Padding has two primary uses in cryptography, ensuring messages are the proper length necessary for certain ciphers (e.g., block ciphers) or to provide assurances not built into the core cipher (e.g., semantic security)

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Why should a signature use PSS padding in RSA?

Suppose I send a message using AES (private keys already negotiated securely) and I send a hash of this message using RSA (encrypted with private key) with OAEP to verify the authenticity and ...
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Is OAEP reversible?

Given nothing more than some integer $m =$ OAEP($M$), is it possible to recover the original plaintext $M$? In other words, without being given the hash functions or the random string used for ...