CSIDH: An Efficient Post-Quantum Commutative Group Action

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Presented at Asiacrypt2018 2018 by

Tanja Lange

Joost Renes

Wouter Castryck

Chloe Martindale

Lorenz Panny

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 Fp , 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.