[5462] in cryptography@c2.net mail archive
RE: ecc question
daemon@ATHENA.MIT.EDU (William Whyte)
Tue Aug 24 10:09:44 1999
From: "William Whyte" <wwhyte@baltimore.ie>
To: "Dan Bailey" <dan@milliways.org>, <staym@accessdata.com>,
<cryptography@c2.net>
Date: Tue, 24 Aug 1999 14:46:12 +0100
In-Reply-To: <3.0.5.32.19990823191024.0315a2f0@pop.ma.ultranet.com>
> >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
