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RSA Laboratories

7.10 What is OAEP?

Optimal Asymmetric Encryption Padding (OAEP) is a method for encoding messages developed by Mihir Bellare and Phil Rogaway [BR94]. The technique of encoding a message with OAEP and then encrypting it with RSA is provably secure in the random oracle model. Informally, this means that if hash functions are truly random, then an adversary who can recover such a message must be able to break RSA.

An OAEP encoded message consists of a ``masked data'' string concatenated with a ``masked random number''. In the simplest form of OAEP, the masked data is formed by taking the XOR of the plaintext message M and the hash G of a random string r. The masked random number is the XOR of r with the hash H of the masked data. The input to the RSA encryption function is then

[M ÅG(r)]  ||  [r ÅH(M ÅG(r))]

Often, OAEP is used to encode small items such as keys. There are other variations on OAEP (differing only slightly from the above) that include a feature called ``plaintext-awareness''. This means that to construct a valid OAEP encoded message, an adversary must know the original plaintext. To accomplish this, the plaintext message M is first padded (for example, with a string of zeroes) before the masked data is formed. OAEP is supported in the ANSI X9.44, IEEE P1363 and SET standards.

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