Differential Addition in generalized Edwards Coordinates

Thursday 04 November 2010, 15.00, b-it 1.25 (cosec meeting room)

We use two parametrizations of points on elliptic curves in generalized Edwards form x^2 + y^2 = c^2 (1+d x^2 y^2) that omit the x-coordinate. 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 the literature for the special case c = 1.

For both parametrizations the formula for recovering the missing X-coordinate is also provided.

This is a joint work with Benjamin Justus.