Is Hybrid Encryption CCA secure? If Enc is a PKE(Public Key Encryption) with key generation algorithm KG and message space $M = \{0, 1\}^n$, and SE is a Symmetric Key Encryption(SKE) with key space $\{0, 1\}^n$ and message space $M' = \{0, 1\}^*$ then the hybrid encryption
uses the same key generation KG, but its message space is $M' = \{0, 1\}^*$ and its encryption procedure $Enc'(p_k, m)$ picks a random symmetric key $k \gets \{0, 1\}^n$ and outputs ciphertext $(c, c')$ where $c = Enc(p_k, k)$ and $c' = SE(k, m)$. The decryption given $(c, c')$ decrypts $k$ from $c$ using the private key corresponding to pk and then decrypts $m$ from $c'$ using $k$.

If Enc is a CPA secure PKE on $M = \{0, 1\}^n$ and SE is IND secure SKE on$ M' = \{0, 1\}^*$,  is Enc' CPA secure PKE on $M'$?

If Enc is CPA secure PKE and SE is CCA secure SKE, is Enc'
 CCA secure?
If the KEM is only CPA-secure, then the resulting scheme might not be CCA-secure. For example, consider a CPA-secure KEM that ignores the last bit of its ciphertext. Then it is possible to modify a KEM ciphertext in a way that doesn't affect its payload, which is enough to break CCA security of the hybrid scheme.

If the KEM and DEM are both CCA-secure, then the overall hybrid scheme is also CCA-secure. This is proved formally in Section 7 of: 


  Cramer, Shoup: Design and Analysis of Practical Public-Key Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack


However, it is possible to have a CCA-secure hybrid encryption scheme where the KEM is (slightly) weaker than CCA secure. This was first demonstrated in:


  Kurosawa, Desmedt: A New Paradigm of Hybrid Encryption Scheme


The weakened KEM security definition and composition theorem for hybrid encryption were formalized/generalized in:


  Hofheinz, Kiltz: Secure Hybrid Encryption from Weakened Key Encapsulation