On the Concept of Cryptographic Quantum Hashing

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.