Chosen Cipher Text Security for Double Encryption

Question

If $E_k$ is a CCA secure encryption scheme then why is $E′_{(k_1,k_2)}(M)=E_{k_2}(E_{k_1}(M))$, $D′_{(k_1,k_2)}(C)=D_{k_1}(D_{k_2}(C))$ not CCA secure when $k_2$ is known. Is there a way I can make a new cipher with keys $(k_1, k_2)$ such that its CCA secure regardless of which key the adversary finds?

My confusion here is how can I use the fact that key $k_2$ is known to break CCA security and why would that matter, because don't we treat these schemes as black-box when performing attack? What if I had $k_1$ instead, would that make any difference? And I'm quite clueless about the second part about new cipher using $k_1, k_2$ and still a secure CCA. Any idea or hint would be greatly appreciated.

Answer 1

To understand the case of double encryption's CCA security, I read the paper Chosen-Ciphertext Security of Multiple Encryption by Yevgeniy Dodis and Jonathan Katz in 2005.

With the help of this paper, now I'm able to understand why for the mentioned encryption scheme it will be no longer CCA secure when the key $k_2$ is known! Do give it a read for those having issues understanding CCA multiple encryption schemes.