> >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?
> 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?
Of course, in the EC cryptography case, you know that B has been generated
as xA, so you know that this equation has a solution.
Cheers,
William Whyte
Senior Cryptographer
Baltimore Technologies Ltd, IFSC House, Dublin 1, Ireland
