Comment by adamvenis
I think I get it. You're using the Ring isomorphism from the Chinese Remainder Theorem to do "parallel computation". This is the same principle as how boolean algebra on binary strings computes the pairwise results of each bit in parallel. Unfortunately, there's no free lunch - if you want to perform K operations on N-bit integers in parallel, you still need to work with (K * N)-bit-wide vectors, which is essentially what SIMD does anyway.
I’m also unsure where finite fields are coming into play. Finite fields have orders that are prime powers, and the author is talking about a “finite field” of order 7x9x11. But if we aren’t dealing with fields, why is the author mentioning plans for implementing division? It definitely needs more explanation but I’m not sure if the idea is coherent.