one way to enhance the security of AES by increasing the number of active s-boxes .larger MDS matrices are used to increase the number of active s-boxes. using 4x4 MDS matrix generate 25 active s-box after 4 rounds,

How many active s-boxes generated after 4 rounds using 8x8 MDS matrix?

  • $\begingroup$ without actually doing the math, I would say 49? $\endgroup$ – Richie Frame Mar 1 '16 at 10:37
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    $\begingroup$ Thank you for the answer. could you please show the math? $\endgroup$ – hardyrama Mar 2 '16 at 9:19

It seems that using an 8x8 MDS will have 27 Active Sboxes after 4 Rounds(There may exist a trail shorter than 27). The image below shows the counting of active Sboxes.

  1. The Active and non-Active byte is shown as 1 and 0 respectively.
  2. The 8 bytes of state which become input to the 8x8 MDS matrix are colored in similar color (pink or blue).
  3. The shift rows step shows new byte position in pink and white color.
  4. The calculation is done under the assumption that 8x8 MDS matrix has optimal branch number of 9 i.e change in one byte will change all the 8 output bytes.
  5. If 8x8 Matrix similar to Camellia is used which has branch number of 5, then count of active Sbox may be reduced.

enter image description here

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    $\begingroup$ it seems you made a mistake in last round . The number of active S-box in round 4 is 8 not 7 , so the total number is 27. $\endgroup$ – hardyrama Sep 9 '19 at 17:10
  • $\begingroup$ @hardyrama thanks for pointing out the issue. I have updated the image now. $\endgroup$ – abraza Sep 11 '19 at 9:43

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