Edwards curves have attracted great interest for several reasons. When curve parameters are chosen properly, the addition formulas use only 10M¿+¿1S. The formulas are strongly unified, i.e., work without change for doublings; even better, they are complete, i.e., work without change for all inputs. Dedicated doubling formulas use only 3M¿+¿4S, and dedicated tripling formulas use only 9M¿+¿4S.
This paper introduces inverted Edwards coordinates. Inverted Edwards coordinates (X 1:Y 1:Z 1) represent the affine point (Z 1/X 1,Z 1/Y 1) on an Edwards curve; for comparison, standard Edwards coordinates (X 1:Y 1:Z 1) represent the affine point (X 1/Z 1,Y 1/Z 1).
This paper presents addition formulas for inverted Edwards coordinates using only 9M¿+¿1S. The formulas are not complete but still are strongly unified. Dedicated doubling formulas use only 3M¿+¿4S, and dedicated tripling formulas use only 9M¿+¿4S. Inverted Edwards coordinates thus save 1M for each addition, without slowing down doubling or tripling.
|Name||Lecture Notes in Computer Science|
|Conference||conference; AAECC 17, Bangalore, India; 2007-12-16; 2007-12-20|
|Period||16/12/07 → 20/12/07|
|Other||AAECC 17, Bangalore, India|