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

Re: [PrimeNumbers] Re: Cracking RSA: Relationship between prime numbers and quantum theory

Expand Messages
  • Aleksey D. Tetyorko
    ... Hi, Kent! I took a look at your paper. As I see it there *is* function C1-- (P1, P2), but existence does not mean fast computability . If C1=P1*P2 and
    Message 1 of 12 , Aug 1, 2001
    • 0 Attachment
      > > > I'm actively trying to crack the RSA code. My paper:
      > > >
      > > > http://www.mslinux.com/research/cracking_pki/cracking_pki.html
      Hi, Kent!
      I took a look at your paper. As I see it there *is* function
      C1-->(P1, P2), but 'existence' does not mean 'fast
      computability'. If C1=P1*P2 and Pi are odd primes, then we
      can use the following (where sigma(n) is the sum of all the
      divisors of n).

      {sigma(C1)=1+P1+P2+C1
      {C1=P1*P2

      And we have the equation:

      x^2-(sigma(C1)-C1-1)*x+C1=0
      {P1,P2}=
      {((sigma(C1)-C1-1)+-sqrt((sigma(C1)-C1-1)^2-4*C1))/2}

      Then sigma(x) can be computed from the following
      equations:

      sigma(1)=1
      sum(((x-1)-5*k*(k+1))/2*sigma(x-k*(k+1)),
      for k=0 to FLOOR((SQRT(1+4*x)-1)/2))=0

      These equations make the infinite matrix equation for
      sigma(x). Maybe you can use it as density matrix equation.
      But I don't know how it can be done, alas.

      Aleksey
    • Kent Nguyen
      ... occupy precisely ... can you elaborate? Why don t you use the word occupy exactly ? ... If there is a wavefunction to describe prime number, and I
      Message 2 of 12 , Aug 1, 2001
      • 0 Attachment
        On Wednesday 01 August 2001 08:10, Paul Leyland wrote:
        > > One of the postulate in quantum theory states that no two
        > > particle can occupy the same place at the same time.
        >
        > Not true in general. It is true for fermions (particles with spin
        > (2i+1)/2) and is known as the Pauli exclusion principle. For bosons
        > (particles with integral spin) particles can, and do, occupy precisely
        > the same state at the same time. It's why lasers, superfluids and
        > superconductors have such interesting properties.

        "occupy precisely" ... can you elaborate? Why don't you use the word "occupy
        exactly"?

        >
        > I fail to see what any of this has to do with factorization, but it will
        > be interesting to see if anything comes from it.

        If there is a wavefunction to describe prime number, and I believe there is.
        A few scientists have report a spectral in nature that resemble prime number
        sequence.

        If this wavefunction exist we can use the "position" of the prime numbers to
        figure out primes to a composite number.

        (1, 2) (2, 3) (3, 5) (4, 7) ... (n, p)

        Rather than finding p we find n for the wavefunction.

        Such that sigma(C1) = { n1, n2 }.

        --kent
      • Kent Nguyen
        ... Hi Aleksey! ... If I find the wavefunction, I will use Newton s method of approximation to find out the primes. In order to use Newton s method, I need to
        Message 3 of 12 , Aug 1, 2001
        • 0 Attachment
          On Wednesday 01 August 2001 11:41, Aleksey D. Tetyorko wrote:
          > > > > I'm actively trying to crack the RSA code. My paper:
          > > > >
          > > > > http://www.mslinux.com/research/cracking_pki/cracking_pki.html
          >
          > Hi, Kent!

          Hi Aleksey!

          > I took a look at your paper. As I see it there *is* function
          > C1-->(P1, P2), but 'existence' does not mean 'fast
          > computability'. If C1=P1*P2 and Pi are odd primes, then we
          > can use the following (where sigma(n) is the sum of all the
          > divisors of n).
          >
          > {sigma(C1)=1+P1+P2+C1
          > {C1=P1*P2
          >
          > And we have the equation:
          >
          > x^2-(sigma(C1)-C1-1)*x+C1=0
          > {P1,P2}=
          > {((sigma(C1)-C1-1)+-sqrt((sigma(C1)-C1-1)^2-4*C1))/2}
          >
          > Then sigma(x) can be computed from the following
          > equations:
          >
          > sigma(1)=1
          > sum(((x-1)-5*k*(k+1))/2*sigma(x-k*(k+1)),
          > for k=0 to FLOOR((SQRT(1+4*x)-1)/2))=0
          >
          > These equations make the infinite matrix equation for
          > sigma(x). Maybe you can use it as density matrix equation.
          > But I don't know how it can be done, alas.

          If I find the wavefunction, I will use Newton's method of approximation to
          find out the primes. In order to use Newton's method, I need to make a good
          guess, a good guess is sqrt(C1)/2. Newton's method of approximation is very
          fast, it is the method used in calculator to find square root, cubic root,
          and inverses.

          For example to find sqrt of 2, using Netwon's method, it only takes 5 adding,
          dividing, and multiplying iterations to come close to the answer you see in
          your calculator.

          A good reference of Newton's method:
          http://gamba.ugrad.math.ubc.ca/coursedoc/math100/notes/approx/newton.html

          --kent
        • Paul Leyland
          ... precisely ... You re quibbling. If you prefer it, I m equally happy with occupy exactly . If you really want to get pedantic, I d be even happier with
          Message 4 of 12 , Aug 1, 2001
          • 0 Attachment
            > > Not true in general. It is true for fermions (particles with spin
            > > (2i+1)/2) and is known as the Pauli exclusion principle. For bosons
            > > (particles with integral spin) particles can, and do, occupy
            precisely
            > > the same state at the same time. It's why lasers, superfluids and
            > > superconductors have such interesting properties.
            >
            > "occupy precisely" ... can you elaborate? Why don't you use
            > the word "occupy exactly"?

            You're quibbling. If you prefer it, I'm equally happy with "occupy
            exactly". If you really want to get pedantic, I'd be even happier with
            phrasing along the lines of "there is no constraint on the occupancy
            number of an eigenstate of a system of bosons" but that seems unduly
            wordy.

            If we're being pedantic, your original statement is unequivocably false.
            It's not even strictly true for fermions in that the Pauli exclusion
            principle is not really a postulate of quantum mechanics (in the sense
            of a presupposed truth which is not amenable to question) but rather a
            consequence of the anticommutativity of operators acting on fermion
            quantum fields. I was being generous and assumed you meant
            "consequence" or "feature" where you wrote "postulate".

            Even being that generous, your statement "no two particle (sic) can
            occupy the same place at the same time" is false, if by "place" you mean
            spatial location. For a start, two fermions differing only in spin can
            occupy the same energy state. Further, from Heisenberg's uncertainty
            principle, the spatial location of each of two particles can only be
            precisely determined if their momenta are completely undetermined. If
            you know anything about the momenta of the particles, their wave
            functions *will* overlap in space. Trying to nail down "the same time"
            is equally difficult: the particle's energy is then the conjugate
            quantity. But I'll be generous again and assume that by "particle" you
            meant fermion and that by "place" you meant eigenstate.

            If you really want to make progress, I suggest that you consult an
            introductory text or two on quantum field theory. It's 19 years since I
            last studied QFT so the references I can quote from memory are now
            outdated and possibly unavailable, but I'm sure there must be
            contemporary works available.

            (Just checked on Amazon: a search on Quantum Field Theory yields 596
            hits, so you ought to be able to find something. Further, the book I
            own, Elements of Advanced Quantum Theory written by John M Ziman in
            1975, is still in print.)


            Paul
          • Paul Leyland
            ... precisely ... You re quibbling. If you prefer it, I m equally happy with occupy exactly . If you really want to get pedantic, I d be even happier with
            Message 5 of 12 , Aug 1, 2001
            • 0 Attachment
              > > Not true in general. It is true for fermions (particles with spin
              > > (2i+1)/2) and is known as the Pauli exclusion principle. For bosons
              > > (particles with integral spin) particles can, and do, occupy
              precisely
              > > the same state at the same time. It's why lasers, superfluids and
              > > superconductors have such interesting properties.
              >
              > "occupy precisely" ... can you elaborate? Why don't you use
              > the word "occupy exactly"?

              You're quibbling. If you prefer it, I'm equally happy with "occupy
              exactly". If you really want to get pedantic, I'd be even happier with
              phrasing along the lines of "there is no constraint on the occupancy
              number of an eigenstate of a system of bosons" but that seems unduly
              wordy.

              If we're being pedantic, your original statement is unequivocably false.
              It's not even strictly true for fermions in that the Pauli exclusion
              principle is not really a postulate of quantum mechanics (in the sense
              of a presupposed truth which is not amenable to question) but rather a
              consequence of the anticommutativity of operators acting on fermion
              quantum fields. I was being generous and assumed you meant
              "consequence" or "feature" where you wrote "postulate".

              Even being that generous, your statement "no two particle (sic) can
              occupy the same place at the same time" is false, if by "place" you mean
              spatial location. For a start, two fermions differing only in spin can
              occupy the same energy state. Further, from Heisenberg's uncertainty
              principle, the spatial location of each of two particles can only be
              precisely determined if their momenta are completely undetermined. If
              you know anything about the momenta of the particles, their wave
              functions *will* overlap in space. Trying to nail down "the same time"
              is equally difficult: the particle's energy is then the conjugate
              quantity. But I'll be generous again and assume that by "particle" you
              meant fermion and that by "place" you meant eigenstate.

              If you really want to make progress, I suggest that you consult an
              introductory text or two on quantum field theory. It's 19 years since I
              last studied QFT so the references I can quote from memory are now
              outdated and possibly unavailable, but I'm sure there must be
              contemporary works available.

              (Just checked on Amazon: a search on Quantum Field Theory yields 596
              hits, so you ought to be able to find something. Further, the book I
              own, Elements of Advanced Quantum Theory written by John M Ziman in
              1975, is still in print.)


              Paul
            • Kent Nguyen
              ... First Pauli exclusion principle states: In a closed system, no two electrons can occupy the same state. http://theory.uwinnipeg.ca/mod_tech/node168.html
              Message 6 of 12 , Aug 1, 2001
              • 0 Attachment
                On Wednesday 01 August 2001 13:01, Paul Leyland wrote:
                > > > Not true in general. It is true for fermions (particles with spin
                > > > (2i+1)/2) and is known as the Pauli exclusion principle. For bosons
                > > > (particles with integral spin) particles can, and do, occupy
                >
                > precisely
                >
                > > > the same state at the same time. It's why lasers, superfluids and
                > > > superconductors have such interesting properties.
                > >
                > > "occupy precisely" ... can you elaborate? Why don't you use
                > > the word "occupy exactly"?
                >
                > You're quibbling. If you prefer it, I'm equally happy with "occupy
                > exactly". If you really want to get pedantic, I'd be even happier with
                > phrasing along the lines of "there is no constraint on the occupancy
                > number of an eigenstate of a system of bosons" but that seems unduly
                > wordy.

                First Pauli exclusion principle states:
                "In a closed system, no two electrons can occupy the same state."
                http://theory.uwinnipeg.ca/mod_tech/node168.html

                Note Pauli only states for occupance of same state not same time.

                This isn't "exactly" what I'm saying. Go back and read "exactly" what I
                said. Because when you say "occupy exactly" ... I'm very suspicious whether
                you've figured a way to violate Heinsberg uncertainity principle.
                http://www.srikant.org/core/node12.html

                >
                > If we're being pedantic, your original statement is unequivocably false.
                > It's not even strictly true for fermions in that the Pauli exclusion
                > principle is not really a postulate of quantum mechanics (in the sense
                > of a presupposed truth which is not amenable to question) but rather a
                > consequence of the anticommutativity of operators acting on fermion
                > quantum fields. I was being generous and assumed you meant
                > "consequence" or "feature" where you wrote "postulate".

                You don't have to be generous. You need to understand what I wrote. You are
                assuming what I wrote is "Pauli exclusion principle". Having bad assumption
                leads to bad argument.

                >
                > If you really want to make progress, I suggest that you consult an
                > introductory text or two on quantum field theory. It's 19 years since I
                > last studied QFT so the references I can quote from memory are now
                > outdated and possibly unavailable, but I'm sure there must be
                > contemporary works available.

                Working for your employer really makes you *think* you are making progress.
                :)

                >
                > (Just checked on Amazon: a search on Quantum Field Theory yields 596
                > hits, so you ought to be able to find something. Further, the book I
                > own, Elements of Advanced Quantum Theory written by John M Ziman in
                > 1975, is still in print.)

                Thanks for using amazon.com, it's better than bn.com don't you think? :)

                --kent
              • Paul Leyland
                ... No it does not! Just because that web page makes that claim that doesn t mean that the PEP is as stated. The PEP states that no two fermions can occupy
                Message 7 of 12 , Aug 1, 2001
                • 0 Attachment
                  > First Pauli exclusion principle states:
                  > "In a closed system, no two electrons can occupy the same state."
                  > http://theory.uwinnipeg.ca/mod_tech/node168.html

                  No it does not! Just because that web page makes that claim that
                  doesn't mean that the PEP is as stated. The PEP states that no two
                  fermions can occupy the same quantum state. Electrons are fermions,
                  indeed, but electrons can pair up to form "Cooper pairs" which
                  themselves are bosons. These bosons can indeed occupy the same quantum
                  state and, when they do, give rise to the phenomenon of
                  supercoductivity.

                  The web page itself goes on to state "actually, protons and neutrons
                  obey the same principle, while photons do not)" something you seem to
                  have missed. Lasers function precisely because photons do not obey the
                  same principle. Protons and neutrons are spin-half particles and thus
                  fermions; photons are spin-zero bosons. Photons, as far as we know,
                  have no sub-structure but both protons and neutrons are composite
                  particles (as are Cooper pairs and helium nuclei). The helium-4 nucleus
                  is a spin-zero boson and so can violate the PEP. When it does, bulk
                  helium-4 becomes superfluid. The helium-3 nucleus is a spin-half
                  fermion and so liquid helium-3 doesn't become superfluid until the
                  temperature is low enough for pairs of nuclei to form spin-zero bosons,
                  whereupon it too shows superfluidity.

                  > This isn't "exactly" what I'm saying. Go back and read
                  > "exactly" what I said.

                  Very well, I quote: "One of the postulate in quantum theory states that
                  no two particle can occupy the same place at the same time."

                  This statement is just plain wrong, for the reasons I went into
                  previously.

                  > Because when you say "occupy exactly" ... I'm very
                  > suspicious whether
                  > you've figured a way to violate Heinsberg uncertainity principle.
                  > http://www.srikant.org/core/node12.html

                  For a start, Heisenberg's uncertainty principle only applies to
                  conjugate quantities, such as energy/time and linear momentum/position
                  (these two quantities are, of course, special cases of the more general
                  4-momentum / spacetime coordinates). It does *not* apply to
                  non-conjugate measurements, such as the x-component of momentum and the
                  y coordinate, which can be simultaneously measured to arbitrary
                  accuracy.

                  In general, if the operators corresponding to observables anti-commute,
                  HUP applies. If they commute, they do not.

                  Please read some real books on quantum theory.


                  > assuming what I wrote is "Pauli exclusion principle". Having
                  > bad assumption leads to bad argument.

                  But that is precisely what you did write!

                  > Working for your employer really makes you *think* you are
                  > making progress. :)

                  I don't think I understand that comment. Don't bother elucidating, as
                  the smiley suggests that it's probably not that important.


                  I'm becoming ever more convinced that this thread has very little, if
                  anything, to do with prime numbers. I've probably already bored the
                  majority of readers, so I'll drop out of it here.


                  Paul
                • Kent Nguyen
                  ... You miss the point of the relation to prime number. Cracking the RSA code is a linear problem, thus a one-dimensional problem. You come and talk about the
                  Message 8 of 12 , Aug 1, 2001
                  • 0 Attachment
                    > I'm becoming ever more convinced that this thread has very little, if
                    > anything, to do with prime numbers. I've probably already bored the
                    > majority of readers, so I'll drop out of it here.

                    You miss the point of the relation to prime number.

                    Cracking the RSA code is a linear problem, thus a one-dimensional problem.
                    You come and talk about the 4th dimension, which to me doesn't seem relevant.
                    So you ya, you convince yourself.

                    As I've said before, there exist a very close spectra that resemble prime
                    number sequence.
                    http://www.maths.ex.ac.uk/~mwatkins/zeta/physics1.htm

                    My equation with two variables:

                    Assume = C1 = P1*P2
                    f(x) = x^2 - (P1 + P2)*x + C1 = 0

                    I only have one equation with two variables. I need another equation to
                    solve for P1 and P2. That's what lead me to quantum mechanic in trying to
                    find the wavefunction that describes prime number sequence.

                    If P1 = P2, I can use the quadraic formula to solve for x. Resulting in
                    sqrt(C1).

                    If P1 < P2 or P1 > P2, it's a more difficult situation.

                    --kent
                  Your message has been successfully submitted and would be delivered to recipients shortly.