# [curves] Fwd: Crash Course on ECC poster

Paul Lambert paul at marvell.com
Wed Jul 8 09:23:07 PDT 2015

```On Tue, Jul 7, 2015 at 11:01 PM, Tanja Lange <tanja at hyperelliptic.org<mailto:tanja at hyperelliptic.org>> wrote:
I've seen 'clock arithmetic' used for computing mod p but I think
Dan Bernstein and I were introducing 'clock crypto' for real clocks.
Of course you're  'clock crypto' any way you want but I find it to
be confusing with our way of presenting elliptic curves via clocks,

Nice chart! On analogies ...
I've always like the 'pool table' model to describe ECC.   Rather than slices, you show A=a*G as point multiplication drawing lines from G, 2*3, 3*G up to a.
For a circle this shows nicely and can be described a ball bouncing around a pool table many times.  For a simple shape (circle), the path is reversible ... for a complex shape it's very difficult to calculate how many 'bounces' of the ball it took to get from G to the end point.  A small Edwards curve next to a circle with a few lines might be an interesting illustration.

Another minor comment - the multiplicative notation A=a*G versus A=g^a reads better for ECC descriptions (IMHO).

Paul

where we use proper arithmetic on the clock (=circle). For our
presentation the comment about 'distorted clocks' makes sense, I
don't understand what it means if you take the clock to be just the
integers mod some prime.

I got similar feedback from Tom Ptacek so... duly noted.

I was trying to make a visual allusion to hours being points on a circle, without really describing that in prose (or arithmetic). Hence the big red points on the circle. And really I was trying to use that all as a lead in to the Dali analogy.

One thing that I think might help that is completely abandoning the clock face metaphor and just using a simple circle with the hours. I might have the space to attempt to describe the hours as points on a unit circle and show those on each of the respective "clocks".

Here's a new version that does away with the clock face metaphor and replaces it with a simple circle, and hopefully addresses your other nits:

https://i.imgur.com/0v4kWYy.png

--
Tony Arcieri

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