0
$\begingroup$

In this paper Simplifying Quotient Determination in High-Radix Modular Multiplication, the authors have proposed to replace the original modulus $M$ in Montgomery Multiplication $ABR^{-1} \bmod{M}$ to a new value $\tilde{M} = (M' \bmod{2^k}) M$, where $(-MM')\bmod{2^k}=1$.

The new modulus $\tilde{M}$ is used to improve the original Montgomery multiplication algorithm but also gives an output in the range of $[0, 2\tilde{M})$ instead of the range $[0, 2M)$ I actually need. However, the paper does not mention how to convert the result back to the desired range. What should I do to retrieve the actual result of $ABR^{-1} \bmod{M}$?

$\endgroup$
  • $\begingroup$ taking $\mod M$ doesn't enough? $\endgroup$ – kelalaka Feb 10 at 20:22

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.