Paper 2022/624

Cryptanalysis of Three Quantum Money Schemes

Andriyan Bilyk, Javad Doliskani, and Zhiyong Gong

Abstract

We investigate the security assumptions behind three public-key quantum money schemes. Aaronson and Christiano proposed a scheme based on hidden subspaces of the vector space $\mathbb{F}_2^n$ in 2012. It was conjectured by Pena et al in 2015 that the hard problem underlying the scheme can be solved in quasi-polynomial time. We confirm this conjecture by giving a polynomial time quantum algorithm for the underlying problem. Our algorithm is based on computing the Zariski tangent space of a random point in the hidden subspace. Zhandry proposed a scheme based on multivariate hash functions in 2017. We give a polynomial time quantum algorithm for cloning a money state with high probability. Our algorithm uses the verification circuit of the scheme to produce a banknote from a given serial number. Kane proposed a scheme based on modular forms in 2018. The underlying hard problem in Kane's scheme is cloning a quantum state that represents an eigenvector of a set of Hecke operators. We give a polynomial time quantum reduction from this hard problem to a linear algebra problem. The latter problem is much easier to understand, and we hope that our reduction opens new avenues to future cryptanalyses of this scheme.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Quantum CryptographyQuantum MoneyCryptanalysis
Contact author(s)
javad doliskani @ ryerson ca
History
2022-05-23: received
Short URL
https://ia.cr/2022/624
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2022/624,
      author = {Andriyan Bilyk and Javad Doliskani and Zhiyong Gong},
      title = {Cryptanalysis of Three Quantum Money Schemes},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/624},
      year = {2022},
      url = {https://eprint.iacr.org/2022/624}
}
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