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Crypto-Archaeology: unearthing design methodology of DES s-boxes

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US defence sponsored the DES program in 1974 and released it in 1977. It remained as a well-known and well accepted block cipher until 1998. Thirty-two 4-bit DES S-Boxes are grouped in eight each with four and are put in public domain without any mention of their design methodology. S-Boxes, 4-bit, 8-bit or 32-bit, find a permanent seat in all future block ciphers. In this paper, while looking into the design methodology of DES S-Boxes, we find that S-Boxes have 128 balanced and non-linear Boolean Functions, of which 102 used once, while 13 used twice and 92 of 102 satisfy the Boolean Function-level Strict Avalanche Criterion. All the S-Boxes satisfy the Bit Independence Criterion. Their Differential Cryptanalysis exhibits better results than the Linear Cryptanalysis. However, no S-Boxes satisfy the S-Box-level SAC analyses. It seems that the designer emphasized satisfaction of Boolean-Function-level SAC and S-Box-level BIC and DC, not the S-Box-level LC and SAC.
Title: Crypto-Archaeology: unearthing design methodology of DES s-boxes
Description:
US defence sponsored the DES program in 1974 and released it in 1977.
It remained as a well-known and well accepted block cipher until 1998.
Thirty-two 4-bit DES S-Boxes are grouped in eight each with four and are put in public domain without any mention of their design methodology.
S-Boxes, 4-bit, 8-bit or 32-bit, find a permanent seat in all future block ciphers.
In this paper, while looking into the design methodology of DES S-Boxes, we find that S-Boxes have 128 balanced and non-linear Boolean Functions, of which 102 used once, while 13 used twice and 92 of 102 satisfy the Boolean Function-level Strict Avalanche Criterion.
All the S-Boxes satisfy the Bit Independence Criterion.
Their Differential Cryptanalysis exhibits better results than the Linear Cryptanalysis.
However, no S-Boxes satisfy the S-Box-level SAC analyses.
It seems that the designer emphasized satisfaction of Boolean-Function-level SAC and S-Box-level BIC and DC, not the S-Box-level LC and SAC.

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