making greco-latin squares from bit patterns


image

http://www.grogono.com/magic/4x4alpha.php

 

Lets contrast the above type rules with DES “design criteria”:

 

imageimage

http://securespeech.cs.cmu.edu/reports/coppersmith.pdf

 

If we look at the  5*5 magic square, we even see the use of coding, and base changing (in which invariants are preserved):

image

via http://www.grogono.com/magic/5×5.php

The model magic square rules do not express the characteristic, they define a generator for the characteristic so it can be replicated. In the case of the DES sbox design criteria, we see the same on bit flows (best compared with the 4*4 example, above).

DES goes a bit further than the model generative process, now considering inter-round bit flows – that constrain the convergence. Furthermore, there is an interplay between multiple parallel computations – as if we were computing several magic squares at the same time noting how they impose side-effects upon each other, since the computations are designed to be interleaved.

One thinks back to the work on early shift register electronics in both Colossus, where we saw how easy it was to observe side-effects to the computation due to the limits of the amplifiers of the day (that reacted to too many bits in a run); or due to the ripple effect of early bistable circuits put into too long a series.

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