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In general, we execute key-mixing, substitution and permutation sequentially in a single round in a n-round SPN, but if we execute n-round key-mixing firstly, n-round substitution secondly and n-round permutation finally, how is the security of this modified SPN?

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  • $\begingroup$ possible duplicate of Increase number of rounds for SPN and Feistel ciphers $\endgroup$ – e-sushi Sep 18 '14 at 18:06
  • $\begingroup$ @e-sushi Disagree with the duplicate vote as suggested duplicate is about increasing the number of permutations (rounds) whereas this question is about changing the order of substitutions and permutations. $\endgroup$ – rath Oct 2 '14 at 0:29
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I think this would effectively make your cipher a single round.

Key mixing is usually an XOR operation of the round key on the current state. XORing all of the round keys at once is effectively only xoring a single key.

If you have an $n\times n$ bit s-box $s(x)$ (e.g. Rijndael's sbox), then $s(s(x))$ is just another sbox which can be expressed as a lookup table.

The same logic applies to the permutation. If you have a permutation $p(x)$ then $p(p(x))$ is itself a permutation.

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