Loading ...
Sorry, an error occurred while loading the content.

new kind of numbers?

Expand Messages
  • Hislat Nasanov
    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,
    Message 1 of 10 , Apr 3, 2002
    • 0 Attachment
      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). An example is the modulo 91 for
      which (13*7)-1=90 is multiple to (13-1) + (7-1) = 18,
      that is 90/18 = 5. Next example of such modules
      integers is 18721,481, for which 18721-1=18720, (18720
      / (96+150)) = 65, 481-1=480, (480 / (12+36)) =10. Such
      numbers have the some properties as Carmichael
      numbers, but unique difference of Carmichael numbers
      consists that Carmichael numbers are the product of
      least three distinct primes and necessary what P-1
      divides n-1 for every prime divisor P of n, n={P1, P2,
      P3...Pk}. For new kind of numbers it is not necessary.



      __________________________________________________
      Do You Yahoo!?
      Yahoo! Tax Center - online filing with TurboTax
      http://taxes.yahoo.com/
    • Phil Carmody
      ... What do you mean by it is impossible to use . Modular exponentiation doesn t suddenly stop working because you re using a modulus of a particular form,
      Message 2 of 10 , Apr 3, 2002
      • 0 Attachment
        --- Hislat Nasanov <hislat@...> 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'. Modular exponentiation
        doesn't suddenly stop working because you're using a modulus of a
        particular form, and RSA is little more than modular exponentiation.

        > An example is the modulo 91 for
        > which (13*7)-1=90 is multiple to (13-1) + (7-1) = 18,
        > that is 90/18 = 5.

        That exponent makes RSA impossible, does it?

        Exponent = 91
        Select e=5, which is relatively prime to Phi(91)=(13-1)(7-1)
        Therefore d=29, as 29.5 == 1 (mod Phi(91))
        Select message 11 arbitrarily
        E(11) = 11^5 (mod 91) = 72
        D(72) = 72^29 (mod 91) = 11
        Do you have any examples where D(E(x)) != x for that exponent?

        RSA is simply the exponentiation modulo composite c of a number by
        k.Phi(c)+1 in two stages, by using any bipartite split of j.Phi(c)+1.
        The laws of Number Theory (courtesy of Fermat and Legendre)
        _guarantee_ that the two stages combined give you the original number
        back.

        If you are trying to say that RSA is less secure as it's easier to
        calculate Phi(c) for such composites c, then that's a completely
        different claim. And if so, what evidence or proof do you have for
        the claim? I know of no factoring algorithm which is explicitly more
        capable of finding factors of numbers of the above form.

        Phil

        __________________________________________________
        Do You Yahoo!?
        Yahoo! Tax Center - online filing with TurboTax
        http://taxes.yahoo.com/
      • hislat
        ... What I means? Please visit to our site http://hasanov.ilm.uz/prime6e.htm You can find answer for your question.
        Message 3 of 10 , Apr 3, 2002
        • 0 Attachment
          --- 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. > __________________________________________________
          > Do You Yahoo!?
          > Yahoo! Tax Center - online filing with TurboTax
          > http://taxes.yahoo.com/
        • Hadley, Thomas H (Tom), ALINF
          Hislat, I kindly request that you answer Phil s question in a post to this e-group. Thanks, Tom Hadley ... What I means? Please visit to our site
          Message 4 of 10 , Apr 3, 2002
          • 0 Attachment
            Hislat,

            I kindly request that you answer Phil's question in a post to
            this e-group.

            Thanks,
            Tom Hadley
            -----Original Message-----
            --- 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. > __________________________________________________
          • 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 5 of 10 , Apr 4, 2002
            • 0 Attachment
              --- 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


              __________________________________________________
              Do You Yahoo!?
              Yahoo! Tax Center - online filing with TurboTax
              http://taxes.yahoo.com/
            • 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 6 of 10 , Apr 4, 2002
              • 0 Attachment
                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 7 of 10 , Apr 4, 2002
                • 0 Attachment
                  --- 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

                  __________________________________________________
                  Do You Yahoo!?
                  Yahoo! Tax Center - online filing with TurboTax
                  http://taxes.yahoo.com/
                • 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 8 of 10 , Apr 4, 2002
                  • 0 Attachment
                    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 9 of 10 , Apr 4, 2002
                    • 0 Attachment
                      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 10 of 10 , May 11, 2002
                      • 0 Attachment
                        --- 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.
                      Your message has been successfully submitted and would be delivered to recipients shortly.