Quantum Money from Quaternion Algebras


quantum money
quaternion algebras
quantum cryptography

How to Cite

Kane, D. M., Sharif, S., & Silverberg, A. (2022). Quantum Money from Quaternion Algebras. Mathematical Cryptology, 2(1), 60–83. Retrieved from https://journals.flvc.org/mathcryptology/article/view/132132


We propose a new idea for public key quantum money and quantum lightning. 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.

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2022 Daniel M. Kane, Shahed Sharif, Alice Silverberg