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Investigation of the Structure of the Isogeny Graph for Postquantum Cryptography Protocols

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Abstract

The isogeny graphs of supersingular curves are one of the promising mathematical structures in postquantum cryptography algorithms. However, the recently reported attack on the SIDH protocol [1] demonstrates that the isogeny graphs require a more detailed investigation when applied to real protocols. In this study, we analyze the structure of the graphs of isogenies of degree \(\ell > 2\) and consider the set of vertices of a special type to which an attack on reconstruction of the path in the graph is applicable [7].

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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  1. Peter the Great St. Petersburg Polytechnic University, 195251, St. Petersburg, Russia

    S. O. Kostin & E. B. Aleksandrova

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  1. S. O. Kostin
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  2. E. B. Aleksandrova
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Correspondence to S. O. Kostin.

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Translated by E. Smirnova

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Kostin, S.O., Aleksandrova, E.B. Investigation of the Structure of the Isogeny Graph for Postquantum Cryptography Protocols. Aut. Control Comp. Sci. 57, 904–913 (2023). https://doi.org/10.3103/S0146411623080102

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