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Recently, at Crypto 2008, Boneh, Halevi, Hamburg, and Ostrovsky (BHHO) solved the longstanding open problem of "Circular encryption," by presenting a public key encryption scheme and proving that it is semantically secure against key dependent chosen plaintext attack (KDMCPA security) under standard assumptions (and without resorting to random oracles). However, they left as an open problem that of designing an encryption scheme that simultaneously provides security against both key dependent chosen plaintext and adaptive chosen ciphertext attack (KDM-CCA2 security).
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