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Date: Sat, 15 Aug 2015 10:28:47 -0700
From: Bill Cox <waywardgeek@...il.com>
To: "discussions@...sword-hashing.net" <discussions@...sword-hashing.net>
Subject: Re: [PHC] Dumb idea of the day: Public key crypto based on random permutations

By the way, applying this to an Edwards curve, I just proved that the
addition law when d == -1 for the x coordinate can be restated:

    x3 = JacobiSN[EllipticF[ArcSin[x1], -1] + EllipticF[ArcSin[x2], -1], -1]

The regular rule is:

    x3 = (x1*y2 + x2*y1)/(1 - x1*y1*x2*y2)

where

    y = sqrt((x^4 + 1)/(x^2 + 1))

Now, I don't yet know what the JacobiSN function is, but that's something
I'll read about :)  However, the ArcSin function, AFAIK, can not be
computed using modular arithmetic.  However, the overall function is very
efficient with modular arithmetic.  This is all easier to see with circle
based groups.

Bill

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