**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 satifies condition (1) if its hash function is $t$-wise independent for appopriate $t$ and that RSA satisfies condition (2) under the $\Phi$-Hiding Assumption of Cachin {\em et al.}~(Eurocrypt 1999).
This appears to be the first non-trivial {\em positive} result about the instantiability of RSA-OAEP. In particular, it increases our 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

**Publication Info: **CRYPTO 2010

**Date: **received 13 Oct 2011

**Contact author: **amoneill at bu edu

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

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

**Version: **20111017:194114 (All versions of this report)

**Discussion forum: **Show discussion | Start new discussion

[ Cryptology ePrint archive ]