Investigation of the Structure of the Isogeny Graph for Postquantum Cryptography Protocols
Pages 904 - 913
Abstract
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 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].
References
[1]
Castryck W. and Decru T. An efficient key recovery attack on SIDH, Advances in Cryptology–EUROCRYPT 2023 2023 Cham Springer
[2]
Castryck-Decru Key Recovery Attack on SIDH. https://github.com/jack4818/Castryck-Decru-SageMath. Cited June 14, 2023.
[3]
Oudompheng, R., A note on implementing direct isogeny determination in the Castryck-Decru sike attack, 2022. https://www.normalesup.org/~oudomphe/textes/202208-castryck-decru-shortcut.pdf. Cited May 14, 2023.
[4]
Oudompheng, R. and Pope, G., A note on reimplementing the Castryck-Decru attack and lessons learned for SageMath, 2022. https://eprint.iacr.org/2022/1283.pdf. Cited May 17, 2023.
[5]
Damien, R., Breaking SIDH in polynomial time. https://eprint.iacr.org/2022/1038.pdf. Cited May 19, 2023.
[6]
Arpin S., Camacho-Navarro C., Lauter K., Lim J., Nelson K., Scholl T., and Sotáková J. Adventures in Supersingularland Exp. Math. 2023 32 241-268
[7]
Delfs C. and Galbraith S.D. Computing isogenies between supersingular elliptic curves over Fp Des., Codes Cryptography 2016 78 425-440
[8]
Silverman J.H. Algorithmic aspects of elliptic curves, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics 2009 New York Springer
[9]
Moriya, T., Masked-degree SIDH. https://eprint.iacr.org/2022/1019.pdf. Cited May 20, 2023.
[10]
Shor, P.W., Algorithms for quantum computation: Discrete logarithms and factoring, Proc. 35th Annu. Symp. on Foundations of Computer Science, Santa Fe, N.M., IEEE, 1994, pp. 124–134.
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© Allerton Press, Inc. 2023. ISSN 0146-4116, Automatic Control and Computer Sciences, 2023, Vol. 57, No. 8, pp. 904–913. © Allerton Press, Inc., 2023. Russian Text © The Author(s), 2023, published in Problemy Informatsionnoi Bezopasnosti, Komp’yuternye Sistemy.
Publisher
Allerton Press, Inc.
United States
Publication History
Published: 01 December 2023
Accepted: 11 August 2023
Revision received: 31 July 2023
Received: 15 July 2023
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