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We know in CCA1 security, after seeing the challenge ciphertext,
no more decryption oracles are allowed to the adversary.
But in adaptive security, what should the adversary do? ​ Please help me solve the puzzle.

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    $\begingroup$ Where have you heard of "adaptive security"? How was it defined there? $\endgroup$ – fkraiem Feb 15 '17 at 16:46
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The word adaptive security could possibly refer to:

  • security with respect to the definitions of IND-CCA2, possibly emphaizing that is the adaptive case of IND-CCA (IND-CCA1 is called non-adaptive)
  • Real-time adaptive security, but that's not really in the field of cryptography but network security.
  • Gartner published a paper Designing an Adaptive Security Architecture for Protection From Advanced Attacks (behind a paywall), and is referred to in various blogs. It seemed to have stirred some interest, but google mostly gives you results for "what is adaptive security", and after a quick glance none of those articles seem to be about cryptography. It seems to be mostly about network security and business management (including things like risk management, incident response, continuous monitoring etc. )

I don't think there is any (commonly used) security definition stricly between IND-CCA1 and IND-CCA2.

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