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Can a substitution cipher achieve confusion and diffusion?

By a substitution cipher I mean one where each character is replaced by another. By confusion my definition is that to solve the question, find key $k$ such that $E_k(m) = c$, should be difficult and diffusion is where non-uniformities in the message are distributed by the encryption function to make it more uniform.

So is it possible for a substitution cipher to achieve both? I believe it can't achieve diffusion since it treats each character independently but it may be able to achieve confusion (possibly the mono-alphabetic substitution cipher).

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  • $\begingroup$ The modern version of poly-alphabetic ciphers is the block ciphers. $\endgroup$
    – kelalaka
    Commented Apr 26 at 7:38
  • $\begingroup$ @kelalaka I understand that but my question was what does this basic mono-alphabetic substitution achieve. Does it achieve confusion and diffusion? $\endgroup$
    – revision
    Commented Apr 26 at 22:24
  • $\begingroup$ I don't know what you are trying to achieve. Construct 8 char blocks, apply usual permutation then permute the positions then make this 16 round with different permutation in each round, done! $\endgroup$
    – kelalaka
    Commented Apr 27 at 9:15
  • $\begingroup$ @kelalaka This is just theoretical, I am learning about Shannon's diffusion and confusion and was wondering if this can be achieved by something as simple as a caesar cipher or mono-alphabetic cipher which only changes a plaintext char by char instead of something like a feistel structure you described. $\endgroup$
    – revision
    Commented Apr 27 at 10:55
  • $\begingroup$ did you search for similar questions on this site? $\endgroup$
    – kodlu
    Commented Apr 27 at 13:55

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Well yes, but actually no.

If you have a large enough alphabet in your substitution cipher, combining several original message character to a single entrance to your substitution. And when your message is longer than a single entry you ensure different blocks are handled differently in a secure manner, e.g CBC or CTR. And incorporate a source of diversity so even same messages won't come out the same using an IV or nonce, you could get a secure result also with regards to your definition. But if we did that are we still using a substitution cipher? Is AES a substitution cipher? argueably yes. Is GCM AES? I would say no.

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  • $\begingroup$ I don't really understand the need for the first sentence and the subsequent setup . I do agree now that AES is abstractly a substitution though. $\endgroup$
    – revision
    Commented May 3 at 10:05

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