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