A complete set of addition laws for incomplete Edwards curves
Daniel J. Bernstein, Tanja Lange · Journal of Number Theory · 2010
Edwards curves were the first curves shown to have a complete addition law. However, the completeness of the addition law depends on the curve parameters and even a complete Edwards curve becomes incomplete over a quadratic field extension. This paper covers arbitrary Edwards curves and gives a set of two addition laws that for any pair of input points P1, P2 produce the sum P1+P2.