Re: effective Method to calculate n-th power

On Wed, 8 Jun 2005, Jyrki Lahtonen wrote:

> > If q is the order of g^x, then the order of g^x^n can be calculated
> > as I hinted in other post. That is different than the value of g^x^n
> > which, knowing the order, can be 'simplified'.
>
> How can you compute the order of g^x^n starting from the
> order of g^x alone??
>
g^x^n = (g^x)^x^(n-1)
o(a^k) = o(a)/(k,o(a))

> E.g. consider the multiplicative group Z_{17}^* of order 16.
> Assume that the other given data is g^x=4 and n=3.
> Now we could have
> A) g=2,x=2, so the answer would be g^x^n=2^8=1 (mod 17),
> an element of order 1, or
> B) g=4,x=1, so the answer would be g^x^n=4^1=4 (mod 17),
> an element of order 4.
>
> Do you now see that we are given insufficient information?
No,Iofternavoideyestrain,bynotreadingequationswithoutspaces.
.

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