OAEP 3-Round:A Generic and Secure Asymmetric Encryption Padding
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 two-fold, 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.)
KeywordsRandom Oracle Random String Asymmetric Encryption Challenge Ciphertext Decryption Oracle
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