Quantum circuits for the CSIDH: optimizing quantum evaluation of isogenies

Daniel J.  Bernstein; Tanja Lange; Chloe Martindale; Lorenz Panny

Paper 2018/1059

Quantum circuits for the CSIDH: optimizing quantum evaluation of isogenies

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

Abstract

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: A major revision of an IACR publication in EUROCRYPT 2019
Keywords: Elliptic curves isogenies circuits constant-time computation reversible computation quantum computation cryptanalysis
Contact author(s): authorcontact-qisog @ box cr yp to
History: 2019-03-05: revised; 2018-11-02: received; See all versions
Short URL: https://ia.cr/2018/1059
License: CC BY

BibTeX

@misc{cryptoeprint:2018/1059,
      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},
      url = {https://eprint.iacr.org/2018/1059}
}