Group Key Exchange from CSIDH and Its Application to Trusted Setup in Supersingular Isogeny Cryptosystems

Tomoki Moriya; Katsuyuki Takashima; Tsuyoshi Takagi

doi:10.1007/978-3-030-42921-8_5

Group Key Exchange from CSIDH and Its Application to Trusted Setup in Supersingular Isogeny Cryptosystems

Tomoki Moriya^*, Katsuyuki Takashima, Tsuyoshi Takagi

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

Abstract

In this paper, we propose a multi-party (group) key exchange protocol based on CSIDH (Commutative Supersingular Isogeny Diffie–Hellman), which is a post-quantum Diffie-Hellman type key exchange protocol from a commutative group action. The proposed group key exchange protocol called G-CSIDH uses the same size prime modulus p as that in CSIDH for the same security level, and the security of G-CSIDH is reduced to the security of CSIDH. In addition, we propose the trusted protocol of generating public parameters of supersingular isogeny cryptosystems by using the proposed G-CSIDH. Trust in the setup based on G-CSIDH is reduced to the security of G-CSIDH, and then that of CSIDH. The trusted protocol can be applied to any supersingular isogeny cryptosystem, which uses a supersingular elliptic curve as a public parameter.

Original language	English
Title of host publication	Information Security and Cryptology - 15th International Conference, Inscrypt 2019, Revised Selected Papers
Editors	Zhe Liu, Moti Yung
Publisher	Springer
Pages	86-98
Number of pages	13
ISBN (Print)	9783030429201
DOIs	https://doi.org/10.1007/978-3-030-42921-8_5
Publication status	Published - 2020
Externally published	Yes
Event	15th International Conference on Information Security and Cryptology, Inscrypt 2019 - Nanjing, China Duration: 2019 Dec 6 → 2019 Dec 8

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12020 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	15th International Conference on Information Security and Cryptology, Inscrypt 2019
Country/Territory	China
City	Nanjing
Period	19/12/6 → 19/12/8

Keywords

CSIDH
Group key exchange
Isogeny-based cryptography

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-030-42921-8_5

Cite this

Moriya, T., Takashima, K., & Takagi, T. (2020). Group Key Exchange from CSIDH and Its Application to Trusted Setup in Supersingular Isogeny Cryptosystems. In Z. Liu, & M. Yung (Eds.), Information Security and Cryptology - 15th International Conference, Inscrypt 2019, Revised Selected Papers (pp. 86-98). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12020 LNCS). Springer. https://doi.org/10.1007/978-3-030-42921-8_5

Group Key Exchange from CSIDH and Its Application to Trusted Setup in Supersingular Isogeny Cryptosystems. / Moriya, Tomoki; Takashima, Katsuyuki; Takagi, Tsuyoshi.
Information Security and Cryptology - 15th International Conference, Inscrypt 2019, Revised Selected Papers. ed. / Zhe Liu; Moti Yung. Springer, 2020. p. 86-98 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12020 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Moriya, T, Takashima, K & Takagi, T 2020, Group Key Exchange from CSIDH and Its Application to Trusted Setup in Supersingular Isogeny Cryptosystems. in Z Liu & M Yung (eds), Information Security and Cryptology - 15th International Conference, Inscrypt 2019, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12020 LNCS, Springer, pp. 86-98, 15th International Conference on Information Security and Cryptology, Inscrypt 2019, Nanjing, China, 19/12/6. https://doi.org/10.1007/978-3-030-42921-8_5

Moriya T, Takashima K, Takagi T. Group Key Exchange from CSIDH and Its Application to Trusted Setup in Supersingular Isogeny Cryptosystems. In Liu Z, Yung M, editors, Information Security and Cryptology - 15th International Conference, Inscrypt 2019, Revised Selected Papers. Springer. 2020. p. 86-98. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-42921-8_5

Moriya, Tomoki ; Takashima, Katsuyuki ; Takagi, Tsuyoshi. / Group Key Exchange from CSIDH and Its Application to Trusted Setup in Supersingular Isogeny Cryptosystems. Information Security and Cryptology - 15th International Conference, Inscrypt 2019, Revised Selected Papers. editor / Zhe Liu ; Moti Yung. Springer, 2020. pp. 86-98 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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N2 - In this paper, we propose a multi-party (group) key exchange protocol based on CSIDH (Commutative Supersingular Isogeny Diffie–Hellman), which is a post-quantum Diffie-Hellman type key exchange protocol from a commutative group action. The proposed group key exchange protocol called G-CSIDH uses the same size prime modulus p as that in CSIDH for the same security level, and the security of G-CSIDH is reduced to the security of CSIDH. In addition, we propose the trusted protocol of generating public parameters of supersingular isogeny cryptosystems by using the proposed G-CSIDH. Trust in the setup based on G-CSIDH is reduced to the security of G-CSIDH, and then that of CSIDH. The trusted protocol can be applied to any supersingular isogeny cryptosystem, which uses a supersingular elliptic curve as a public parameter.

AB - In this paper, we propose a multi-party (group) key exchange protocol based on CSIDH (Commutative Supersingular Isogeny Diffie–Hellman), which is a post-quantum Diffie-Hellman type key exchange protocol from a commutative group action. The proposed group key exchange protocol called G-CSIDH uses the same size prime modulus p as that in CSIDH for the same security level, and the security of G-CSIDH is reduced to the security of CSIDH. In addition, we propose the trusted protocol of generating public parameters of supersingular isogeny cryptosystems by using the proposed G-CSIDH. Trust in the setup based on G-CSIDH is reduced to the security of G-CSIDH, and then that of CSIDH. The trusted protocol can be applied to any supersingular isogeny cryptosystem, which uses a supersingular elliptic curve as a public parameter.

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Group Key Exchange from CSIDH and Its Application to Trusted Setup in Supersingular Isogeny Cryptosystems

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