Efficient Algorithms for Isogeny Sequences and Their Cryptographic Applications

We summarize efficient isogeny sequence computations on elliptic and genus 2 Jacobians. For cryptographic purposes, sequences of low-degree isogenies are important. Then we focus on sequences of 2- and 3-isogenies on elliptic curves and (2, 2)- and (3, 3)-isogenies on genus 2 Jacobians. Our aim is to explicitly describe the low-degree isogeny sequence computations and improve them for cryptographic applications such as post-quantum cryptosystems and random self-reducibility of discrete logarithm problem (DLP).

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