RSA Cheat Sheet

Setup

$p=$ random prime number

$q=$ random prime number

$n=p\ast q$

$\Phi \left(n\right)=(p-1)(q-1)$ (this is called the totient function)

$e=$ some number smaller than $\Phi \left(n\right)$ that's coprime with it (shares no factors)

Calculate d with:

$de=1\mathrm{mod}\Phi \left(n\right)$

Public key: $n,e$

Private key: $p,q,d$

$m=$ message, $c=$ ciphertext

Encryption

$c=m^e\mathrm{mod}n$

Decryption

$m=c^d\mathrm{mod}n$

Signing

$s$ is signature

$s=m^d\mathrm{mod}n$

Verification

Verify by checking if $s^e=m$