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Re: [PrimeNumbers] Re: new kind of numbers?

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  • Phil Carmody
    ... I think I see what your attack is now. The property you ve found is a real one. However, as I said before, it doesn t make RSA _impossible_, simply
    Message 1 of 10 , Apr 4 6:28 AM
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      --- hislat <hislat@...> wrote:
      > --- In primenumbers@y..., Phil Carmody <thefatphil@y...> wrote:
      > > --- Hislat Nasanov <hislat@y...> wrote:
      > > > Is it new kind of numbers(modulo)?
      > > >
      > > > Our researches show, that in RSA cryptosystems it is
      > > > impossible to use as the modulo product of such prime
      > > > numbers P1, P2, for which ((P1*P2)-1) will be multiple
      > > > to (P1-1) + (P2-1).
      > >
      > > What do you mean by 'it is impossible to use'.
      >
      > What I means? Please visit to our site
      > http://hasanov.ilm.uz/prime6e.htm You can find answer for your
      > question. >

      I think I see what your attack is now.
      The property you've found is a real one. However, as I said before,
      it doesn't make RSA _impossible_, simply _weaker_.
      However, it appears that the main property that makes them weak is
      smoothness.

      in 91, 13-1 is 3-smooth, 7 is 3-smooth.
      in 481, 13-1 is 3-smooth, 37-1 is 3-smooth.
      in 18721, 18721 != 97*151, so your page needs correcting, but anyway,
      97-1 is 3-smooth, 193-1 is 3-smooth.

      Basically you've found numbers that can be split using P-1 factoring
      using exponent P1.P2-1. This exponent is less likely to split most
      numbers than a traditionally chosen exponent (product of small prime
      powers). You've used this new attack to crack something that can be
      cracked using P-1 with exponent 2^5.3^2. i.e. there's already a
      simpler attack against these numbers.

      But it's /already/ recommended that primes do not have smooth P-1 or
      P+1, which would make the product easily factorable.

      Can you find an example which wouldn't be immediately thrown out by
      looking at the factors of P1+/-1 and P2+/-1?

      Can you find any examples amongst the 'safe' primes?

      Don't get me wrong, you've found a very interesting property (I must
      have spent half an hour bouncing equations and relations around
      before writing this, it was quite fun trying to get to the root of
      it), it's just that it seems to be contained inside a more general
      property that is already defended against.

      Phil


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    • Chris Caldwell
      Now that is an odd subject line eh? I ve got a problem maybe one of you can help me with. I have one image on my pages which I do not have the rights to use,
      Message 2 of 10 , Apr 4 7:49 AM
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        Now that is an odd subject line eh?

        I've got a problem maybe one of you can help me with. I have one image on
        my pages which I do not have the rights to use, it is the image of a
        postage mark which says "2^11213-1 is prime"

        http://www.utm.edu/research/primes/gifs/postage.gif

        I would like a similar image which I can use on these pages, in articles,
        books... In fact, I also wonder if there are any originals laying around,
        I'd like to have an envelope with this stamp as well (to frame and put on
        my wall).

        Can any of you provide me with either the real thing, or a clean image
        that I can use (with appropriate acknowledgment of course)? I have
        limited funds to buy an envelop, but I would indeed bid on one if I saw it
        on e-bay!

        (Otherwise I'll ned to try to figure out what text I copied this from, and
        get permission from the publisher, or try to figure out who to ask at
        Illinois about getting an image of a postage mark they used 40 years ago)

        Chris.

        By the way--a Japanese group is translating a subset of my pages into a
        book of roughly 440 pages; they need the image, this prompted me to fix
        this old copyright permission problem... Luke Welsh also let me copy his
        old Mersenne site, and I have written a new Mersenne bio (he was
        amazing!), I hope to redo the /mersenne/ pages before too long and get
        Luke's stuff back up (permission problems purgatory!)
      • Phil Carmody
        ... If you don t have the rights to use it then you ve probably just dug yourself deeper... :-) However, I m curious where the rights to this lie. As far as
        Message 3 of 10 , Apr 4 8:43 AM
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          --- Chris Caldwell <caldwell@...> wrote:
          > Now that is an odd subject line eh?
          >
          > I've got a problem maybe one of you can help me with. I have one
          > image on
          > my pages which I do not have the rights to use, it is the image of
          > a
          > postage mark which says "2^11213-1 is prime"
          >
          > http://www.utm.edu/research/primes/gifs/postage.gif

          If you don't have the rights to use it then you've probably just dug
          yourself deeper... :-)

          However, I'm curious where the 'rights' to this lie.

          As far as I can tell, the image created by stamp itself was
          'broadcast', and thus cannot be copyrighted (IANAL, but I followed
          the CO$ vs. Xenon Panousis trial quite closely, and the wide
          distribution of the OTs was cited as a reason why no copyright could
          be claimed.).

          > I would like a similar image which I can use on these pages, in
          > articles,
          > books... In fact, I also wonder if there are any originals laying
          > around,
          > I'd like to have an envelope with this stamp as well (to frame and
          > put on
          > my wall).
          >
          > Can any of you provide me with either the real thing, or a clean
          > image
          > that I can use (with appropriate acknowledgment of course)? I have
          > limited funds to buy an envelop, but I would indeed bid on one if I
          > saw it
          > on e-bay!
          >
          > (Otherwise I'll ned to try to figure out what text I copied this
          > from, and
          > get permission from the publisher, or try to figure out who to ask
          > at
          > Illinois about getting an image of a postage mark they used 40
          > years ago)

          /Mathematics Teacher/ magazine?

          Google's cache provided the following, whose original is no longer
          available:

          http://216.239.35.100/search?q=cache:dDDkdjHiRA8C:www.kcnet.com/~v523/archoct1.html+11213+is+prime+stamp&hl=en

          <<<
          ...
          And then today while flipping through an old issue of Mathematics
          Teacher magazine, I found an article about the first 36 perfect even
          numbers
          ...
          Three of my favorite parts of the article:
          ...
          2) A postage meter stamp taken from 1986 reading "2^11213-1 is
          prime."
          ...
          >>>

          HTH,

          Phil

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        • Jon Perry
          If you go to: http://turnbull.dcs.st-and.ac.uk/~history/PictDisplay/Riemann.html this is where I obtained a picture of Riemann for:
          Message 4 of 10 , Apr 4 9:39 AM
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            If you go to:

            http://turnbull.dcs.st-and.ac.uk/~history/PictDisplay/Riemann.html

            this is where I obtained a picture of Riemann for:

            http://www.users.globalnet.co.uk/~perry/maths/riemannshypothesis/riemannshyp
            othesis.htm

            Clicking on the copyright link (bottom right) you get:

            ---

            We do not own the copyright to the images used on this website.

            We believe that most of the images are in the public domain and that
            provided you use them on a website you are unlikely to encounter any
            difficulty.
            However, if you wish to use them in any other way -- in "paper" publishing
            or on a CD for example -- we cannot guarantee that there may not be
            outstanding copyright problems.

            We have not kept a record of where we found any of the images we have used.

            If you believe that you own the rights to any of the images we use, please
            contact us and we will either withdraw that picture or add an
            acknowledgement.

            JOC/EFR August 2001

            ---

            Jon Perry
            perry@...
            http://www.users.globalnet.co.uk/~perry/maths
            BrainBench MVP for HTML and JavaScript
            http://www.brainbench.com
          • Dan Morenus
            You can find images of Urbana s 2^11213-1 is prime postmark and IBM s 2^19937-1 is prime letterhead in Figure 72 on page 166 of _Mathematical Magic Show_,
            Message 5 of 10 , Apr 4 9:49 AM
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              You can find images of Urbana's "2^11213-1 is prime"
              postmark and IBM's "2^19937-1 is prime" letterhead in Figure
              72 on page 166 of _Mathematical Magic Show_, by Martin
              Gardner, (c) 1977 by Martin Gardner, published by Alfred A.
              Knopf, Inc.

              Hope this helps,
              That bloody top-poster Dan Morenus

              Chris Caldwell wrote:
              >
              > Now that is an odd subject line eh?
              >
              > I've got a problem maybe one of you can help me with. I have one image on
              > my pages which I do not have the rights to use, it is the image of a
              > postage mark which says "2^11213-1 is prime"
              >
              > http://www.utm.edu/research/primes/gifs/postage.gif
              >
              > I would like a similar image which I can use on these pages, in articles,
              > books... In fact, I also wonder if there are any originals laying around,
              > I'd like to have an envelope with this stamp as well (to frame and put on
              > my wall).
              >
              > Can any of you provide me with either the real thing, or a clean image
              > that I can use (with appropriate acknowledgment of course)? I have
              > limited funds to buy an envelop, but I would indeed bid on one if I saw it
              > on e-bay!
              >
              > (Otherwise I'll ned to try to figure out what text I copied this from, and
              > get permission from the publisher, or try to figure out who to ask at
              > Illinois about getting an image of a postage mark they used 40 years ago)
              >
              > Chris.
              >
              > By the way--a Japanese group is translating a subset of my pages into a
              > book of roughly 440 pages; they need the image, this prompted me to fix
              > this old copyright permission problem... Luke Welsh also let me copy his
              > old Mersenne site, and I have written a new Mersenne bio (he was
              > amazing!), I hope to redo the /mersenne/ pages before too long and get
              > Luke's stuff back up (permission problems purgatory!)

              -- Dan Morenus (dmorenus@...)

              -- This parachute is not warranted to be suitable --
              -- for any purpose, including descending safely --
              -- from an airplane to the ground. --
            • primemogul
              ... Who knows... but now I have the real thing! Paul Bateman, who created both of the famous stamps there (the other was four colors suffice ) sent me an
              Message 6 of 10 , May 11, 2002
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                --- In primenumbers@y..., Phil Carmody <thefatphil@y...> wrote:
                > --- Chris Caldwell <caldwell@u...> wrote:
                > > I have one image on my pages which I do not have
                > > the rights to use, it is the image of a
                > > postage mark which says "2^11213-1 is prime"
                > >
                > > http://www.utm.edu/research/primes/gifs/postage.gif
                >
                > If you don't have the rights to use it then you've probably just
                > dug yourself deeper... :-)
                > However, I'm curious where the 'rights' to this lie.

                Who knows... but now I have the real thing! Paul Bateman,
                who created both of the famous stamps there (the other was
                "four colors suffice") sent me an original he created in
                1985 (plus his permission):

                http://www.utm.edu/research/primes/gifs/stamp.gif

                The Mersenne was used from 1966 to 1976, then the four colors was
                implemented. Apparantly the original template was discarded
                by a non-academic employee when the campus switched to a new
                postage system.

                Chris.
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