The paper has not yet been peer-reviewed, so some caution is warranted. It isin mathematics to disseminate research results before they have undergone peer review.
In our paper, we use FFTs with 1,729 dimensions. This is tricky to visualise, but mathematically no more troublesome than the 2-dimensional case. On the other hand, we are hopeful that with further refinements, the algorithm might become practical for numbers with merely billions or trillions of digits. If so, it may well become an indispensable tool in the computational mathematician's arsenal.
Forget numbers (almost) and even more obscure Log and use lines and dots instead. See the Japanese Multiplication Method YouTube
My calculator does it easier and quicker!
Taking the log of the numbers, adding them together and then the inverse log for the result would be order N (for the addition) assuming the log tables are already available. I learned this in grade 7 before calculators were available. Blew my young mind. Now have a PhD in maths.