You have a software for an asymmetric encryption scheme AE$=($K$,$E$,$D$)$AE $=($K$,$ E$,$ D$)$AE$=($K$,$E$,$D$)$ that is known to be IND$-$CCA secure under some reasonable assumptions. However, the message space for this scheme is limited to messages up to $1$MB in length. At some point, you needed to encrypt messages larger than $1$MB but less than $2$MB$.$ To address this, you decide to use the existing software as follows:

To encrypt a message MMM$,$ split it into equal parts M$1$M$\_1$M$1$ and M$2$M$\_2$M$2($for simplicity, assume all messages have even lengths$).$ The ciphertext is computed as:

E$($pk$1,$M$1)$E$($pk$2,$M$2)$E$($pk$\_1,$ M$\_1)\backslash$parallel E$($pk$\_2,$ M$\_2)$E$($pk$1,$M$1)$E$($pk$2,$M$2)$

for any public key pkpkpk$,$ where $\backslash$parallel$$ denotes concatenation.

The decryption algorithm decrypts both halves of the ciphertext:

M$1$D$($sk$1,$C$1),$M$2$D$($sk$2,$C$2)$M$\_1\backslash$gets D$($sk$\_1,$ C$\_1),\backslash$quad M$\_2\backslash$gets D$($sk$\_2,$ C$\_2)$M$1$D$($sk$1,$C$1),$M$2$D$($sk$2,$C$2)$

and returns M$1$M$2$M$\_1\backslash$parallel M$\_2$M$1$M$2$ if neither decryption rejects. If either decryption rejects, the output is rejection. Let$$s call this modified scheme AE$=($K$,$E$,$D$)$AE$\text{'}=($K$,$ E$\text{'},$ D$\text{'})$AE$=($K$,$E$,$D$).$

Question:

Do you think AE$$AE$\text{'}$AE$$ is IND$-$CPA? IND$-$CCA? Justify your answers.