TY - GEN

T1 - Inverted Edwards coordinates

AU - Bernstein, D.J.

AU - Lange, T.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-540-77224-8_4

DO - 10.1007/978-3-540-77224-8_4

M3 - Conference contribution

SN - 978-3-540-77223-1

T3 - Lecture Notes in Computer Science

SP - 20

EP - 27

BT - Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (17th International Conference, AAECC-17, Bangalore, India, December 16-20, 2007. Proceedings)

A2 - Boztas, S.

A2 - Lu, H.

PB - Springer

CY - Berlin

T2 - conference; AAECC 17, Bangalore, India; 2007-12-16; 2007-12-20

Y2 - 16 December 2007 through 20 December 2007

ER -