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Offline jnesselr

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Re: New RSA Algorithm discussion
« Reply #180 on: July 18, 2011, 11:04:10 pm »
That's fine, indeed.  Please let us know if that turns up anything interesting.  I don't fully understand how it's prime in one number set, and not in the other, but okay.
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Offline calc84maniac

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Re: New RSA Algorithm discussion
« Reply #181 on: July 18, 2011, 11:08:09 pm »
Quote from: Xeda112358 on July 18, 2011, 02:49:41 pm
So for ideas, what if you defined a number to be prime so long as it is relatively prime to every number in the set?
Over the set of natural numbers, by that definition only 1 is prime. Pick any other number, and you can find another number that is not relatively prime to it (for example, the number times 2)
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Offline AngelFish

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Re: New RSA Algorithm discussion
« Reply #182 on: July 18, 2011, 11:10:40 pm »
Actually, all of the normal primes would be prime according to that definition, since no other number evenly divides them. I'm not sure where Xeda's going with that, though, since integer factorization is only NP-complete if the numbers are prime relative to the set of natural numbers.
« Last Edit: July 18, 2011, 11:11:42 pm by Qwerty.55 »
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Offline Xeda112358

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Re: New RSA Algorithm discussion
« Reply #183 on: July 19, 2011, 03:34:02 pm »
I was only going with the idea that if I could find any relations there with the double prime numbers in those sets, they may be able to be applied to the set of natural numbers. On a different note, a triangle that I have been working on has been yielding some very nice patterns (by triangle, I mean things like Pascals Triangle). Interestingly enough, setting it up as a square and eliminating the first row and column as well as the diagonal, most of the numbers are appearing to be prime and all of the values can be easily computed. I had not designed the triangle specifically for this purpose, but it would be nice if there was a predictable pattern in it. If there is, I have furthered that interpolation stuff I was working on before to handle multiple variables, so I could easily make the equation. I will try to describe the triangle though if anybody is interested.
-The first diagonal going from the top number to the left to infinity is modeled by X2
-The diagonal going right is modeled by -X2
-These diagonals can be called P0 and Z0, respectively.
-The second diagonals are P1 and Z1
-The diagonals are labeled as Ps and Zr
-Ps(r)=Zr(n)=r2+rs-s2

I think I may have switched that last rule around, but the first few terms look like:

          0
        1   -1
     4   1   -4
   9   5   -1   -9

The triangle was originally formed through other means, but after finding this pattern, this is how I am defining it for the moment. I do not have much more time, but if anybody wants to have fun, you can try to find how the Fibonacci and Lucas sequence tie into this 3:-)
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Offline Tribal

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Re: New RSA Algorithm discussion
« Reply #184 on: July 21, 2011, 08:17:01 pm »
An update on the way I've been approaching this issue, storing the frequency as the x-coordinate instead of the number it's currently on seems to fit a logistic curve quite nicely.  The curve seems to fit pretty well with basically any primes as well, it's just the height of the curve that seems to be variable.
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Offline Xeda112358

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Re: New RSA Algorithm discussion
« Reply #185 on: August 12, 2011, 06:49:31 pm »
My computer is about to die and my charger is broken. Anyway, I am onto something that might let me give y'all an equation that produces all the primes in the form of 2n+1. Would that help in any way? Also, I cannot make any guarantees about this, it is just a hunch.

Spoiler For Spoiler:
If I am right, this is a prime number (assuming my calculations are correct):
20035299304068464649790723515602557504478254755697514192650169737108940595563114530895061308809333481010382343429072631818229493821188126688695063647615470291650418719163515879663472194429309279820843091048559905701593189596395248633723672030029169695921561087649488892540908059114570376752085002066715637023661263597471448071117748158809141357427209671901518362825606180914588526998261414250301233911082736038437678764490432059603791244909057075603140350761625624760318637931264847037437829549756137709816046144133086921181024859591523801953310302921628001605686701056516467505680387415294638422448452925373614425336143737290883037946012747249584148649159306472520151556939226281806916507963810641322753072671439981585088112926289011342377827055674210800700652839633221550778312142885516755540733451072131124273995629827197691500548839052238043570458481979563931578535100189920000241419637068135598404640394721940160695176901561197269823378900176415171900511334663068981402193834814354263873065395529696913880241581618595611006403621197961018595348027871672001226046424923851113934004643516238675670787452594646709038865477434832178970127644555294090920219595857516229733335761595523948852975799540284719435299135437637059869289137571537400019863943324648900525431066296691652434191746913896324765602894151997754777031380647813423095961909606545913008901888875880847336259560654448885014473357060588170901621084997145295683440619796905654698136311620535793697914032363284962330464210661362002201757878518574091620504897117818204001872829399434461862243280098373237649318147898481194527130074402207656809103762039992034920239066262644919091679854615157788390603977207592793788522412943010174580868622633692847258514030396155585643303854506886522131148136384083847782637904596071868767285097634712719888906804782432303947186505256609781507298611414303058169279249714091610594171853522758875044775922183011587807019755357222414000195481020056617735897814995323252085897534635470077866904064290167638081617405504051176700936732028045493390279924918673065399316407204922384748152806191669009338057321208163507076343516698696250209690231628593500718741905791612415368975148082619048479465717366010058924766554458408383347905441448176842553272073155863493476051374197795251903650321980201087647383686825310251833775339088614261848003740080822381040764688784716475529453269476617004244610633112380211345886945322001165640763270230742924260515828110703870183453245676356259514300320374327407808790562836634069650308442258559670392718694611585137933864756997485686700798239606043934788508616492603049450617434123658283521448067266768418070837548622114082365798029612000274413244384324023312574035450193524287764308802328508558860899627744581646808578751158070147437638679769550499916439982843572904153781434388473034842619033888414940313661398542576355771053355802066221855770600825512888933322264362819848386132395706761914096385338323743437588308592337222846442879962456054769324289984326526773783731732880632107532112386806046747084280511664887090847702912081611049125555983223662448685566514026846412096949825905655192161881043412268389962830716548685255369148502995396755039549383718534059000961874894739928804324963731657538036735867101757839948184717984982469480605320819960661834340124760966395197780214411997525467040806084993441782562850927265237098986515394621930046073645079262129759176982938923670151709920915315678144397912484757062378046000099182933213068805700465914583872080880168874458355579262584651247630871485663135289341661174906175266714926721761283308452739364692445828925713888778390563004824837998396920292222154861459023734782226825216399574408017271441461795592261750838890200741699262383002822862492841826712434057514241885699942723316069987129868827718206172144531425749440150661394631691976291815065797455262361912248480638900336690743659892263495641146655030629659601997206362026035219177767406687774635493753188995878662821254697971020657472327213729181446666594218720034745089428309115351892711142871083761592223802766053278233516615551493693757784666701457179719012271178127804502400263847587883393968179629506907988171216906869295382485298300234760684541141781391106485602365497542274972310076151318700240539105109138178437217914225285874320985249578780346837033378184214440171386881242499844186181292711985333153825673218704215306311977485352146709553346263366108646673322924098798492566911095161436186015489097402419135096230436121961281659505186660220307156136847323646608689050142639139065150639081993788523183650598972991254044794434251667742996598118492331515552728832740283526884424087528112832899806259126736995462473415433335001472314306127503903073971352520693381738433229507010490618675394331307847980156551303847581556852362180104196502555961819349863159132330360964619059902361126811960234418433633345949276319461017166529138237171823942992162725384617760656945422978770713831988170369645886898118632109769003557358846244648357062914530527571012788720279653644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« Last Edit: August 12, 2011, 07:21:32 pm by Xeda112358 »
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Offline Goplat

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Re: New RSA Algorithm discussion
« Reply #186 on: August 12, 2011, 08:51:41 pm »
Numbers of the form 22n + 1 are called Fermat numbers. Yours is F16 and is already known to be divisible by 825753601 and 188981757975021318420037633.
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Offline AngelFish

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Re: New RSA Algorithm discussion
« Reply #187 on: August 12, 2011, 09:05:03 pm »
Well, Ninja'd.
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Offline fb39ca4

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Re: New RSA Algorithm discussion
« Reply #188 on: August 13, 2011, 12:17:09 am »
Xeda, you're not the only one that has tried that. I had thought about that when I was ten, and I thought I had discovered something huge :P.
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Offline jnesselr

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Re: New RSA Algorithm discussion
« Reply #189 on: August 15, 2011, 03:52:12 pm »
Indeed, unfortunately, nothing new here.  I have no new ideas about this right now either, unfortunately.
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Offline sammyMaX

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Re: New RSA Algorithm discussion
« Reply #190 on: August 15, 2011, 05:26:21 pm »
Is there any way to do this without brute-force factoring? Even with the fastest algorithm, GNFS (a very complicated one as well), it is predicted that 1024 bit semiprimes will not be factored for another 3 to 4 years, and that is on supercomputers. It is arguable that a community-wide (distributed computing) project could perform as fast as a supercomputer, but it would take such a long time that most people would drop out.

My idea is, can we view the Nspire decrypt the OS during an installation and obtain the private keys from there?
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Offline AngelFish

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Re: New RSA Algorithm discussion
« Reply #191 on: August 15, 2011, 05:27:09 pm »
The private keys are not located anywhere in the OS. That's why they're called private keys.
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Offline sammyMaX

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Re: New RSA Algorithm discussion
« Reply #192 on: August 15, 2011, 05:30:51 pm »
How does the Nspire update an OS without decrypting it? Decryption has to happen somewhere.
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Offline fb39ca4

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Re: New RSA Algorithm discussion
« Reply #193 on: August 15, 2011, 05:34:56 pm »
It is not encrypted, it is digitally signed. On boot, the calculator verifies the signature of the OS, if even one byte of it was changed, the signature is invalid. We want to find the signing keys so we can make valid signatures of our own.
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Offline sammyMaX

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Re: New RSA Algorithm discussion
« Reply #194 on: August 15, 2011, 05:37:37 pm »
Does boot1 do this? If so, are we able to modify boot1?
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