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By the time you arrive at the current state-of-the-art (and a lattice problem, or other hard problem, worth stating), the answer would be very off-topic to the question.. In any case, it seemed worth answering the dangling question from two years ago.
The question, as-asked: "Would someone care to share with us the problem about lattices that is alluded to here?" ...is difficult to answer directly. The point is that there is no hard lattice problem underlying the proposed scheme's security.
Also, if anyone knows of a technique or paper/set of papers that could be useful for approaching this and would link it in comments, I would be very appreciative as well!