【摘要】 最近Castryck和Decru提出了有效破解SIDH的攻击方法，其主要计算步骤之一是超椭圆曲线的Jacobian、椭圆曲线乘积之间(2,2)-同源的计算。这一同源计算也是亏格2的超奇异同源密码交换协议G2SIDH的主要计算过程。本文针对这一同源的已有快速计算方法提出了改进的优化算法，并用实验验证了算法正确性，对比分析了改进前后的计算复杂度。更多还原

【Abstract】 Recently, Castryck and Decru proposed an effective attack method to crack the SIDH, where computing the(2,2)-isogenies between the Jacobians of the hyperelliptic curves and the products of two elliptic curves is a main computation step, which is also the main computation process of the G2SIDH(a genus-2 variant of the SIDH protocol). Based on existing efficient computation methods for the(2,2)-isogenies, an improved algorithm is proposed, whose validity is verified by experiments and computation complexity is compared.更多还原