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One-Round Authenticated Group Key Exchange from Isogenies

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Abstract

This paper proposes two one-round authenticated group key exchange protocols from newly employed cryptographic invariant maps (CIMs): one is secure in the quantum random oracle model and the other resists against maximum exposure where a non-trivial combination of secret keys is revealed. The security of the former (resp. latter) is proved under the n-way decisional (resp. n-way gap) Diffie–Hellman assumption on the CIMs in the quantum random (resp. random) oracle model.

We instantiate the proposed protocols on the hard homogeneous spaces with limitation where the number of the user group is two. In particular, the protocols instantiated by using the CSIDH, commutative supersingular isogeny Diffie–Hellman, key exchange are currently more realistic than the general n-party CIM-based ones due to its realizability. Our two-party one-round protocols are secure against quantum adversaries.

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Notes

  1. 1.

    \(T_i\) and \(R_i\) are indexed in the cyclic manner in modulo n. For example, when \(i=n\), then \(Z_1 = e_{n-1}(t_n *T_1, \dots , T_n)\) and \(Z_2 = e_{n-1}(r_n *R_1, \dots , R_n)\).

  2. 2.

    \(T_{i}\) and \(R_{i}\) are indexed in the cyclic manner in modulo n.

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Authors and Affiliations

  1. Kanagawa University, Yokohama, Japan

    Atsushi Fujioka

  2. Mitsubishi Electric, Kamakura, Japan

    Katsuyuki Takashima

  3. Ibaraki University, Hitachi, Japan

    Kazuki Yoneyama

Authors
  1. Atsushi Fujioka
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  2. Katsuyuki Takashima
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  3. Kazuki Yoneyama
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Corresponding author

Correspondence to Kazuki Yoneyama .

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Editors and Affiliations

  1. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

  2. The University of Hong Kong, Pok Fu Lam, Hong Kong

    Tsz Hon Yuen

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Fujioka, A., Takashima, K., Yoneyama, K. (2019). One-Round Authenticated Group Key Exchange from Isogenies. In: Steinfeld, R., Yuen, T. (eds) Provable Security. ProvSec 2019. Lecture Notes in Computer Science(), vol 11821. Springer, Cham. https://doi.org/10.1007/978-3-030-31919-9_20

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  • DOI: https://doi.org/10.1007/978-3-030-31919-9_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-31918-2

  • Online ISBN: 978-3-030-31919-9

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