Cryptology ePrint Archive: Report 2019/558

How to not break SIDH

Chloe Martindale and Lorenz Panny

Abstract: We give a number of approaches which, to a newcomer, may seem like natural ways to attack the SIDH/SIKE protocol, and explain why each of these approaches seems to fail, at least with the specific setup and parameters of SIKE. Our aim is to save some time for others who are looking to assess the security of SIDH/SIKE. We include methods that fail to attack the pure isogeny problem, namely: looking at the $\mathbb F_p$-subgraph, lifting to characteristic zero, and using Weil restrictions. We also include methods that fail to make use of the public 2-power and 3-power torsion points, namely: interpolation techniques, any purely group-theoretic approaches, and constructing an endomorphism la Petit to exploit the auxiliary points, but with balanced parameters.

Category / Keywords: public-key cryptography / isogenies, SIDH, cryptanalysis, negative results

Original Publication (in the same form): CFAIL 2019

Date: received 24 May 2019

Contact author: chloemartindale at gmail com,l s panny@tue nl

Available format(s): PDF | BibTeX Citation

Version: 20190525:180202 (All versions of this report)

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