Re: ECC point of inf question

From: Jean-Luc Cooke (jlcooke_at_engsoc.org)
Date: 10/20/05 

Date: 20 Oct 2005 18:43:30 GMT

tomstdenis@gmail.com wrote:

> Ben Livengood wrote:
> > > \infty = (x, y) + (x, -y)
> >
> > The point at infinity is defined precisely because the slope is
> > undefined between (x,y) and (x,-y). For points on a curve to be a group
> > under addition there has to be an element that is the result of such an
> > addition.

> That doesn't make any sense. My question was whether the point at
> infty has a value. and "x/0" is not it, that's undefined.

> If anything the point at infinity is a concept and can't be explicitly
> represented.

Right. the 'point at inf' in ECC isn't real. All that matters is that
it would require an unrepresentable operation to get there. It could be
(1,0) or (1/0, 1/0)

JLC

> > > My take is that if some pair (x, y) do satisfy the above and the > curve is of prime order then the pair is valid for use in ECC
> > > operations? Is that right?
> >
> > There are several important checks to make sure a curve and points on
> > the curve are valid, including the MOV test. The document "Elliptic
> > Curve Cryptography" from the Standards for Effecient Cryptography Group
> > (www.secg.org/collateral/sec1.pdf) is a very complete reference, and
> > section 3.1 describes the validation procedure for curves and base
> > points.

> The PDF you linked to doesn't render with gpdf properly. [nor do the
> ANSI specs where it appears to be coming from]. I blame this on the
> fact they've never heard of LaTeX and decide to do all their equations
> in word...

> Tom 

--

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