I have a question that I have not found the answers to in many books.
Does the expansion permutation have to map values to the same space? For example, in DES, 32 bits are expanded into 48 bits via an expansion permutation where the values are shuffled around but do not change.
Consider the following expansion function for 4 bits into 6 bits
Is this a legal permutation? or is it not cause it can map to new values in which we didn't posses before, for example
1001 can be mapped into a new value
110011 that didn't exist before.
I understand the encryption would encrypt regardless, but is using that permutation allows for us to reverse the encryption by running the keys in reverse?