Towards practical key exchange from ordinary isogeny graphs

TL;DR

This paper improves algorithms for ordinary isogeny-graph based cryptosystems, making key exchange more practical and secure against quantum attacks, and introduces efficient validation techniques for post-quantum security.

Contribution

It provides algorithmic enhancements, security proofs, and parameter generation methods for practical, post-quantum isogeny-based key exchange systems.

Findings

Accelerated key exchange algorithms for isogeny graphs

Security proofs in the Canetti-Krawczyk model and IND-CPA

Efficient key-validation enabling CCA-secure encryption

Abstract

We revisit the ordinary isogeny-graph based cryptosystems of Couveignes and Rostovtsev-Stolbunov, long dismissed as impractical. We give algorithmic improvements that accelerate key exchange in this framework, and explore the problem of generating suitable system parameters for contemporary pre-and post-quantum security that take advantage of these new algorithms. We also prove the session-key security of this key exchange in the Canetti-Krawczyk model, and the IND-CPA security of the related public-key encryption scheme, under reasonable assumptions on the hardness of computing isogeny walks. Our systems admit efficient key-validation techniques that yield CCA-secure encryp-tion, thus providing an important step towards efficient post-quantum non-interactive key exchange (NIKE).