x is just an integer in this case. Since there's no multiplication
operator (we hope) in the curves used for crypto, x is just an indicator of
how many times to square and multiply.
Now as to whether you always have an x such that xA=B exists, that depends
on the following:
Are A and B both points on the curve?
Is A a generator of the group? Or, more specifically, does the orbit
generated by A include B?
The latter question is what you're interested in. If A is a generator, B
is in A's orbit. Otherwise, I see no way short of solving the discrete log
problem of deciding whether B is in A's orbit.
Cheers
Dan
At 02:11 PM 8/23/99 -0600, you wrote:
>The ecc discrete log problem is given points A and B, find integer x
>such that xA=B if it exists. I assume that most crypto implementations
>of ecc use finite fields; in a finite field can you assume that x
>exists?
>--
>Mike Stay
>Cryptographer / Programmer
>AccessData Corp.
>mailto:[EMAIL PROTECTED]
>
>
