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Comparing efficiency of factoring methods

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  • Kermit Rose
    I m wondering how my current factoring program compares to other methods used in terms of the amount of work needed to find the factors. Factored here are
    Message 1 of 2 , Aug 4, 2006
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      I'm wondering how my current factoring program compares to other methods
      used

      in terms of the amount of work needed to find the factors.

      Factored here are 10^16 + 37 and 10^16+39.


      The difficulty number is the number of trial difference of squares used in
      the algorithm.

      z = 10000000000000037 x = 168040027 y = 59509631 difficulty = 1382382
      z = 10000000000000039 x = 1830629 y = 5462603291 difficulty = 655091



      Kermit < kermit@... >
    • Phil Carmody
      ... If you really wondered how it compares to other methods, why have you not compared it to other methods? Grab Miracl, and see how quickly P-1, P+1, Rho, and
      Message 2 of 2 , Aug 4, 2006
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        --- Kermit Rose <kermit@...> wrote:
        > I'm wondering how my current factoring program compares to other methods
        > used in terms of the amount of work needed to find the factors.
        >
        > Factored here are 10^16 + 37 and 10^16+39.
        >
        > The difficulty number is the number of trial difference of squares used in
        > the algorithm.
        >
        > z = 10000000000000037 x = 168040027 y = 59509631 difficulty = 1382382
        > z = 10000000000000039 x = 1830629 y = 5462603291 difficulty = 655091

        If you really wondered how it compares to other methods, why have you not
        compared it to other methods?

        Grab Miracl, and see how quickly P-1, P+1, Rho, and ECM can split those
        numbers.

        168040027 will be found by P-1, and often P+1, trivially.
        59509631 will be found by P+1 trivially.
        1830629 will be found by P+1 trivially.

        Most things that P+/-1 can find trivially Rho and ECM can too.

        Phil


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