Turing, actions from rep of permutation swap, Chi/Characteristic, expander graph family


 

image

https://yorkporc.wordpress.com/2014/04/05/quantum-random-walks-along-turing-era-world-lines-with-swaps-built-into-1950s-rotor-machine/

We can see now that Turing was modeling this, using a rotor wiring plan etc. The alternating group is a manifestation of the constant group.

So we can see that GCHQ has had qudit computational models for 50+ years (even for discrete computing and their algorithm designs, for cryptanalytical searching)

we can just look at the above picture as 3 oscillators, with the line of wave1 wapping between +1/-1, the wave2 between –2/+2, etc. Each is a branching space, and the 3 oscillators combine to create a tree of simple  combinations that expands leftwards, from origin point 1.

Now one can imagine that the field in which this is all calculating is some RS ring, so that it can be implemented using a finite state machine. Now we can easily see how, by 1950s, that the pure rotor cage is augmented by a simple set of shift registers that allow the production of binary linear convolutional codes. They can be producing systematic codebooks (when one wants signatures) or non-systematic (for a OAEP-style padding regime). taking a couple of shift registers boards from the colossus design and applying it to a rotor cage sounds eminently doable, in 1946 for things like aircraft I&A. This feels like the kind of thing Fiestel was doing.

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About home_pw@msn.com

Computer Programmer who often does network administration with focus on security servers. Very strong in Microsoft Azure cloud!
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