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Re: [PrimeNumbers] How is important?

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  • 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 1 of 2 , Apr 4, 2002
      --- 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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