# Padding on RSA signature and RSA encryption

Why use a random padding on RSA encryption and not on RSA signature?

For signature schemes on the other hand, the usual security definition asks you (the attacker) to find a $(m,s)$-pair (where $m$ is a message and $s$ is its corresponding signature) that you haven't seen before or that you haven't received from the oracle (ie any ressources you're allowed to use). As you can see, there's nothing that would require for randomness in this definition and as such there are fully deterministic schemes with "provable" security, such as RSA-FDH.