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Forty years ago, Wiesner pointed out that quantum mechanics raises the striking possibility of money that cannot be counterfeited according to the laws of physics. The authors propose the first quantum money scheme that is; public-key - meaning that anyone can verify a banknote as genuine, not only the bank that printed it and cryptographically secure, under a "Classical" hardness assumption that has nothing to do with quantum money. Their scheme is based on hidden subspaces, encoded as the zero-sets of random multivariate polynomials. A main technical advance is to show that the "Black-box" version of their scheme, where the polynomials are replaced by classical oracles, is unconditionally secure.
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