Cryptology ePrint Archive: Report 2021/1294

Quantum Money from Quaternion Algebras

Daniel M. Kane and Shahed Sharif and Alice Silverberg

Abstract: We propose a new idea for public key quantum money. In the abstract sense, our bills are encoded as a joint eigenstate of a fixed system of commuting unitary operators. We perform some basic analysis of this black box system and show that it is resistant to black box attacks. In order to instantiate this protocol, one needs to find a cryptographically complicated system of computable, commuting, unitary operators. To fill this need, we propose using Brandt operators acting on the Brandt modules associated to certain quaternion algebras. We explain why we believe this instantiation is likely to be secure.

Category / Keywords: cryptographic protocols / quantum money, quantum cryptography, electronic commerce and payment, quaternion algebras

Date: received 26 Sep 2021

Contact author: ssharif at csusm edu

Available format(s): PDF | BibTeX Citation

Note: This paper can be viewed as an extended version of "Quantum Money from Modular Forms" by Daniel M. Kane (arXiv:1809.05925v2).

Version: 20210927:130406 (All versions of this report)

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