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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 encoding, or even the length of it.

EDIT: This is being used in tandem with RSA, but I don't know the hash functions that OAEP usually uses with RSA; they might be public, for all I know.

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    $\begingroup$ Why would the hash-functions be unknown? Those should usually be considered public information. $\endgroup$
    – Maeher
    Apr 27, 2013 at 20:22
  • $\begingroup$ Does OAEP use certain standard hash functions when RSA is used (edited question to reflect that this is being used with RSA). $\endgroup$ Apr 27, 2013 at 23:07
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    $\begingroup$ there's a limited set of hash functions that can be used (i.e. are expected to be secure enough to be used), just iterated over them $\endgroup$ Apr 28, 2013 at 0:04

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If you know the hash functions, yes. If the hash functions are secret, no—but how would you come into a situation where OAEP is being used with a secret hash function?

For any hash functions $G$ and $H$, OAEP is a fixed permutation involving no secret keys. Specifically, given a message $m$ and randomization $r$, OAEP returns $(a, b)$ where

\begin{align} a &= m \oplus G(r), \\ b &= r \oplus H(a), \end{align}

which can be inverted by

\begin{align} r &= b \oplus H(a), \\ m &= a \oplus G(r). \end{align}

So if you have $(a, b)$ and you can compute $G$ and $H$, you can recover $m$ (and $r$). This is exactly what RSAES-OAEP decryption does, after it completes the RSA private key operation.

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