I want a way to encrypt files using this process: https://crypto.stackexchange.com/a/15 . That is: generate a random password, use that to AES-encrypt a file, and use an RSA public key to encrypt the random password.
I can arrange for the password (= AES key) to be randomly generated every single time, and can arrange things so that doing so again with either the same or a different RSA key will result in a new AES password being generated. My question is whether I need to use padding when doing RSA encryption of the unique AES key.
I've read the answers to several closely related questions, especially Is RSA of a random nonce with no padding safe? and also Does RSA padding have to be unpredictable if the payload is?, which state that padding is necessary. But, as I read the replies, it seems to be necessary in the context of multiple recipients, in which there multiple RSA public keys, but only one random AES password (random but generated once only, not generated anew for each RSA key / recipient).
Basically, in my case, I don't see how padding an already known-to-be-uniquely-random message would make it any more random.
So: Am I just confused and missing something, or are the linked answers only emphasizing the need for padding in multiple recipient cases (where the password stays the same)?