Differential Addition On Twisted Edwards Curves

This paper presents new differential addition (i.e., the addition of two points with the known difference) and doubling formulas, as the core step in Montgomery scalar multiplication, for twisted Edwards curves. The formulas are provided with cost of 5M + 4S + 1D, 3M + 7S + 1D and 3M + 6S + 3D when the given difference point is in affine form. Here, M, S, D denote the costs of a field multiplication, a field squaring and a field multiplication by a constant, respectively.