From: eric@remailer.net (Eric Hughes)
Date: Tue, 13 Dec 94 00:06:13 PST
To: cypherpunks@toad.com
Subject: Re: What, exactly is elliptic encryption?
In-Reply-To: <9412130723.AA14508@tadpole.tadpole.com>
Message-ID: <199412130903.BAA01594@largo.remailer.net>
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   From: db@Tadpole.COM (Doug Barnes)

   For the different isomorphisms of the curves, you can then
   construct addition of coordinates, subtraction, multiplication
   and division, such that the results are also points on the
   curve. This makes this set of points an abelian group too. 

Well, you actually get just addition and subtraction as binary
operations.  Multiplication is integers by elliptic curve elements and
is shorthand for multiple additions.  Division doesn't always make
sense.

   You can then do a Diffie Hellman analogue substituting
   multiplication for exponentiation, and a El Gamal analogue
   substituting multiplication for exponentiation and addition
   for multiplication. 

The multiplication takes an integer (the exponent analogue) by a curve
element (the base analogue).

   There is an IEEE group 
   working on a proposed standard at the moment; I need to get back 
   to my contact with them to find out where they are at now.

Burt Kaliski of RSA Labs is the chair of P1363.  Archives are at
rsa.com.

Eric