Toric forms of elliptic curves and their arithmetic

Wouter Castryck, Frederik Vercauteren
2011 Journal of symbolic computation  
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
more » ... f this algorithm is further illustrated by computing uniform addition formulas and formulas for generalized Montgomery arithmetic.
doi:10.1016/j.jsc.2011.02.003 fatcat:xl7orq4jmbcjfg42bebmk5hg3u