Cryptographic quantum hashing

We present a version of quantum hash functions based on non-binary discrete functions. The proposed quantum procedure is 'classical-quantum', that is, it takes a classical bit string as an input and produces a quantum state. The resulting function has the property of a one-way function (pre-image resistance); in addition it has properties analogous to classical cryptographic hash second pre-image resistance and collision resistance. We also show that the proposed function can be naturally used in a quantum digital signature protocol.