I saw this awesome video which shows how encryption works using "discrete logarithm".
The example says: $3^x\mod17$. I understood that $3$ is called “generator”, because it has no "straight" root and when used with any exponents it walks through entire clock (till $17$ in that case).
- Would saying $3^x \mod 449825$ make it any weaker, easier to crack, or anything alike? Is there anything I should watch out for when choosing that number?
- If it's a logarithm, why is it the function having $\mod x$ in it? I have $\log(x)$ on my calculator, not $\mod x$. Is it correct that $\mod x$ stands for modulo?