论文标题
在超专门的阿贝尔表面之间计算richelot的同基因
Counting Richelot isogenies between superspecial abelian surfaces
论文作者
论文摘要
Castryck，depu和Smith使用了Superspecial属-2曲线及其Richelot等值映射图来基于Genus-2等速密码学，最近，Costello和Smith在GenUS-2设置中设计了一种改进的等质激素途径求解算法。为了建立密码结构和分析的牢固基础，我们根据{\ em涉及涉及的自动形态学}属属（\ em）在有限的领域的{\ em涉及的自动形态学}方面给出了新的表征表面。作为推论，我们在Castryck等人的论文中给出了定理2的另一代代数几何证明。
Castryck, Decru, and Smith used superspecial genus-2 curves and their Richelot isogeny graph for basing genus-2 isogeny cryptography, and recently, Costello and Smith devised an improved isogeny path-finding algorithm in the genus-2 setting. In order to establish a firm ground for the cryptographic construction and analysis, we give a new characterization of {\em decomposed Richelot isogenies} in terms of {\em involutive reduced automorphisms} of genus-2 curves over a finite field, and explicitly count such decomposed (and non-decomposed) Richelot isogenies between {\em superspecial} principally polarized abelian surfaces. As a corollary, we give another algebraic geometric proof of Theorem 2 in the paper of Castryck et al.
