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Towards Practical Key Exchange from Ordinary Isogeny Graphs

Authors:
Luca De Feo
Jean Kieffer
Benjamin Smith
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DOI: 10.1007/978-3-030-03332-3_14
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Presentation: Slides
Conference: ASIACRYPT 2018
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 encryption, thus providing an important step towards efficient post-quantum non-interactive key exchange (NIKE).
BibTeX
@inproceedings{asiacrypt-2018-29195,
  title={Towards Practical Key Exchange from Ordinary Isogeny Graphs},
  booktitle={Advances in Cryptology – ASIACRYPT 2018},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={11274},
  pages={365-394},
  doi={10.1007/978-3-030-03332-3_14},
  author={Luca De Feo and Jean Kieffer and Benjamin Smith},
  year=2018
}