Abstract
We introduce a private quantum money scheme with the note verification procedure based on sampling matching, a problem in a one-way communication complexity model. Our scheme involves a bank who produces and distributes quantum notes, noteholders who are untrusted, and trusted local verifiers of the bank to whom the holders send their notes in order to carry out transactions. The key aspects of our money scheme include: note verification procedure requiring a single round classical interaction between the local verifier and bank; fixed verification circuit that uses only passive linear optical components; re-usability of each note in our scheme which grows linearly with the size of note; and an unconditional security against any adversary trying to forge the banknote while tolerating the noise of up to 21.4%. We further describe a practical implementation technique of our money scheme using weak coherent states of light and the verification circuit involving a single 50/50 beam splitter and two single-photon threshold detectors. Previous best-known matching based money scheme proposal involves a verification circuit where the number of optical components increase proportional to the increase in desired noise tolerance (robustness). In contrast, we achieve any desired noise tolerance (up to a maximal threshold value) with only a fixed number of optical components. This considerable reduction of components in our scheme enables us to reach the robustness values that is not feasible for any existing money scheme with the current technology.
Highlights
In the 1980s, Wiesner [1] proposed the idea of quantum money to create unforgeable banknotes with quantum states
Note verification procedure requiring a single round classical communication between the local verifier and the bank, Fixed verification circuit for a given input size of the note, Multiple note re-usability, meaning the same note can be reused by the holder a number of times, Unconditional security against any adversary trying to forge the banknote while tolerating a noise of up to 21.4%
We have introduced the private quantum money scheme as a cryptographic task using the sampling matching verification scheme
Summary
In the 1980s, Wiesner [1] proposed the idea of quantum money to create unforgeable banknotes with quantum states In his scheme, the banknotes are several BB84 states prepared by an honest authority, a bank, which distributes them to the untrusted holders. The unforgeability property of the note in Wiesner’s scheme relies on the no-cloning property of quantum mechanics which prevents the holder from creating multiple copies of the notes with just a single copy [2]. This idea was incidentally among the first quantum cryptographic primitives to be introduced. Other cryptographic tasks based on quantum mechanics have been proposed such as quantum key distribution, digital signatures, coin flipping, secure multi-party computation, etc [3,4,5,6,7,8]
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