Abstract
In 2013, Farid and Vasiliev [arXiv:1310.4922 [quant-ph]] for the first time proposed a way to construct a protocol for the realisation of “Classical to Quantum” one-way hash function, a derivative of the quantum one-way function as defined by Gottesman and Chuang [Technical Report arXiv:quant-ph/0105032] and used it for constructing quantum digital signatures. We, on the other hand, for the first time, propose the idea of a different kind of one-way function, which is “quantum-classical” in nature, that is, it takes an n-qubit quantum state of a definite kind as its input and produces a classical output. We formally define such a one-way function and propose a way to construct and realise it. The proposed one-way function turns out to be very useful in authenticating a quantum state in any quantum money scheme, and so we can construct many different quantum money schemes based on such a one-way function. Later in the paper, we also give explicit constructions of some interesting quantum money schemes like quantum bitcoins and quantum currency schemes, solely based on the proposed one-way function. The security of such schemes can be explained on the basis of the security of the underlying one-way functions.
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Notes
The set \({\mathcal {G}}\) depends upon n and should be written as \(\mathcal {G}(n)\). Since we would be using \({\mathcal {G}}(n)\) for a fixed n throughout the paper, we simply refer to the set as \({\mathcal {G}}\).
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Part of this work was done while Amit Behera was visiting R. C. Bose Centre for Cryptology and Security, Indian Statistical Institute, Kolkata during the Summer of 2017 (between the 2nd and the 3rd semester of his BSc (Honours) Mathematics and Computer Science course) for internship under the supervision of Goutam Paul.
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Behera, A., Paul, G. Quantum to classical one-way function and its applications in quantum money authentication. Quantum Inf Process 17, 200 (2018). https://doi.org/10.1007/s11128-018-1965-z
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DOI: https://doi.org/10.1007/s11128-018-1965-z