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Toric forms of elliptic curves and their arithmetic
<span title="">2011</span>
<i title="Elsevier BV">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ezljl2d3lzga5efenbxdvvfcpa" style="color: black;">Journal of symbolic computation</a>
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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
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... f this algorithm is further illustrated by computing uniform addition formulas and formulas for generalized Montgomery arithmetic.
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