**Instantiability of RSA-OAEP under Chosen-Plaintext Attack**

*Eike Kiltz and Adam O'Neill and Adam Smith*

**Abstract: **We show that the widely deployed RSA-OAEP encryption scheme of Bellare and Rogaway (Eurocrypt 1994), which combines RSA with two rounds of an underlying Feistel network whose hash ({\em i.e.}, round) functions are modeled as random oracles, meets indistinguishability under chosen-plaintext attack (IND-CPA) in the {\em standard model} based on simple, non-interactive, and non-interdependent assumptions on RSA and the hash functions. To prove this, we first give a result on a more general notion called ``padding-based'' encryption, saying that such a scheme is IND-CPA if (1) its underlying padding transform satisfies a ``fooling" condition against small-range distinguishers on a class of high-entropy input distributions, and (2) its trapdoor permutation is sufficiently {\em lossy} as defined by Peikert and Waters (STOC 2008). We then show that the first round of OAEP satisfies condition (1) if its hash function is $t$-wise independent for $t$ roughly proportional to the allowed message length. We clarify that this result requires the hash function to be keyed, and for its key to be included in the public-key of RSA-OAEP. We also show that RSA satisfies condition (2) under the $\Phi$-Hiding Assumption of Cachin \emph{et al.}~(Eurocrypt 1999).
This is the first {\em positive} result about the instantiability of RSA-OAEP.
In particular, it increases confidence that chosen-plaintext attacks are unlikely to be found against the scheme. In contrast, RSA-OAEP's predecessor in PKCS \#1 v1.5 was shown to be vulnerable to such attacks by Coron {\em et
al}.~(Eurocrypt 2000).

**Category / Keywords: **public-key cryptography / RSA, OAEP, padding-based encryption, lossy trapdoor functions, leftover hash lemma, standard model

**Original Publication**** (in the same form): **To appear in Journal of Cryptology

**Date: **received 13 Oct 2011, last revised 4 Jul 2016

**Contact author: **amoneill at gmail com

**Available format(s): **PDF | BibTeX Citation

**Note: **This is the full version.

**Version: **20160704:154207 (All versions of this report)

**Short URL: **ia.cr/2011/559

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