Re: ecc question

[Dan Bailey]

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]

RE: ecc question

[William Whyte]

 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