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Topic: why RSA has already been factored or why 2 is one of the factors of
the RSA numbers

Replies: 3   Last Post: Jan 18, 2014 9:32 PM

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Daniel Joyce

Posts: 197
Registered: 1/5/14
Re: why RSA has already been factored or why 2 is one of the factors
of the RSA numbers

Posted: Jan 18, 2014 7:36 PM
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On Saturday, January 18, 2014 5:19:44 PM UTC-5, Port563 wrote:
> "me" <idatarm@gmail.com> wrote in message
>
> news:842b8661-d52e-4506-ae35-767371d7bc86@googlegroups.com...
>

> > read
>
> > https://davesinvoice.sharefile.com/d/s37070319f4d49a7a
>
> >
>
>
>
> "why RSA has already been factored or why 2 is one of the factors of the RSA
>
> numbers
>
>
>
> 1 Introduction
>
> Factoring is a major problem in crytography. Factoring is seen as an
>
> extremely complex
>
> problem. This paper is about why all that work is a waste because factoring
>
> is impractical
>
> since it lacks veri cation. The objective of the paper is to highlight the
>
> fact that the
>
> whole problem lacks veri cation, and therefore lets you conclude 2 is one of
>
> the factors
>
> of RSA numbers because it lacks veri cation.
>
> 1.1 Proof
>
> Guess a number. It is the factor because it lacks veri cation and for the
>
> following
>
> reasons. There are many things to notice. Most people cannot type. Most
>
> programmers
>
> make errors while typing. Most programs dont compile the rst time. Most
>
> compilers
>
> do not compile ther rst time. Compilers have bugs in them. There is a
>
> history of buggy
>
> compilers being built on top of buggy compilers, which were once again built
>
> on buggy
>
> compilers. Hardware is also
>
> aky. For many years since the 40s, computers were kindof
>
> aky and did not work correctly. Modern computers are built on top of the
>
> logic built
>
> by these buggy computers. So, the list goes on. The whole problem lacks
>
> veri cation.
>
> There is no way to correctly know if anything really works. Therefore, it is
>
> possible
>
> to conclude that he given number is a factor and just cannot be absolutely
>
> veri ed.
>
> Suppose this number was 2, problem solved. All RSA numbers have been
>
> factored by 2."
>
>
>
>
>
> Sorry, but this is simply nonsense.
>
>
>
> It is also uninteresting.
>
>
>
> The only interesting thing I observed in or about it is that when I
>
> copy/pasted the PDF
>
> into OE, all occurrences of "fi" were changed into a blob and "fl" was
>
> broken entirely.
>
> I guess this is to do with Adobe character "kerning". I will look into
>
> that.
>
>
>
> I'm not being rude, I hope, but giving you the reality will save your own
>
> time.

Port563,

How about this --

RSA-210 has 210 decimal digits (696 bits), and has not been factored so far.

245246644900278211976517663573088018467026787678332759743414451715061600830038587216952208399332071549103626827191679864079776723243005600592035631246561218465817904100131859299619933817012149335034875870551067

Just looking at this old file now and found out it was factored
in 2013 and I will check against my closest seed polynomial divider
prime lookup. I completed a mess of polynomial ratio's for this composite.

It looks like my 1.3 ratio below is the closest so I will use that
polynomial divisor first for the prime look-up.


Actual factors for rsa210

435958568325940791799951965387214406385470910265220196318705482144524085345275999740244625255428455944579
x
562545761726884103756277007304447481743876944007510545104946851094548396577479473472146228550799322939273

My prime search polynomial divisor is 1.3 ratio the
closest high order value to the actual smallest factor.
4.34340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394496487329e+104

A list of 39 prime pairs below.
I factored the product of the first prime pair in the list below
and here is the factored results.

Factorization complete in 0d 0h 16m 41s
ECM: 100279859 modular multiplications
Prime checking: 1099399 modular multiplications

Timings:
Primality test of 3 numbers: 0d 0h 0m 3.0s
Factoring 1 number using ECM: 0d 0h 16m 38.3s

0 days 16 min. 41s for a 210 digit composite --Wow!!

Port563, they are definitly a strange composite.

I wonder how long it actually took to factor because I guess it was
a tough one because larger rsa composites were factored before this one.

The product of these two factors were used =
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394496596739
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207579807901
---------------------------------------------------------------------------------------------------------
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394496655119
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207579732007
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394496709779
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207579660949
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394496781599
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207579567583
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394496928599
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207579376483
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394497585299
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207578522773
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394497861719
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207578163427
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394497871739
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207578150401
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394498253939
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207577653541
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394498551839
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207577266271
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394498603679
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207577198879
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394499107799
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207576543523
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394499437799
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207576114523
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394499546879
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207575972719
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394499824439
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207575611891
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394499874479
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207575546839
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394500773099
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207574378633
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394500906419
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207574205317
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394501103519
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207573949087
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394501344779
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207573635449
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394501799999
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207573043663
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394501874399
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207572946943
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394502007119
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207572774407
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394502431979
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207572222089
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394502500739
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207572132701
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394502616239
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207571982551
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394502958539
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207571537561
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394503204179
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207571218229
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394503618239
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207570679951
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394504110599
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207570039883
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394504639379
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207569352469
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394504684199
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207569294203
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394504811279
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207569128999
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394504971899
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207568920193
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394504982219
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207568906777
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394505243339
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207568567321
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394505707979
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207567963289
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394505733839
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207567929671
434340034198905405143300959414546121023970003167087896008932318652337325416792515287970627670394506462479
564642044458577026686291247238909957331161004117214223379094765013128713554515217114221059706207566982439

I am sure most of these pairs will factor under a half hour.

Dan




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