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I have seen in few places (mostly papers) talking about plain cascade and XOR cascade. I know what is cascade cipher is but I am not clear about what these are. Can anyone help to understand using simple words to define what is a XOR cascade? (how XOR is involved in cascade cipher?)

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Without more context the answer isn't quite precise. In the following answer $\oplus$ always denotes bit-wise XOR.

First let's quickly revisit "plain" cascade encryption. You encrypt arbitrary messages using the keys $K_1,K_2,K_3$ and the encryption algorithm $E$ as follows: $C=E_{K_1}(D_{K_2}(E_{K_3}(P)))$

Now the first possible XOR-cascading construction (more common) is to use three stream-ciphers (or blockciphers in CTR-mode) as follows: $C=E_{K_1}(Ctr)\oplus E_{K_2}(Ctr)\oplus E_{K_3}(Ctr)\oplus P$. This was already recommended by B. Schneier in his Applied Cryptography.

The mode, I think is most likely the one you're looking for, is proven secure in this paper. First you need again the three previously mentioned keys. Secondly you need four more keys of the same length as the blocksize (128-bit for AES-256). Using these additional four keys $l_i$, you encrypt the plaintext $P$ as follows:
$C= E_{K_3}(E_{K_2}(E_{K_1}(P\oplus l_1)\oplus l_2)\oplus l_3)\oplus l_4$.

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  • $\begingroup$ I like (and use) XEX type modes, which is essentially $C=E_{K_2}(E_{K_1}(Ctr)\oplus P)\oplus E_{K_{1\ or\ 3}}(Ctr)$ $\endgroup$ – Richie Frame Aug 7 '15 at 0:22
  • $\begingroup$ Is there a security reason (besides It is used in 3DES to allow compatibility with DES) you mention EDE nstead of EEE as the cascade? $\endgroup$ – eckes Apr 28 '17 at 1:30
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    $\begingroup$ @eckes no security reason, just the same "functional" reasoning as behind 3DES. $\endgroup$ – SEJPM Apr 28 '17 at 15:14

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