Problem
Research questions and friction points this paper is trying to address.
Differential Addition
Twisted Edwards Curves
Montgomery Scalar Multiplication
Point Addition
Elliptic Curve Cryptography
Differential Addition on Twisted Edwards Curves
🤖 AI Summary
This work addresses the inefficiency of differential addition in Montgomery scalar multiplication on twisted Edwards curves by proposing novel differential addition and doubling formulas. When the difference point is given in affine coordinates, the new formulas require only 5M + 4S + 1D for differential addition and 3M + 7S + 1D for doubling, where M denotes field multiplication, S squaring, and D multiplication by a constant. These operation counts represent a significant reduction in computational cost compared to existing methods. By optimizing the core operations of scalar multiplication, the proposed approach achieves the most efficient differential arithmetic known to date on twisted Edwards curves, thereby substantially enhancing overall performance.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Differential Addition
Twisted Edwards Curves
Montgomery Scalar Multiplication
Efficient Formulas
Elliptic Curve Cryptography
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