Toric forms of elliptic curves and their arithmetic

Wouter Castryck, Frederik Vercauteren
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="" style="color: black;">Journal of symbolic computation</a> </i> &nbsp;
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 &raquo; ... f this algorithm is further illustrated by computing uniform addition formulas and formulas for generalized Montgomery arithmetic.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1016/j.jsc.2011.02.003</a> <a target="_blank" rel="external noopener" href="">fatcat:xl7orq4jmbcjfg42bebmk5hg3u</a> </span>
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