Paper 2018/1059

Quantum circuits for the CSIDH: optimizing quantum evaluation of isogenies

Daniel J. Bernstein, Tanja Lange, Chloe Martindale, and Lorenz Panny


Choosing safe post-quantum parameters for the new CSIDH isogeny-based key-exchange system requires concrete analysis of the cost of quantum attacks. The two main contributions to attack cost are the number of queries in hidden-shift algorithms and the cost of each query. This paper analyzes algorithms for each query, introducing several new speedups while showing that some previous claims were too optimistic for the attacker. This paper includes a full computer-verified simulation of its main algorithm down to the bit-operation level.

Available format(s)
Public-key cryptography
Publication info
A major revision of an IACR publication in EUROCRYPT 2019
Elliptic curvesisogeniescircuitsconstant-time computationreversible computationquantum computationcryptanalysis
Contact author(s)
authorcontact-qisog @ box cr yp to
2019-03-05: revised
2018-11-02: received
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Creative Commons Attribution


      author = {Daniel J.  Bernstein and Tanja Lange and Chloe Martindale and Lorenz Panny},
      title = {Quantum circuits for the CSIDH: optimizing quantum evaluation of isogenies},
      howpublished = {Cryptology ePrint Archive, Paper 2018/1059},
      year = {2018},
      note = {\url{}},
      url = {}
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