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How is important?

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  • hislat
    How is important value of function Y = X^i mod P, when i=P-1? I think every colleague is agree, when P=P1*P2 , value of function Y = X ^((P1-1) +(P2-1))mod P =
    Message 1 of 2 , Apr 4, 2002
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      How is important value of function Y = X^i mod P, when i=P-1?
      I think every colleague is agree, when P=P1*P2 , value of function

      Y = X ^((P1-1) +(P2-1))mod P = X^(P-1)mod P will true.

      Let's look to function Y=X^i mod35

      In this case Y=X^10 mod35=X^34mod35

      and value of function Y from X=1 to 35 is looking follows:

      1 9 4 11 30 1 14 29 16 25 11 9 29 21 15 16 4 4 16 15 21 29 9 11 25 16
      29 14 1 30 11 4 9 1 0


      I am sorry I can make some grammatically mistaks
    • Phil Carmody
      ... X^(P-1) . X == 1 (mod P) for prime P and Carmichaels too. ... 5*7, lambda(35) = lcm(4,6) = 12 ... Yup, as P1.P2-1 == P1+P2-2 (mod lambda(P1.P2)) But what s
      Message 2 of 2 , Apr 4, 2002
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        --- hislat <hislat@...> wrote:
        > How is important value of function Y = X^i mod P, when i=P-1?

        X^(P-1) . X == 1 (mod P) for prime P and Carmichaels too.

        > I think every colleague is agree, when P=P1*P2 , value of function
        >
        > Y = X ^((P1-1) +(P2-1))mod P = X^(P-1)mod P will true.
        >
        > Let's look to function Y=X^i mod35

        5*7, lambda(35) = lcm(4,6) = 12

        > In this case Y=X^10 mod35=X^34mod35

        Yup, as P1.P2-1 == P1+P2-2 (mod lambda(P1.P2))

        But what's the actaul attack on RSA you're proposing?

        There will always be an exponent x, < (P1-1)(P2-1) such that
        b^x == 1 (mod P1.P2). Having one of size ~sqrt(P1.P2) is no more a
        weakness than P1.P2 having a factor < sqrt(P1.P2), as far as I can
        see.

        Phil


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