Tuesday, March 25, 2014 (3:00 – 4:30 p.m. in Yost 306)

Title: Inverted Binary Edwards Coordinates (Maire Model of an Elliptic Curve)

Speaker: Steven Maire (Case Western Reserve University)

Abstract: Edwards curves are a fairly new way of expressing a family of elliptic curves that contain extremely desirable cryptographic properties over other forms that have been used. The most  notable is the notion of a complete and unified addition law. This property makes Edwards curves extremely strong against side-channel attacks.  In the analysis and continual development of Edwards curves, it has been seen in the original Edwards form that the use of inverted coordinates creates a more efficient addition/doubling algorithm. Using inverted coordinates the field operations drop from 10M + 1S (given correctly chosen curve parameters), to 9M + 1S. The sacrifice is the loss of completeness, but unification remains. We examine the use of the inverted coorordinate system over the binary Edwards form, and shows the underlying advantages of this transformation.