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Yes. $\:$ NME-CPA is such a notion, and is equivalent to modifying the IND-CCA notion so that $\;$ the adversary can submit more than one ciphertext simultaneously $\;\;\;\;$ and $\;$ the adversary can only submit ciphertext(s) one time $\;\;\;\;$ and $\;$ that time must be after receiving the challenge ciphertext $\;\;\;\;$ and $\;$ after submitting ...

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