Re: [PrimeNumbers] How is important?
- --- 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 function5*7, lambda(35) = lcm(4,6) = 12
> 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^34mod35Yup, 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
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