On 08/03/2017 02:54 PM, \0xDynamite wrote:
Speaking of cryptography (harhar), I was contemplating an idea to generate random streams of random numbers using chaos theory (not the first), specifically the logistic equation [3.5x(1-x)], when I came across the argument (http://www.cs.utsa.edu/~wagner/laws/chaos.html) that such generators are "psuedo-random", but I don't think is true.
The equation is capable of producing an infinite stream of numbers that get more random as you continue to use the equation. The amount of true randomness approaches the depth of your word size, but in theory you can create an implementation with arbitrary depth (say 10000 bits).
Is this interesting to anyone?
Thing is, the output of an equation that takes one iteration's output as input for the next round, etc. is 100% deterministic: The same equation, with same initial input, produces the same output every time. Being unable to predict an iterated feedback function's 9 millionth digit on its 9 millionth iteration by any means other than actually iterating it 9 million times qualifies the function as "chaotic." But chaos is not entropy: Actually running an iterated function does enable one to reconstruct the output stream perfectly, while in cryptography "entropy" means completely unpredictable data that can not be predicted or reproduced by any means other than recovering a physical record of the data set in question. Only physical sources can generate real entropy in this sense: Decaying isotopes, noise from a leaky diode, tumbling dice, snapshots of variable hardware states in a computer (least significant n. digits of CPU temperature, fan speed, keystroke intervals, etc.) do qualify as entropy; the Mandlebrot set does not. This does leave open the possibility of using a true random number (n. bits of entropy) to seed an iterated function that will "inflate" that number to any size desired - but no matter how cunning the algorithm, those n. bits of entropy are all there is, and define the difficulty (or otherwise) of brute force breaking resulting ciphertexts. In cryptography, common sense is a major pitfall. When I first got interested in modern cryptography, I made the same mistake: I was quite sure that the Mandlebrot set would make a super-powerful cryptosystem possible. But alas... deterministic functions, however "chaotic" the output, add no entropy to the initial input. Math is my weakest subject, so I am indecently proud of having studied the RSA cipher until I actually understood it well enough to trust it - 20 years ago. My grand accomplishment was possible because RSA is surprisingly simple, once presented and explained. Today: Don't ask me, math is my weakest subject. :o)