Editing Optimal asymmetric encryption padding (section)

{{Short description|Scheme often used with RSA encryption}}
{{redirect|OAEP|the division of the Thailand Ministry of Science Technology and Environment previously known as the Office of Atomic Energy for Peace|Office of Atoms for Peace}}

In [[cryptography]], '''Optimal Asymmetric Encryption Padding''' ('''OAEP''') is a [[padding (cryptography)|padding scheme]] often used together with [[RSA (cryptosystem)|RSA encryption]]. OAEP was introduced by [[Mihir Bellare|Bellare]] and [[Phillip Rogaway|Rogaway]],<ref>[[Mihir Bellare|M. Bellare]], [[Phillip Rogaway|P. Rogaway]]. ''Optimal Asymmetric Encryption -- How to encrypt with RSA''.  Extended abstract in Advances in Cryptology – [[Eurocrypt]] '94 Proceedings, [[Lecture Notes in Computer Science]] Vol. 950, A. De Santis ed, [[Springer-Verlag]], 1995. [http://www-cse.ucsd.edu/users/mihir/papers/oaep.pdf full version (pdf)]</ref> and subsequently standardized in [[PKCS1|PKCS#1 v2]] and RFC 2437.

The OAEP algorithm is a form of [[Feistel network]] which uses a pair of [[random oracle]]s G and H to process the plaintext prior to [[asymmetric encryption]].  When combined with any secure [[trapdoor one-way function|trapdoor one-way permutation]] <math>f</math>, this processing is proved in the [[random oracle model]] to result in a combined scheme which is [[semantic security|semantically secure]] under [[chosen plaintext attack]] [[ciphertext indistinguishability|(IND-CPA)]].  When implemented with certain trapdoor permutations (e.g., RSA), OAEP is also proven to be secure against [[chosen ciphertext attack]].  OAEP can be used to build an [[all-or-nothing transform]].

OAEP satisfies the following two goals:

#Add an element of randomness which can be used to convert a [[deterministic encryption]] scheme (e.g., traditional [[RSA (algorithm)|RSA]]) into a [[probabilistic encryption|probabilistic]] scheme.
#Prevent partial decryption of ciphertexts (or other information leakage) by ensuring that an adversary cannot recover any portion of the plaintext without being able to invert the [[trapdoor one-way function|trapdoor one-way permutation]] <math>f</math>.

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]]. ''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 model (cryptography)|standard model]] (that is, when hash functions are not modeled as random oracles) it is impossible to prove the IND-CCA2 security of RSA-OAEP under the assumed hardness of the [[RSA problem]].<ref>
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>