---
# System prepended metadata

title: mont mul

---

# mont mul 
<!-- by a const -->

## setup
- N := 2^384
- p is the prime number for the field
- R := N % p 

conver integer $a$ to its montgomery form:

$$\texttt{mont}(a) = a * R % N$$

Task: input $\texttt{mont}(a)$ a variable, and $c:= 9$ (or 3, or 12) is a constant, compute $d := a * c$ and output $\texttt{mont}(d)$.

<!-- ## option 1: convert constant to mont

trivial. 

## option 2:
 -->
 
\begin{align}
\texttt{mont}(d) &:= d * R \bmod N \\
&= c * a * R \bmod N \\
&= c * (a * R \bmod N) \bmod N \\
&= c * \texttt{mont}(a) \bmod N
\end{align}
