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The original version of OAEP (Bellare/Rogaway, 1994) showed a form of "[[plaintext-aware encryption|plaintext awareness]]" (which they claimed implies security against [[chosen ciphertext attack]]) in the random oracle model when OAEP is used with any trapdoor permutation. Subsequent results contradicted this claim, showing that OAEP was only [[ciphertext indistinguishability|IND-CCA1]] secure. However, the original scheme was proved in the [[random oracle model]] to be [[ciphertext indistinguishability|IND-CCA2]] secure when OAEP is used with the RSA permutation using standard encryption exponents, as in the case of RSA-OAEP.<ref>
Eiichiro Fujisaki, Tatsuaki Okamoto, David Pointcheval, and [[Jacques Stern (cryptographer)|Jacques Stern]]. ''RSA-- OAEP is secure under the RSA assumption''. In J. Kilian, ed., Advances in Cryptology – [[CRYPTO]] 2001, vol. 2139 of Lecture Notes in Computer Science, SpringerVerlag, 2001. [http://eprint.iacr.org/2000/061.pdf full version (pdf)]</ref>
An improved scheme (called OAEP+) that works with any trapdoor one-way permutation was offered by [[Victor Shoup]] to solve this problem.<ref>
Victor Shoup. ''OAEP Reconsidered''. IBM Zurich Research Lab, Saumerstr. 4, 8803 Ruschlikon, Switzerland. September 18, 2001. [http://www.shoup.net/papers/oaep.pdf full version (pdf)]</ref>
More recent work has shown that in the [[Standard
P. Paillier and J. Villar, ''Trading One-Wayness against Chosen-Ciphertext Security in Factoring-Based Encryption'', Advances in Cryptology – [[Asiacrypt]] 2006.</ref><ref>
D. Brown, [http://eprint.iacr.org/2006/223 ''What Hashes Make RSA-OAEP Secure?''], IACR ePrint 2006/233.</ref>
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