[math-fun] true random generators based on iterating map, analog electrical
My idea for that, which I had since the 1990s, was also thought of by: TonI Stojanovski, Johnny Pihl, Ljupco Kocarev: IEEE Trans Circuits & Systems 48,3 (2001) 281-288 & 382-385. They iterate a map which is (approximately) a 2-piece piecewise linear function with one discontinuous jump. They provide a plot of the function. They had conducted an exhaustive search over a 3D parameter space to find the best function of their form, where "best" for them basically meant "most likely to keep working after parameters perturbed." They also give a circuit diagram with 29 MOSFETs, 2 resistors, and 2 capacitors which computes and iterates function. They implemented it on a chip using 0.8-micron CMOS process. It appears to work and generates 1 million true-random bits per second. Looks like they did a pretty good job. I had actually considered maps of their form but dismissed them as too dangerously likely to fall into an attracting fixed point or 2-cycle. Their plot shows they avoid that fate, but not by much -- perturbing their plot a little would break their generator. I meanwhile had preferred piecewise linear maps with 3 pieces and no discontinuities -- those seemed more robust -- but I had not searched for the best parameter set. Their bits of course are going to be biased and correlated, but the correlations should fall off exponentially with time-separation. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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Warren D Smith