Sciweavers

JSC
2011

Toric forms of elliptic curves and their arithmetic

13 years 3 months ago
Toric forms of elliptic curves and their arithmetic
We scan a large class of one-parameter families of elliptic curves for efficient arithmetic. The construction of the class is inspired by toric geometry, which provides a natural framework for the study of various forms of elliptic curves. The class both encompasses many prominent known forms and includes thousands of new forms. A powerful algorithm is described that automatically computes the most compact group operation formulas for any parameterized family of elliptic curves. The generality of this algorithm is further illustrated by computing uniform addition formulas and formulas for generalized Montgomery arithmetic. Key words: elliptic curve, cryptography, arithmetic, newton polytope, toric geometry
Wouter Castryck, Frederik Vercauteren
Added 16 Sep 2011
Updated 16 Sep 2011
Type Journal
Year 2011
Where JSC
Authors Wouter Castryck, Frederik Vercauteren
Comments (0)