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Quantum Money from Abelian Group Actions

Author Mark Zhandry

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Mark Zhandry
  • NTT Research, Sunnyvale, CA, USA

Acknowledgements

We thank Hart Montgomery for many helpful discussions about isogenies.

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Mark Zhandry. Quantum Money from Abelian Group Actions. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 101:1-101:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.101

Abstract

We give a construction of public key quantum money, and even a strengthened version called quantum lightning, from abelian group actions, which can in turn be constructed from suitable isogenies over elliptic curves. We prove security in the generic group model for group actions under a plausible computational assumption, and develop a general toolkit for proving quantum security in this model. Along the way, we explore knowledge assumptions and algebraic group actions in the quantum setting, finding significant limitations of these assumptions/models compared to generic group actions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • Quantum Money
  • Cryptographic Group Actions
  • Isogenies

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