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Nice poster, Tony!<br>
<br>
An interesting variant of the "clock cryptography" is to imagine
Diffie-Hellman on the complex unit clock, as described in Bernstein
and Lange's intro. I think it's a more intuitive analogy to ECC
than powers of the generator, and you don't necessarily need
primitive roots.<br>
<br>
So pick some amount of time -- 1/q of the day -- and Alice tells Bob
where the clock hands are pointing at a/q of the day, and Bob tells
Alice where they're pointing at b/q of the day. They can both
compute where the hands are pointing at ab/q of the day, and that's
the DH secret.<br>
<br>
They express where the hands are pointing as (x,y), where x^2 + y^2
= 1. The identity is (0,1) = midnight. The formulas for adding
times are the same as multiplication of complex numbers, except x
and y are swapped because midnight is at the top: (x,y)+(X,Y) =
(xY+Xy, yY-xX).<br>
<br>
With real numbers this is a pain because of rounding errors. It
actually works and is not trivially breakable if you do it mod a
prime, particularly a 3-mod-4 prime. But it's susceptible to index
calculus.<br>
<br>
Then if you want you can say "... but on a warped clock ..." and get
an Edwards curve. The Edwards curve has equation x^2 + y^2 = 1 +
dx^2y^2. It has addition formulas ((xY+Xy)/(1+dxXyY),
(yY-xX)/(1-dxXyY)), limiting to the circle when d=0. There's also
sooort of a way to turn it into the Weierstrass equation, but it's
probably not worth doing.<br>
<br>
Just my two cents.<br>
<br>
Cheers,<br>
-- Mike<br>
<br>
<br>
<div class="moz-cite-prefix">On 07/07/2015 08:12 PM, Tony Arcieri
wrote:<br>
</div>
<blockquote
cite="mid:CAHOTMVKZctwAF2tQaEHf-XX7FMzSD_WRcBbHuvunDO4HrwQRcw@mail.gmail.com"
type="cite">
<div dir="ltr">
<div class="gmail_quote">
<div dir="ltr">I made this poster for the DEFCON Crypto and
Privacy Village. It's intended for audiences of mixed
ability levels:</div>
<div dir="ltr"><br>
</div>
<div dir="ltr"><a moz-do-not-send="true"
href="https://i.imgur.com/hwbSRHh.png">https://i.imgur.com/hwbSRHh.png</a><br>
<div><br>
</div>
<div>Would appreciate technical feedback on it. If you'd
like to suggest copy changes, please consider design
constraints (i.e. available room on the page).</div>
<div><br>
</div>
<div>Thanks!</div>
<div><br>
</div>
</div>
</div>
-- <br>
<div class="gmail_signature">Tony Arcieri<br>
</div>
</div>
<br>
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