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Diffie-Hellman Key Exchange from Commutativity to Group Laws

Authors Dung Hoang Duong , Youming Qiao , Chuanqi Zhang

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LIPIcs.ITCS.2026.52.pdf
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ACM Subject Classification
  • Security and privacy → Mathematical foundations of cryptography
Keywords
  • Diffie-Hellman
  • Key Exchange
  • Group Laws
  • Group Actions
  • Code Equivalence

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Abstract

In Diffie-Hellman key exchange, the commutativity of power operations is instrumental in the agreement of keys. Viewing commutativity as a law in abelian groups, we propose Diffie-Hellman key exchange in the group action framework (Brassard-Yung, Crypto'90; Ji-Qiao-Song-Yun, TCC'19), for actions of non-abelian groups with laws. The security of this protocol is shown, following Fischlin, Günther, Schmidt, and Warinschi (IEEE S&P'16), based on a pseudorandom group action assumption. A concrete instantiation is proposed based on the monomial code equivalence problem.

Cite As Get BibTex

Dung Hoang Duong, Youming Qiao, and Chuanqi Zhang. Diffie-Hellman Key Exchange from Commutativity to Group Laws. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 52:1-52:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.52

Author Details

Dung Hoang Duong
  • Institute of Cybersecurity and Cryptology, School of Computing and Information Technology, University of Wollongong, Australia
Youming Qiao
  • School of Computer Science and Engineering, University of New South Wales, Sydney, Australia
  • Centre for Quantum Software and Information, University of Technology Sydney, Australia
Chuanqi Zhang
  • Centre for Quantum Software and Information, University of Technology Sydney, Australia

Funding

  • Duong, Dung Hoang: Research supported in part by Australian Research Council LP220100332.
  • Qiao, Youming: Research supported in part by Australian Research Council DP200100950 and LP220100332.
  • Zhang, Chuanqi: Research supported in part by Australian Research Council DP200100950 and LP220100332, and the Sydney Quantum Academy, Sydney, NSW, Australia.

Acknowledgements

We thank the anonymous reviewers for their insightful feedback.

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