Research Article
A Key Selected S-Box Mechanism and Its Investigation in Modern Block Cipher Design
Table 7
The bias distribution tables of
, , , and
S-boxes.
| Input mask | Output mask | | | | | | | | | | | | | | | | |
| Bias distribution table of | | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 2 | −2 | 0 | 0 | −2 | 2 | 0 | 4 | −2 | −2 | 0 | 4 | 2 | 2 | | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | −4 | 4 | | 0 | 0 | 2 | −2 | 0 | 0 | 2 | −2 | 4 | 0 | 2 | 2 | −4 | 0 | 2 | 2 | | 0 | −2 | 0 | −2 | 0 | 2 | 0 | 2 | -2 | 0 | 2 | −4 | −2 | −4 | 2 | 0 | | 0 | −2 | −2 | 0 | −4 | −2 | −2 | 4 | 2 | 0 | 0 | 2 | −2 | 0 | 0 | −2 | | 0 | 2 | 0 | 2 | −4 | 2 | 0 | −2 | 2 | 0 | −2 | −4 | −2 | 0 | −2 | 0 | | 0 | 2 | −2 | −4 | 0 | −2 | −2 | 0 | 2 | −4 | 0 | −2 | 2 | 0 | 0 | 2 | | 0 | 0 | −2 | −2 | 0 | 0 | −2 | −2 | 0 | 4 | −2 | 2 | 0 | −4 | −2 | 2 | | 0 | 0 | 0 | −4 | 0 | 0 | 4 | 0 | 0 | 0 | −4 | 0 | 0 | 0 | 0 | −4 | | 0 | −4 | −2 | 2 | 0 | −4 | 2 | −2 | 0 | 0 | −2 | −2 | 0 | 0 | 2 | 2 | | 0 | 4 | 0 | 0 | 0 | −4 | 0 | 0 | -4 | 0 | 0 | 0 | −4 | 0 | 0 | 0 | | 0 | 2 | −2 | 0 | −4 | 2 | 2 | 0 | -2 | 0 | 0 | 2 | 2 | 0 | 4 | 2 | | 0 | 2 | 4 | 2 | 0 | −2 | 0 | 2 | 2 | 0 | −2 | 0 | 2 | −4 | 2 | 0 | | 0 | 2 | −2 | 0 | 0 | −2 | 2 | 0 | 2 | 4 | 4 | −2 | 2 | 0 | 0 | −2 | | 0 | 2 | −4 | 2 | 4 | 2 | 0 | 2 | 2 | 0 | −2 | 0 | −2 | 0 | 2 | 0 | Bias distribution table of | | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | −4 | 2 | −2 | 0 | 0 | −2 | −2 | 2 | −2 | 0 | 4 | −2 | −2 | 0 | 0 | | 0 | −2 | 0 | 2 | −2 | 0 | 2 | 0 | 4 | 2 | 4 | −2 | −2 | 0 | 2 | 0 | | 0 | 2 | 2 | 0 | −2 | 0 | 0 | −2 | 2 | −4 | 0 | −2 | 0 | 2 | −2 | −4 | | 0 | 0 | 2 | 2 | 4 | −4 | −2 | −2 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | −4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | −4 | −4 | 0 | | 0 | 2 | 2 | 0 | 2 | 0 | 0 | 2 | -2 | 0 | 4 | 2 | 0 | −2 | 2 | −4 | | 0 | 2 | 0 | −2 | −2 | 0 | −2 | −4 | 0 | 2 | 0 | −2 | 2 | −4 | 2 | 0 | | 0 | 0 | 2 | −2 | 2 | 2 | 0 | 4 | 4 | 0 | −2 | −2 | 2 | −2 | 0 | 0 | | 0 | −4 | 0 | 0 | −2 | −2 | −2 | 2 | -2 | −2 | 2 | −2 | 4 | 0 | 0 | 0 | | 0 | 2 | 2 | −4 | 0 | −2 | 2 | 0 | 0 | −2 | 2 | 0 | 0 | 2 | 2 | 4 | | 0 | −2 | 0 | −2 | 4 | 2 | 0 | −2 | -2 | 0 | 2 | −4 | −2 | 0 | −2 | 0 | | 0 | 0 | −4 | 0 | 2 | 2 | 2 | −2 | 2 | −2 | 2 | 2 | 4 | 0 | 0 | 0 | | 0 | 0 | −2 | 2 | 2 | −2 | 0 | 0 | 0 | −4 | −2 | −2 | −2 | −2 | 4 | 0 | | 0 | −2 | 4 | 2 | 0 | 2 | 4 | −2 | -2 | 0 | −2 | 0 | 2 | 0 | 2 | 0 | | 0 | −2 | −2 | −4 | 0 | −2 | 2 | 0 | 0 | 2 | −2 | 0 | 0 | 2 | 2 | −4 | Bias distribution table of | | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 4 | 0 | 0 | 4 | 0 | −2 | −2 | −2 | 2 | 2 | 2 | −2 | 2 | | 0 | 0 | −2 | −2 | 2 | 2 | 0 | 0 | −2 | −2 | 0 | 0 | 4 | −4 | −2 | −2 | | 0 | 0 | −2 | 2 | −2 | −2 | 0 | 4 | 0 | 0 | 2 | −2 | −2 | −2 | −4 | 0 | | 0 | 4 | 0 | 0 | −2 | −2 | −2 | 2 | 2 | 2 | −2 | 2 | 4 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 2 | −2 | −2 | 2 | 0 | −4 | 4 | 0 | 2 | 2 | 2 | 2 | | 0 | −4 | −2 | −2 | 0 | 0 | −2 | 2 | 0 | 0 | −2 | 2 | 0 | 4 | −2 | −2 | | 0 | 0 | −2 | −2 | 0 | −4 | 2 | −2 | 2 | −2 | 0 | 4 | −2 | −2 | 0 | 0 | | 0 | 2 | 2 | 0 | 4 | 2 | −2 | 0 | 2 | 0 | 0 | 2 | −2 | 0 | −4 | 2 | | 0 | −2 | 2 | 0 | 4 | −2 | 2 | 4 | 0 | 2 | −2 | 0 | 0 | −2 | 2 | 0 | | 0 | 2 | −4 | 2 | 2 | 0 | −2 | 0 | 0 | −2 | −4 | −2 | −2 | 0 | 2 | 0 | | 0 | −2 | 4 | 2 | −2 | 0 | −2 | 0 | 2 | −4 | −2 | 0 | 0 | −2 | 0 | −2 | | 0 | −2 | −2 | 4 | 2 | 0 | 0 | −2 | 4 | 2 | 2 | 0 | 2 | 0 | 0 | −2 | | 0 | −2 | −2 | 0 | −2 | 4 | 0 | 2 | 2 | 0 | 0 | 2 | 0 | −2 | 2 | 4 | | 0 | −2 | 0 | −2 | 0 | −2 | 0 | −2 | 2 | 0 | −2 | −4 | 2 | 0 | −2 | 4 | | 0 | −2 | 0 | 2 | 0 | −2 | −4 | −2 | −4 | 2 | 0 | 2 | 0 | −2 | 0 | 2 | Bias distribution table of | | 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | −2 | 2 | 0 | −2 | 0 | 0 | 2 | 0 | −2 | −2 | −4 | −2 | 0 | 4 | −2 | | 0 | 0 | −4 | 0 | −2 | −2 | −2 | 2 | 2 | 2 | −2 | 2 | 0 | 0 | 0 | −4 | | 0 | −2 | −2 | 0 | 0 | 2 | 2 | 0 | −2 | 4 | 0 | 2 | −2 | 0 | 4 | 2 | | 0 | −2 | 0 | −2 | 0 | −2 | 4 | 2 | 4 | −2 | 0 | 2 | 0 | 2 | 0 | 2 | | 0 | 0 | −2 | −2 | −2 | 2 | 0 | −4 | 4 | 0 | 2 | −2 | −2 | −2 | 0 | 0 | | 0 | 2 | −4 | 2 | −2 | 0 | 2 | 0 | −2 | −4 | −2 | 0 | 0 | −2 | 0 | 2 | | 0 | 4 | 2 | 2 | 0 | 0 | 2 | −2 | 2 | 2 | −4 | 0 | −2 | 2 | 0 | 0 | | 0 | −2 | −2 | 4 | 2 | 0 | 0 | −2 | 2 | 0 | 0 | −2 | 4 | 2 | 2 | 0 | | 0 | 0 | 0 | 0 | 0 | −4 | 0 | −4 | −2 | −2 | 2 | 2 | −2 | 2 | 2 | −2 | | 0 | −2 | −2 | 0 | 4 | 2 | −2 | 0 | 0 | −2 | −2 | 0 | −4 | 2 | −2 | 0 | | 0 | 0 | 0 | 4 | −2 | 2 | 2 | 2 | 0 | 0 | 4 | 0 | −2 | 2 | −2 | −2 | | 0 | 0 | 2 | 2 | 2 | 2 | 0 | 0 | 2 | −2 | 0 | 4 | 0 | −4 | 2 | −2 | | 0 | −2 | 0 | −2 | 0 | 2 | 4 | −2 | −2 | 0 | −2 | 0 | 2 | 0 | −2 | −4 | | 0 | −4 | 2 | 2 | −4 | 0 | −2 | −2 | 0 | 0 | −2 | 2 | 0 | 0 | −2 | 2 | | 0 | 2 | 0 | −2 | −2 | 4 | −2 | 0 | 0 | −2 | 0 | 2 | 2 | 4 | 2 | 0 |
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