I am self-studying MIT6.042j Mathematics for Computer Science. And I have copied the below text from the reading of chapter 04:
The Nazis see only the encrypted message m* = m.k, so recovering the original message m requires factoring m*.
Could you explain how we can decrypt the encrypted message? I did not understand what does it mean that
recovering the original message m requires factoring m*.
Assuming $m^*=m\times k$ where $m$ and $k$ are both large primes, a recipient of the encrypted message $m^*$ who knows the secret key $k$ recovers the message $m$ by computing $m=\frac{m^*}{k}$. An adversary who is ignorant of $k$ but intercepts $m^*$ can recover both $m$ and $k$ if $m^*$ can be factored. See Chapter 1 here.