## Re: [PrimeNumbers] How is important?

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• ... 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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