Author: Dieter Buerssner
Date: 13:48:58 10/28/03
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On October 28, 2003 at 16:31:45, Dan Andersson wrote: > Finding any periodicity with any reasonable amount of computation if those >criterion are fulfilled should only be possible iff Integer Factorization is >computationally easy. And the current bet is that it is hard as heck. The random >properties of the algorithm are bound to that single assumption. Hmmm, I see it a bit different from a general point of view (without looking into the details of the algorithm). Your formula can never have a period longer M, so it is trivial to find a periodicity in principle. Whether you can predict the output of the next bit after you have known a (possibly large) number of previous outputs, is another question (that seems very important for cryptography). Some random source that produces a bitstream might produce 0 and 1 with different probabilities in a manner that is practically unpredictable. Still, such a source would not be wanted normally (at least not with doing some transformations) for statistical simulations. In most situations, it would give wrong results. I don't say, that the Blum Blum Shub does have this properity - just the "hard as heck" does not mean to me whether it has "good" statistical properities. For example: How long must M be, that it will give me at least once n ones in a row? Regards, Dieter
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