Paper 2018/1215

New Hybrid Method for Isogeny-based Cryptosystems using Edwards Curves

Suhri Kim and Kisoon Yoon and Jihoon Kwon and Young-Ho Park and Seokhie Hong

Abstract

Along with the resistance against quantum computers, isogeny-based cryptography offers attractive cryptosystems due to small key sizes and compatibility with the current elliptic curve primitives. While the state-of-the-art implementation uses Montgomery curves which facilitates efficient elliptic curve arithmetic and isogeny computations, other forms of elliptic curves can be used to produce an efficient result. In this paper, we present the new hybrid method for isogeny-based cryptosystem using Edwards curves. Unlike the previous hybrid methods, we used Edwards curves for isogeny computations and Montgomery curves for other operations. We demonstrated that our hybrid method outperforms the previously proposed hybrid method, and is as fast as Montgomery-only implementation. We present the implementation results of Supersingular Isogeny Diffie--Hellman (SIDH) key exchange using the proposed hybrid method. Our results show that the use of Edwards curves for isogeny-based cryptosystem can be quite practical.