Welcome to the resource topic for 2020/391
Title:
Optimized CSIDH Implementation Using a 2-torsion Point
Authors: Donghoe Heo, Suhri Kim, Kisoon Yoon, Young-Ho Park, Seokhie Hong
Abstract:The implementation of isogeny-based cryptography mainly use Montgomery curves as they offer fast elliptic curve arithmetic and isogeny compuation. However, although Montgomery curves have efficient 3- and 4-isogenies, it becomes inefficient when recovering the coefficient of the image curve for large degree isogenies. This is the main bottleneck of using a Montgomery curve for CSIDH as it requires odd-degree isogenies up to at least 587. In this paper, we present a new optimization method for faster CSIDH protocols entirely on Montgomery curves. To this end, we present a new parameter for CSIDH in which the rational 2-torsion points are defined over \mathbb{F}_p. By using the proposed parameters the CSIDH moves around the surface. The curve coefficient of the image curve can be recovered by a 2-torsion point. We also proved that the CSIDH using the proposed parameter guarantees a free and transitive group action. Additionally, we present the implementation result using our method. We demonstrated that our method is 6.1% faster than the original CSIDH. Our works show that quite higher performance of CSIDH is achieved using only Montgomery curves.
ePrint: https://eprint.iacr.org/2020/391
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