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My professor has posted a couple of practice questions that so far I haven't been able to find the answer for and I was hoping you could help.

DES would remain invertible—it would still be ablockcipher—even if its S-boxes were arbitrarily changed (the number of input and outputbits remaining the same).

AES would remain invertible—it would still be ablockcipher—even if its S-boxes were arbitrarily changed (the number of input and outputbits remaining the same).

I've been trying to figure out the "how" and "why", mostly.

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  • $\begingroup$ Take a look at this DES implementation in excel, and see if it helps you : nayuki.io/page/des-cipher-internals-in-excel $\endgroup$ – John Deters Feb 15 at 4:25
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    $\begingroup$ While we are happy to help with homework, we require that you have at least attempted to answer the questions yourself. We will not do your homework for you. $\endgroup$ – schroeder Feb 15 at 10:53
  • $\begingroup$ Its not homework but thank you for the snarkyness. $\endgroup$ – user3712347 Feb 17 at 23:21
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DES is a Feistel cipher where the round function doesn't need to be invertible. Therefore, when designing a Feistel cipher you will have invertible and non-invertible S-box options.

In contrast, AES is a substitution-permutation network where the structure is completely different. If AES operations are not invertible, you will not be able to decrypt anything. So, the second claim is wrong.

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  • $\begingroup$ the note about the input and output bits remaining the same implies the new s-box would be bijective and thus invertible $\endgroup$ – Richie Frame Feb 19 at 0:20
  • $\begingroup$ @RichieFrame The number of output bits doesn't guarantee that the S-Box will be an onto function. It just defines the range of the S-Box. We can design, though won't be secure, S-Box's that only output even, or similar properties. There are $n!$ one to one functions, and there is a total of $n^n$ functions from $n \to n$. $\endgroup$ – kelalaka Feb 19 at 9:33
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    $\begingroup$ Let's maybe not just answer homework (or non-homework practice) questions outright? One can suggest hints that don't spoil the problem by thoughtlessly revealing the answer. $\endgroup$ – Squeamish Ossifrage Feb 20 at 5:53

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