[curves] Climbing the elliptic learning curve (was: Re: Finalizing XEdDSA)

[Andy Isaacson]

On Tue, Nov 01, 2016 at 12:20:16PM -0700, Ron Garret wrote:
>So let me hard-fork this thread and ask a followup meta-question:  The fact
>that 8 was the cofactor of the curve is apparently something most (if 
>not all) people on this list already knew.  But how?  Neither the 
>Ed25519 paper nor the Curve25519 paper mentions it (AFAICT).

[snip]

>Bottom line: there seems to be a huge disconnect between the importance 
>of cofactors on the one hand and the information available about them 
>on the other.  On the one hand, cofactors seem to be so important that 
>all this stuff that I just learned about seems to be common knowledge, 
>and on the other hand, even now that I know it I *still* can’t figure 
>out how I could have learned it other than asking this apparently 
>stupid question.
>
>So my meta-question is: *was* this a stupid question?  Did everyone 
>really already know this except me?  And if so, how?

I'm deeply unqualified to opine on if it was a stupid question, but it 
didn't seem stupid to me.  As far as I can tell there's a quite 
remarkable pile of specialized knowledge necessary to be able to 
effectively work with elliptic curve cryptography, and this list is 
mostly for folks who already have the knowledge to discuss things. I'm 
just lurking here to keep tabs on the developments.

I'm somewhat embarrassed to note that I'm not even sure which fields of 
study are necessary; I think you're supposed to start by understanding a 
basic graduate level textbook such as Silverman's "Arithmetic of 
Elliptic Curves"
http://www.springer.com/gp/book/9780387094939
but I bounced off of that book pretty hard when I tried reading it a few 
years back.

-andy