For some encryption scheme $(\mathcal{E}, \mathcal{D})$:
In the definition of IND-CCA, the adversary $\mathcal{A}$ can access the decryption oracle $\mathcal{D}$. The deep reason of this setting is to make sure that our scheme is able to "protect the ciphertexts" (e.g. the integrity and authenticity).
So "protecting the ciphertexts" is what an IND-CPA secure scheme can not offer. And that's why IND-CCA is stronger than IND-CPA. Furthermore, IND-CCA2 allows $\mathcal{A}$ to make queries to $\mathcal{D}$ after $\mathcal{A}$ receives the challenge ciphertext $c^{*}$, which is so called "adaptive" query.
Then my question is:
- How should we describe this distinctive ability of resisting adaptive queries in IND-CCA2, in a pellucid way ?
In other words, "random bits-like ciphertexts" leads to IND-CPA security, "the protection of ciphertexts" leads to IND-CCA1 security. Then what leads to IND-CCA2 security?
Thanks in advance!