Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies

URL: https://link.springer.com/chapter/10.1007/978-3-642-25405-5_2 Authors: David Jao, Luca De Feo

Abstract

We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. Previous work on isogeny-based cryptography required the isogeny graph to have a specific structure. We eliminate this restriction by working with random supersingular elliptic curves. We present both a Diffie-Hellman-like key exchange protocol (SIDH) and a public-key encryption scheme, and present preliminary analysis of their security. Our proposals have the advantage of being potentially quantum-resistant, with relatively short key sizes compared to other quantum-resistant schemes.