Summary: Quantum Money from Hidden Subspaces
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. We propose the first
quantum money scheme that is
(1) public-key--meaning that anyone can verify a banknote as genuine, not only the bank
that printed it, and
(2) cryptographically secure, under a "classical" hardness assumption that has nothing to do
with quantum money.
Our 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 our scheme,
where the polynomials are replaced by classical oracles, is unconditionally secure. Previously,
such a result had only been known relative to a quantum oracle (and even there, the proof was
Even in Wiesner's original setting--quantum money that can only be verified by the bank--
we are able to use our techniques to patch a major security hole in Wiesner's scheme. We
give the first private-key quantum money scheme that allows unlimited verifications and that
remains unconditionally secure, even if the counterfeiter can interact adaptively with the bank.