I'm following well with using the shifting method to try out the Montgomery reduction (1st round). However, the computed result is actually equal to:
$$XYR^{-1} \bmod N$$ while the final goal is to obtain the result of
$$XY \bmod N$$
In order to get the final answer, I need to implement an extra step which is
$$(XYR^{-1})(R \bmod N) \bmod N$$
However, What if the product of $(XYR^{-1})(R \bmod N)$ giving me the large integer number?
In this case, how should leverage the same shifting method Montgomery reduction engine until I can obtain the final $Z = XY \bmod N$?
If I repeat the same Montgomery Reduction 2nd round using the product of $(XYR^{-1})(R \bmod N)$, I will just get back the same answer as $(XYR^{-1})$.
May I know what are the missing steps above?
