Ok, so coin age would be your DoS countermeasure?
Note that attackers don't actually have to spend that input if they disrupt the protocol. They can use the same one over and over, even many times simultaneously.
PoW could be an option where participants can set a minimum PoW accepted and a maximum PoW they're themselves willing to perform. So for example if 10 people all have 2^15 work within their range of acceptable PoW (one has 2^15 as their lowest, another as their highest, they'll all generate a common input for PoW and start working on it. Then they start this scheme with the SMPC. That would indeed make the attack costly for somebody trying to break the scheme for as many as possible (DoS) and would make Sybil very costly.
Upthread earlier today I proposed a fee for not completing the transaction. I guess you are not proposing that because of timeouts when the participant can't complete but not due to malice?
Thus you propose PoW an a resource cost, hoping this will rate limit.
Hmm. But the rate limiting has to be severe enough that the adversary can't basically shut down transactions (if all are going to be mixed by default which is what I want) entirely, so I am thinking there needs to be a much more severe cost on the adversary.
All costs that fall on the adversary will also fall on the honest participants, but asymmetrically because the adversary will always incur the cost and the participant will only incur it on network timeout.
It isn't certain that you'd be able to tell WHICH input that the attacker used, at least not with my scheme where you hide who's using what input. Revealing who's using what input might not be optimal if a user want to use inputs already tied to himself AND some inputs that aren't already, and doesn't want the unlinked ones to become linked to him.
Send all inputs to one key first.