Essential requirement for IND-CCA1 and IND-CCA2

Question

I am learning about the concept of two security notions called IND-, which include IND-CPA, IND-CCA1 and IND-CCA2. While I got some grasp understanding about the scenarios between the challenger & attacker for each of these models. I am still not able to comprehend what properties of a security model are required to "upgrade" from IND-CPA to IND-CCA1, thus IND-CCA2.

Starting with IND-CPA, I understood that each encryption request must "result in randomly different outputs".
What are the canonical descriptions for the next 2 transitions (IND-CPA -> IND-CCA1 and IND-CCA1 -> IND-CCA2)? I did some research and got some answers talking about "making the ciphertext tamperproof" (LINK1, LINK2) but still quite confused (e.g., they just mentioned CCA generally).

Thank you in advance.

This is our Canonical Q/A; Easy explanation of "IND-" security notions? What is not clear there for you? — kelalaka, Oct 18 '22 at 17:19
@kelalaka It really helped me understand the context of these notions. But I am still not able to find the condition to reach those type of security. For instance, this LINK mentioned about what the encryption needs to improve to achieve IND-CPA, which is to randomize. I am still looking for stuff like that for IND-CCA1 and IND-CCA2. — John Pham, Oct 19 '22 at 04:02
Ind-CCAx requires a MAC to achive this. The CPA is malleable. — kelalaka, Oct 19 '22 at 09:10
Example 1 How can CPA-secure LWE cryptosystem be broken by an active attacker? 2) Bit Flipping Attack on CBC Mode 3) Padding Oracles and many others due to lack of integrity or not using integrity correctly. You may search for CPA attack for more and see the necessity of the integrity. — kelalaka, Oct 19 '22 at 09:20

Essential requirement for IND-CCA1 and IND-CCA2

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