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RSA mathematics: https://youtu.be/4zahvcJ9glg

I understand how RSA works mathematically.

Can someone explain RSA-OAEP in plain english?

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The plain RSA encryption is not IND-CPA secure.

Suppose that you are trying to encrypting some message m. I do not know exactly what you are encrypting, but I have a rough idea of it, i.e. I know that m is one among m1, m2, m3, .... If you use plain RSA encryption, then I can simply take your public key, and encrypt each one of m1, m2, m3 ... by myself, and compare the result to your ciphertext. Then I can trivially recover m. In many applications this is undesirable.

OAEP is a way to obfuscate m non-deterministically, so that even if I know the potential range of m, I still do not recover any information about m more than if it were randomly drawn from that range.

Internally, it is a Feistel network cipher. Read Wikipedia on its construction details.

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    $\begingroup$ RSA-OAEP additionally guards from Chosen Ciphertext Attacks which use information leaking from a decrypting device in order to decipher a ciphertext. $\endgroup$
    – fgrieu ♦
    Feb 13 at 8:44

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