CSIDH: An Efficient Post-Quantum Commutative Group Action
Wouter Castryck, Tanja Lange, Chloe Martindale, Lorenz Panny, Joost Renes · Lecture notes in computer science · 2018
We propose an efficient commutative group action suitable for non-interactive key exchange in a post-quantum setting. Our construction follows the layout of the Couveignes–Rostovtsev–Stolbunov cryptosystem, but we apply it to supersingular elliptic curves defined over a large prime field $$\mathbb F_p$$ , rather than to ordinary elliptic curves. The Diffie–Hellman scheme resulting from the group action allows for public-key validation at very little cost, runs reasonably fast in practice, and has public keys of only 64 bytes at a conjectured AES-128 security level, matching NIST’s post-quantum security category I.