Solving k^m = q mod N
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From: dannas on 9 Jun 2010 11:44 "JSH" <jstevh(a)gmail.com> wrote in message news:505435b3-d659-4ba0-8a43-3ffcae8b3491(a)t26g2000prt.googlegroups.com... On Jun 8, 8:09 pm, Joshua Cranmer <Pidgeo...(a)verizon.invalid> wrote: > On 06/08/2010 10:44 PM, JSH wrote: > > > I've been playing with the program for a while and watching some of > > the behavior, where yeah, if you put in large squares, less than N-- > > especially near N itself, it solves them freaking fast. > > > And again, that's just m=2. The result covers m, a Natural number. > > As Edsger Dijkstra said, "Testing cannot prove the absence of bugs; it > can only prove the presence of bugs." Empirical results do not a proof > make. >The proof is the trivial part. <snip failed math> >Quit playing at being a mathematician on newsgroups. I, at least, >acknowledge I'm not one. Posters like you play pretend. JSH - you are projecting again.... >You're way away from what's familiar to you. >Basic research is an unknown to you. yes, for sure, wiki "physological projection" >James Harris [one sick little monkey troll]
From: dannas on 9 Jun 2010 16:28 "JSH" <jstevh(a)gmail.com> wrote in message news:b10a7696-f5f0-4016-9a9e-2a098d9c7a58(a)t26g2000prt.googlegroups.com... On Jun 8, 6:26 pm, Rotwang <sg...(a)hotmail.co.uk> wrote: > JSH wrote: > <snip> >> back up"? >I meant number theory textbook. Pick up any of your choice and look >at the first few pages. Usually fairly trivial results are >established first. JSH, you have never picked up a number theory textbook in your short life. >My point is that easy does not equate with worthless. Foundation >level results can be very easy, but their generality makes them still >important. You have no idea of what you are typing about. >James Harris
From: Joshua Cranmer on 9 Jun 2010 18:09 On 06/09/2010 10:11 AM, JSH wrote: > On Jun 8, 8:09 pm, Joshua Cranmer<Pidgeo...(a)verizon.invalid> wrote: >> On 06/08/2010 10:44 PM, JSH wrote: >> As Edsger Dijkstra said, "Testing cannot prove the absence of bugs; it >> can only prove the presence of bugs." Empirical results do not a proof make. > > The proof is the trivial part. > > The examples though show that people like you lack credibility. > > For instance, here's output from my test program again. I think you missed the point of my statement. In textbooks, examples are typically not meant as evidence that something is true but as a supplemental guide to ease comprehension. >> How much are you stress testing them? And how fast is `freaking fast'? > > Stress testing? Why do that? > > Example given. > >> Did you do comparative performance testing with the brute-force method? > > No. You can do so with the example I give above and post your > results!!! So, basically, you don't care to demonstrate that there is some practical benefit to your method, you just want us to accept as it is. > You're a computer geek. Yes, yes I am. > Quit playing at being a mathematician on newsgroups. I, at least, > acknowledge I'm not one. Posters like you play pretend. Did I ever claim to be a mathematician? I have stated numerous times that I don't try to rebut most of your work since I don't have a strong enough math background. > Basic research is an unknown to you. My main field of focus is one where everything interesting is generally trivially proven impossible. Figuring out how to do the impossible qualifies as basic research to me... -- Beware of bugs in the above code; I have only proved it correct, not tried it. -- Donald E. Knuth
From: Tim Little on 10 Jun 2010 00:22 On 2010-06-09, JSH <jstevh(a)gmail.com> wrote: > On Jun 8, 7:35 pm, Tim Little <t...(a)little-possums.net> wrote: >> Why arrogant? What he thought up *is* a general method for solving >> for k. > > Then use it on this example using my approach. > > java QuadRes 169 177 > k=13 (I wrote my program to take m as a parameter) tim(a)perth:~$ java TryPi 2 169 177 Found k = 46 at bits 88-95 of pi 46^2 = 169 mod 177 There are online published lists of binary and/or hexadecimal digits of pi that you can use to verify that the value of k that the program finds is in fact at the specified location. Just for fun, here's another example: tim(a)perth:~$ java TryPi 147 1195 3919 Found k = 1030 at bits 14016-14027 of pi 1030^147 = 1195 mod 3919 Are there any other examples that you'd like me to demonstrate? - Tim
From: MichaelW on 10 Jun 2010 01:33
On Jun 10, 2:22 pm, Tim Little <t...(a)little-possums.net> wrote: > On 2010-06-09, JSH <jst...(a)gmail.com> wrote: > > > On Jun 8, 7:35 pm, Tim Little <t...(a)little-possums.net> wrote: > >> Why arrogant? What he thought up *is* a general method for solving > >> for k. > > > Then use it on this example using my approach. > > > java QuadRes 169 177 > > k=13 > > (I wrote my program to take m as a parameter) > > tim(a)perth:~$ java TryPi 2 169 177 > Found k = 46 at bits 88-95 of pi > 46^2 = 169 mod 177 > > There are online published lists of binary and/or hexadecimal digits > of pi that you can use to verify that the value of k that the program > finds is in fact at the specified location. > > Just for fun, here's another example: > > tim(a)perth:~$ java TryPi 147 1195 3919 > Found k = 1030 at bits 14016-14027 of pi > 1030^147 = 1195 mod 3919 > > Are there any other examples that you'd like me to demonstrate? > > - Tim Tim, I can't decide if that is awesome or weird. Or both. There is actually an interesting maths question behind the algorithm. Does there exist a binary string of some length that never appears in the binary expansion of pi? If such a string exists then the algorithm fails. For more see the Wolfram article on "Normal Number". Regards, Michael W. |