One-Round Authenticated Group Key Exchange from Isogenies

Atsushi Fujioka; Katsuyuki Takashima; Kazuki Yoneyama

Paper 2018/1033

One-Round Authenticated Group Key Exchange from Isogenies

Atsushi Fujioka, Katsuyuki Takashima, and Kazuki Yoneyama

Abstract

We propose two one-round authenticated group-key exchange protocols from newly employed cryptographic invariant maps (CIMs): one is secure under 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 Diffie-Hellman (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 implementability. Our two-party one-round protocols are secure against quantum adversaries.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Major revision. ProvSec 2019 (short paper)
Keywords: one-round authenticated group key exchange cryptographic invariant maps hard homogeneous spaces G-CK model G-CK^+ model quantum adversary
Contact author(s): Takashima Katsuyuki @ aj mitsubishielectric co jp
History: 2019-11-02: last of 2 revisions; 2018-10-30: received; See all versions
Short URL: https://ia.cr/2018/1033
License: CC BY

BibTeX

@misc{cryptoeprint:2018/1033,
      author = {Atsushi Fujioka and Katsuyuki Takashima and Kazuki Yoneyama},
      title = {One-Round Authenticated Group Key Exchange from Isogenies},
      howpublished = {Cryptology {ePrint} Archive, Paper 2018/1033},
      year = {2018},
      url = {https://eprint.iacr.org/2018/1033}
}