  In the paper we define a notion of quantum resistant
($(\epsilon,\delta)$-resistant) hash function which combine together a notion
of pre-image (one-way) resistance ($\epsilon$-resistance) property we define in
the paper and the notion of collision resistance ($\delta$-resistance)
properties.
  We show that in the quantum setting a one-way resistance property and
collision resistance property are correlated: the "more" a quantum function is
one-way resistant the "less" it collision resistant and vice versa. We present
an explicit quantum hash function which is "balanced" one-way resistant and
collision resistant and demonstrate how to build a large family quantum hash
functions. Balanced quantum hash functions need a high degree of entanglement
between the qubits. We use a "phase constructions" technique to express quantum
hashing constructions, which is good to map hash states to coherent states in a
superposition of time-bin modes. The later is ready to be implemented with
current optical technology.
