Differential Addition in Generalized Edwards Coordinates

We use two parametrizations of points on elliptic curves in generalized Edwards form x + y = c(1 + dxy) that omit the xcoordinate. The first parametrization leads to a differential addition formula that can be computed using 6M + 4S, a doubling formula using 1M + 4S and a tripling formula using 4M + 7S. The second one yields a differential addition formula that can be computed using 5M + 2S and a doubling formula using 5S. All formulas apply also for the case c 6= 1 and arbitrary curve parameter d. This generalizes formulas from the literature for the special case c = 1. For both parametrizations the formula for recovering the missing Xcoordinate is also provided.