This paper introduces {\it 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.
Category / Keywords: public-key cryptography / Elliptic curves, addition, doubling, explicit formulas, Edwards coordinates, inverted Edwards coordinates, side-channel countermeasures, unified addition formulas, strongly unified addition formulas. Date: received 25 Oct 2007 Contact author: tanja at hyperelliptic org Available formats: PDF | BibTeX Citation Version: 20071026:095603 (All versions of this report) Discussion forum: Show discussion | Start new discussion