1. CSIDH: An Efficient Post-Quantum Commutative Group Action 2018 Asiacrypt Isogenies KeyExchange PQC
    Wouter Castryck and Tanja Lange and Chloe Martindale and Lorenz Panny and Joost Renes
    [View PDF on eprint.iacr.org]
    [Show BibTex Citation]

    @misc{cryptoeprint:2018:383,
    author = {Wouter Castryck and Tanja Lange and Chloe Martindale and Lorenz Panny and Joost Renes},
    title = {CSIDH: An Efficient Post-Quantum Commutative Group Action},
    howpublished = {Cryptology ePrint Archive, Report 2018/383},
    year = {2018},
    note = {\url{https://eprint.iacr.org/2018/383}},
    }

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.

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