On 05/05/2014 10:37 PM, Marcus Brinkmann wrote:
On 05/05/2014 09:08 PM, Givon Zirkind wrote:
A question about DES. Did anyone ever try & map or graph the routes
through the S-boxes? I mean pictorially. Do the routes produce some
kind of wave or path, that have (or have not) relationships with the
other routes?
[...]
I don't know (but also haven't checked) of any low-degree (quadratic,
cubic) versions of the linear (or affine) analysis mentioned.
Replying to myself, a quick google search turns up a quadratic analysis:
Natalia N. Tokareva, "k-Bent functions and quadratic cryptanalysis of
block ciphers"
http://mc3.i3s.unice.fr/seminaires/seminaires_mc3/2007_2008/08-08-08_tokareva.pdf
"Page 42: "We test permutations with the most high nonlinearity
NL = 4 recommended for using in S-boxes of GOST 28147-89, DES,
s3DES and found that for all of them (excepting one) our crypt-analysis
gives quadratic relations with probability 7/8 whereas any linear
equality has probability not more then 3/4."
Well, in any case, glancing over that paper may give you an idea what is
involved today in such analysis: They are definitely not done visually,
but involve a lot of higher algebra. It's not 1976 anymore :)
Thanks,
Marcus
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