Paper 2022/1620

Another Round of Breaking and Making Quantum Money: How to Not Build It from Lattices, and More

Hart Montgomery, Linux Foundation & Fujitsu Research
Jiahui Liu, The University of Texas at Austin
Mark Zhandry, NTT Research

Public verification of quantum money has been one of the central objects in quantum cryptography ever since Wiesner's pioneering idea of using quantum mechanics to construct banknotes against counterfeiting. So far, we do not know any publicly-verifiable quantum money scheme that is provably secure from standard assumptions. In this work, we provide both negative and positive results for publicly verifiable quantum money. **In the first part, we give a general theorem, showing that a certain natural class of quantum money schemes from lattices cannot be secure. We use this theorem to break the recent quantum money scheme of Khesin, Lu, and Shor. **In the second part, we propose a framework for building quantum money and quantum lightning we call invariant money which abstracts some of the ideas of quantum money from knots by Farhi et al.(ITCS'12). In addition to formalizing this framework, we provide concrete hard computational problems loosely inspired by classical knowledge-of-exponent assumptions, whose hardness would imply the security of quantum lightning, a strengthening of quantum money where not even the bank can duplicate banknotes. **We discuss potential instantiations of our framework, including an oracle construction using cryptographic group actions and instantiations from rerandomizable functional encryption, isogenies over elliptic curves, and knots.

Available format(s)
Publication info
quantum cryptography quantum money lattices post-quantum cryptography
Contact author(s)
hart montgomery @ gmail com
jiahui @ utexas edu
mzhandry @ gmail com
2022-11-21: approved
2022-11-21: received
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      author = {Hart Montgomery and Jiahui Liu and Mark Zhandry},
      title = {Another Round of Breaking and Making Quantum Money: How to Not Build It from Lattices, and More},
      howpublished = {Cryptology ePrint Archive, Paper 2022/1620},
      year = {2022},
      note = {\url{}},
      url = {}
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