On the Key Dependent Message Security of the Fujisaki-Okamoto Constructions

In PKC 1999, Fujisaki and Okamoto showed how to convert any public key encryption (PKE) scheme secure against chosen plaintext attacks (CPA) to a PKE scheme which is secure against chosen ciphertext attacks (CCA) in the random oracle model. Surprisingly, the resulting CCA secure scheme has almost the same efficiency as the underlying CPA secure scheme. Moreover, in J. Cryptology 2013, they proposed the more efficient conversion by using the hybrid encryption framework. In this work, we clarify whether these two constructions are also secure in the sense of key dependent message security against chosen ciphertext attacks (KDM-CCA security), under exactly the same assumptions on the building blocks as those used by Fujisaki and Okamoto. Specifically, we show two results: Firstly, we show that the construction proposed in PKC 1999 does not satisfy KDM-CCA security generally. Secondly, on the other hand, we show that the construction proposed in J. Cryptology 2013 satisfies KDM-CCA security

Naor-Yung paradigm with shared randomness and applications

The Naor-Yung paradigm (Naor and Yung, STOC’90) allows to generically boost security under chosen-plaintext attacks (CPA) to security against chosen-ciphertext attacks (CCA) for public-key encryption (PKE) schemes. The main idea is to encrypt the plaintext twice (under independent public keys), and to append a non-interactive zero-knowledge (NIZK) proof that the two ciphertexts indeed encrypt the same message. Later work by Camenisch, Chandran, and Shoup (Eurocrypt’09) and Naor and Segev (Crypto’09 and SIAM J. Comput.’12) established that the very same techniques can also be used in the settings of key-dependent message (KDM) and key-leakage attacks (respectively). In this paper we study the conditions under which the two ciphertexts in the Naor-Yung construction can share the same random coins. We find that this is possible, provided that the underlying PKE scheme meets an additional simple property. The motivation for re-using the same random coins is that this allows to design much more efficient NIZK proofs. We showcase such an improvement in the random oracle model, under standard complexity assumptions including Decisional Diffie-Hellman, Quadratic Residuosity, and Subset Sum. The length of the resulting ciphertexts is reduced by 50%, yielding truly efficient PKE schemes achieving CCA security under KDM and key-leakage attacks. As an additional contribution, we design the first PKE scheme whose CPA security under KDM attacks can be directly reduced to (low-density instances of) the Subset Sum assumption. The scheme supports keydependent messages computed via any affine function of the secret ke