Differential Addition on Twisted Edwards Curves

Abstract

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 scaler multiplication, for twisted Edwards curves. The formulas are provided with cost of 5M+4S+1D, 3M+7S+1D 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.