Abstract
Isogeny-based cryptography is a promising approach for post-quantum cryptography. The best-known protocol following that approach is the supersingular isogeny Diffie–Hellman protocol (SIDH); this protocol was turned into the CCA-secure key encapsulation mechanism SIKE, which was submitted to and remains in the third round of NIST's post-quantum standardisation process as an ‘alternate’ candidate. Isogeny-based cryptography generally relies on the conjectured hardness of computing an isogeny between two isogenous elliptic curves, and most cryptanalytic work referenced on SIKE's webpage exclusively focusses on that problem. Interestingly, the hardness of this problem is sufficient for neither SIDH nor SIKE. In particular, these protocols reveal additional information on the secret isogeny, in the form of images of specific torsion points through the isogeny. This paper surveys existing cryptanalysis approaches exploiting this often called ‘torsion point information’, summarises their current impact on SIKE and related algorithms, and suggests some research directions that might lead to further impact.
Original language | English |
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Journal | IET Information Security |
Early online date | 4 Jul 2022 |
DOIs | |
Publication status | E-pub ahead of print - 4 Jul 2022 |
Bibliographical note
Funding Information:Péter Kutas and Christophe Petit's work were supported by EPSRC grants EP/S01361X/1 and EP/V011324/1. Péter Kutas was also supported by the Ministry of Innovation and Technology and the National Research, Development and Innovation Office within the Quantum Information National Laboratory of Hungary.
Publisher Copyright:
© 2022 The Authors. IET Information Security published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.
ASJC Scopus subject areas
- Software
- Information Systems
- Computer Networks and Communications