Differential Addition in Generalized Edwards Coordinates

We use two parametrizations of points on elliptic curves in generalized Edwards form x2 + y2 = c2 (1 + dx2 y2 ) 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 = 1 and arbitrary curve parameter d. This generalizes formulas from

• Type: Journal
• Year: 2010
• Where: IWSEC
• Authors: Benjamin Justus, Daniel Loebenberger
• Keywords: Arbitrary Curve Parameter, Elliptic Curves, Formulas, IWSEC 2010, Security Privacy