Comparison Of Integers Using Number Theoretic Transforms

Question

I have been working on a project recently that involves representing integers using DFT-like transforms. Specifically, I am using a number theoretic transform (NTT). Essentially, I break a number into a vector of its digits ( 0 padded such that the vector has a power of 2 length ). For example, the integer 123 may correspond to <3, 2, 1, 0>. I then perform a NTT on that vector. The process is similar to the first part of the Schönhage–Strassen algorithm. This allows for multiplication, addition, and subtraction in linear time. I would like to find an efficient way to compare these two integers without taking the vectors inverse transform. Is this possible? Do you know of any such way to do this? Thanks!