We give algorithms to compute \((\ell ,\ell )\)-isogenies between Jacobians of genus 2 curves and products of elliptic curves in time of \({\tilde{O}}(\ell ^2)\) basic field operations, where \(\ell \) is an odd prime different from the characteristic of the field. The method relies on the notion of a normal Weil set of Weil functions due to Shepherd-Barron, and works for the case of computing \((\ell ,\ell )\)-isogenies between Jacobians of genus 2 curves.

中文翻译：

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计算粘合和分裂 $$(\ell ,\ell )$$ -isogenies

我们给出算法来计算genus 2 曲线的雅可比行列式与椭圆曲线在\({\tilde{O}}(\ell ^2)\)时间的乘积之间的同构域运算，其中\(\ell \)是与域特征不同的奇素数。该方法依赖于 Shepherd-Barron 提出的正常 Weil 函数集的概念，适用于计算2 格曲线的雅可比行列式之间的\((\ell ,\ell )\)等基因的情况。