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 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 $$\text {KDM}\text {-}\text {CCA}$$KDM-CCA security generally. Secondly, on the other hand, we show that the construction proposed in J. Cryptology 2013 satisfies $$\text {KDM}\text {-}\text {CCA}$$KDM-CCA security.