Quantum Money from Abelian Group Actions

Mark Zhandry

Paper 2023/1097

Quantum Money from Abelian Group Actions

Mark Zhandry

, NTT Research

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.

Note: Added attack on the Knowledge of Group Element Assumption, as well as a generic group action model proof

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Major revision. ITCS 2024
Keywords: quantum money isogenies group actions
Contact author(s): mzhandry @ gmail com
History: 2023-11-28: last of 3 revisions; 2023-07-14: received; See all versions
Short URL: https://ia.cr/2023/1097
License: CC BY

BibTeX

@misc{cryptoeprint:2023/1097,
      author = {Mark Zhandry},
      title = {Quantum Money from Abelian Group Actions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/1097},
      year = {2023},
      url = {https://eprint.iacr.org/2023/1097}
}