  In 2013, Farid and Vasiliev [arXiv:quant-ph/1310.4922] for the first time
proposed a way to construct a protocol for the realisation of "{\em 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 "{\em 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.
