We give an algorithm to compute \((\ell ,\ell ,\ell )\)-isogenies from the Jacobians of genus three hyperelliptic curves to the Jacobians of non-hyperelliptic curves over a finite field of characteristic different from 2 in time \(\tilde{O}(\ell ^3)\), where \(\ell \) is an odd prime which is coprime to the characteristic. An important application is to reduce the discrete logarithm problem in the Jacobian of a hyperelliptic curve to the corresponding problem in the Jacobian of a non-hyperelliptic curve.

中文翻译：

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用 $$(\ell ,\ell ,\ell )$$ ( ℓ , ℓ , ℓ ) -Isogenies 翻译 Genus 3 Hyperelliptic Curves 的 Jacobian 离散对数问题

我们给出了一种算法来计算\((\ell ,\ell ,\ell )\) -从属三超椭圆曲线的雅可比到非超椭圆曲线的雅可比在时间上不同于 2 的有限特征域上的同构性\ (\tilde{O}(\ell ^3)\)，其中\(\ell \)是一个奇素数，它是特征的互素数。一个重要的应用是将超椭圆曲线雅可比矩阵中的离散对数问题化简为非超椭圆曲线雅可比矩阵中的相应问题。