The logic here is that the author's credibility would be ruined if this turned out to be a lie. What reason would he have for taking that risk?

No, that was not the claim. My understanding of your parent's post is that he claimed that the research was real scientific research (which may be wrong), not a hoax, without expressing any opinion about the validity of the claims.

If $RANDOMDUDE says something is bullshit without having looked at the research and $PROVENEXPERT after a lot of research says it is not, it doesn't mean the expert is right. The facts should stand on their own, regardless of who made them. However, it means $RANDOMDUDE's opinion is completely uninformed and the research is worth looking into.

Appealing to authority is only a fallacy if the authority isn't actually an authority / is considered infallible. This doesn't seem to be the case here.

If you can't bother to understand the work then heuristics are your best bet. In this case, the authors are leading academics from good computer science departments. This makes the probability of the paper being an outright hoax very low. They would be risking their careers and the respect of their peers - and for what exactly? Shamir in particular is already at the top of the game (full professor + turing award + many millions of dollars from royalties).

Now, mistakes CAN happen. But in this case, it would be very hard to make one. If they built a system that reconstructs the cryptographic key then you could compare the keys on both sides.

Indeed, but his track record isn't absolutely perfect if you remember his misguided analysis of the Bitcoin blockchain, a paper which was subsequently withdrawn[1].

1. https://news.ycombinator.com/item?id=6804440