Mark Zhandry - Quantum Money from Abelian Group Actions

theoretics:13356 - TheoretiCS, August 19, 2025, Volume 4 - https://doi.org/10.46298/theoretics.25.18
Quantum Money from Abelian Group ActionsArticle

Authors: Mark Zhandry ORCID

    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.


    Volume: Volume 4
    Published on: August 19, 2025
    Accepted on: June 29, 2025
    Submitted on: April 6, 2024
    Keywords: Quantum Physics,Cryptography and Security