Browse Groups

• 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
View Source
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
• ... 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
View Source
--- 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

__________________________________________________
Do You Yahoo!?
Yahoo! Tax Center - online filing with TurboTax
http://taxes.yahoo.com/
Your message has been successfully submitted and would be delivered to recipients shortly.
• Changes have not been saved
Press OK to abandon changes or Cancel to continue editing
• Your browser is not supported
Kindly note that Groups does not support 7.0 or earlier versions of Internet Explorer. We recommend upgrading to the latest Internet Explorer, Google Chrome, or Firefox. If you are using IE 9 or later, make sure you turn off Compatibility View.