OAEP 3-Round: A Generic and Secure Asymmetric Encryption Padding

摘要

The OAEP construction is already 10 years old and well-established in many practical applications. But after some doubts about its actual security level, four years ago, the first efficient and provably IND-CCA1 secure encryption padding was formally and fully proven to achieve the expected IND-CCA2 security level, when used with any trapdoor permutation. Even if it requires the partial-domain one-wayness of the permutation, for the main application (with the RSA permutation family) this intractability assumption is equivalent to the classical (full-domain) one-wayness, but at the cost of an extra quadratic-time reduction. The security proof which was already not very tight to the RSA problem is thus much worse. However, the practical optimality of the OAEP construction is twofold, hence its attractivity: from the efficiency point of view because of two extra hashings only, and from the length point of view since the ciphertext has a minimal bit-length (the encoding of an image by the permutation.) But the bandwidth (or the ratio ciphertext/plaintext) is not optimal because of the randomness (required by the semantic security) and the redundancy (required by the plaintext-awareness, the sole way known to provide efficient CCA2 schemes.) At last Asiacrypt '03, the latter intuition had been broken by exhibiting the first IND-CCA2 secure encryption schemes without redundancy, and namely without achieving plaintext-awareness, while in the random-oracle model: the OAEP 3-round construction. But this result achieved only similar practical properties as the original OAEP construction: the security relies on the partial-domain one-wayness, and needs a trapdoor permutation, which limits the application to RSA, with still a quite bad reduction. This paper improves this result: first we show the OAEP 3-round actually relies on the (full-domain) one-wayness of the permutation (which improves the reduction), then we extend the application to a larger class of encryption primitives (including ElGamal, Paillier, etc.) The extended security result is still in the random-oracle model, and in a relaxed CCA2 model (which lies between the original one and the replayable CCA scenario.)