Optimal asymmetric encryption padding

In cryptography, Optimal Asymmetric Encryption Padding (OAEP) is a padding scheme often used together with RSA encryption. The OAEP algorithm is a form of feistel network which uses a pair of random oracles G and H to process the plaintext prior to asymmetric encryption. When combined with any secure trapdoor one-way function ${\displaystyle f}$, this processing is proved in the random oracle model to result in a combined scheme which is semantically secure under chosen plaintext attack (IND-CPA). When implemented with certain trapdoor functions (e.g., RSA), OAEP is also proved secure against chosen ciphertext attack. Some evidence suggests that RSA-OAEP cannot be proved in the standard model as secure as the RSA problem is hard.

OAEP satisfies the following two goals:

1. Add an element of randomness which can be used to convert a deterministic encryption scheme (e.g., traditional RSA) into a probabilistic scheme.
2. Prevent partial decryption of ciphertexts (or other information leakage) by ensuring (as far as we can tell) that an adversary cannot recover any portion of the plaintext without completely defeating the trapdoor one-way function ${\displaystyle f}$.

The original version of OAEP (Bellare/Rogaway, 1994) claimed a form of "plaintext awareness" that implied security against chosen ciphertext attack. Subsequent results contradicted this result. However, for various reasons, the original scheme was proved in the random oracle model to be secure when OAEP is used with the RSA function using standard encryption exponents, as in the case of RSA-OAEP. An improved scheme called OAEP+ was offered by Victor Shoup to solve this problem.

References

• M. Bellare, 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. full version (pdf)

• D. Brown, Unprovable Security of RSA-OAEP in the Standard Model, IACR ePrint 2006/233.

• 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. full version (pdf)

• P. Paillier and J. Villar, Trading One-Wayness against Chosen-Ciphertext Security in Factoring-Based Encryption, Advances in Cryptology -- Asiacrypt 2006.

• Victor Shoup. OAEP Reconsidered. IBM Zurich Research Lab, Saumerstr. 4, 8803 Ruschlikon, Switzerland. September 18, 2001. full version (pdf)