update: shamir secret sharing is post quantum that's good news, and I now suspect that 3 (weak password) probably isn't a problem.
Hmm, the paper I read how-not-to-share-a-secret.pdf is actually about a different scheme to shamir's, that seems to allow sharing multiple sets of secrets at once.
reading Detection and identification of cheaters in (t,n) secret sharing scheme detection-of-cheaters-in-sss.pdf
outlines 3 attacks/problems
- a peer returns an incorrect share by accident (for example, because of a bug)
- malicious peers generating incorrect shares, but without having the chance to see any honest shares first.
- as in 2, except attackers have the chance to see what honest peers reveal first.
3 is obviously a lower bar (thus easier to attack than 2) and is also more relevant to dark-crystal.
Hmm, okay I don't fully understand this paper (too many cryptic math symbols) but they claim they detect cheating in O(1)
and detect who the cheat is in O(j!)
(I think j is the number of cheaters). j factorial is pretty big, but okay since j is small. It's the same as my suggestion would be though. (I need to look at this more though)