# Small e

Last updated

Last updated

If $e$ is sufficiently small, the exponent is ineffective at encrypting $m$.

Let's say $m^e<N$; in this case, we can simply take the $e$th root of $c$. For example, if $e=3$, then we can calculate $m = \sqrt[3]c$.

If $m^e > N$ then this is a *bit* more secure, but we can progressively add more multiples of $N$ until the cube root gives us a valid answer:

$m = \sqrt[3]{c + kn}$

Python

In Python we can use the `gmpy3`

`iroot`

function: