compromised, they could take the coin without approval of the side-chain. But short of that it is the side-chain consensus and miners etc that arbitrate what coins move across the peg.
[...] side-chain concepts are new to me and I want to make sure I understand. Correct me if I'm wrong, but a federated peg would be easier to implement than a SNARK peg or a SPV peg, right? No hard or soft fork?
Right no changes needed.
But on the other hand, am I correct to assume that the failure points of a federated peg are theoretically more dangerous?
Yes failure modes kick in if the threshold of federated servers is compromised or untrustworthy, and could be worse as there is more flexibility on coding smart-contract enforced limits with the spv-peg (or for now hypothetical snark-peg).
Moreover, as one whose company is currently developing private mining hardware, how do these peg/token side chains directly affect the bitcoin mining protocol (in terms of the block header's nonce, merkle root, etc), if at all? Absent a fork, nothing changes?
Nothing changes for hw miners. Any changes are in the pool (local or remote) the miners are connected to - which fullnodes its getting merkle information from.
I'd say outside of side-chains, and just in general, a soft-fork (or even 99% of conceivable hard-forks) the mining algorithm would not change. The miners just need some basic formatting about headers to continue to work and they're fine as is.
I think the unlikely because of self-preservation, but main way hypothetically you'd see mining change is if miners got far too centralised and it became an disruptive day to day problem for bitcoin security, and mining operators rejected or ignored complaints, the economic majority could eventually fell forced to defensively break the current deployed ASICs with a minor software change. The so-called 'big-red-button'. Its not fun in any direction because it leads to erratic hashrate risks from the hash-rate shake up as GPUs & FPGAs are reshuffled and revised ASICs fast-tracked.
Adam