I am gonna write down formulas that I know and use to generate RSA keys.

- we choose
`p`

,`q`

`N = p*q`

`f(n)`

=`(p-1)(q-1)`

- choose e such as

- 1 < e < f(n)
- coprime with N, f(n)

- choose d so that
`d * e (mod f(n) ) = 1`

That’s it. With these, if we have `p=2`

and `q=7`

, I succesfully get `d=11`

and `e=5`

which is correct.

Now Imagine, that I only have private key which is `(11,14)`

(`d=11, N=14`

). How do I get `e=5`

. I understand that with `d`

and `N`

, you can’t directly get `e`

, but as RSA works, it tries different variants of `e`

, then checks and if it’s valid, that’s how you get public key from private key.

Can anyone explain to me what steps should I take here to figure out what `e`

could be and then from those, which `e`

should I choose ?