# Inverted Edwards coordinates

D.J. Bernstein, T. Lange

46 Citaten (Scopus)

## Samenvatting

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.
Originele taal-2 Engels Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (17th International Conference, AAECC-17, Bangalore, India, December 16-20, 2007. Proceedings) S. Boztas, H. Lu Berlin Springer 20-27 978-3-540-77223-1 https://doi.org/10.1007/978-3-540-77224-8_4 Gepubliceerd - 2007 conference; AAECC 17, Bangalore, India; 2007-12-16; 2007-12-20 - Duur: 16 dec 2007 → 20 dec 2007

### Publicatie series

Naam Lecture Notes in Computer Science 4851 0302-9743

### Congres

Congres conference; AAECC 17, Bangalore, India; 2007-12-16; 2007-12-20 16/12/07 → 20/12/07 AAECC 17, Bangalore, India

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