Nice poster, Tony! 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.
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. 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). 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. 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. Just my two cents. Cheers, -- Mike On 07/07/2015 08:12 PM, Tony Arcieri wrote: > I made this poster for the DEFCON Crypto and Privacy Village. It's > intended for audiences of mixed ability levels: > > https://i.imgur.com/hwbSRHh.png > > 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). > > Thanks! > > -- > Tony Arcieri > > > _______________________________________________ > Curves mailing list > [email protected] > https://moderncrypto.org/mailman/listinfo/curves
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