Montgomery multiplication without final subtraction I am looking for methods to avoid the final subtraction in Montgomery multiplication. I found this paper "A Cryptographic Library for the Motorola DSP56000 " (http://goo.gl/DHePEx) In this paper they have said that we can avoid final subtraction if we keep N(modulus)
Brett just asked &amp; answered this question : Confused about final subtraction of modulus in Montgomery Multiplication, during modular exponentiation

You should increase $R$ exponent by $2$.
If you use $n=1024$ , increase it to be $$n=1024 + 2 = 1026.$$
Recalculate the pre-compute $R'$, based on the new exponent.
$$R' = 2^{(2\cdot 1026)} \bmod(M).$$