On quantum (delta, N")-resistant hashing

In the paper we define a notion of quantum resistant ((delta, N")-resistant) hash function which combine together a notion of pre-image (one-way) resistance (delta-resistance) property and the notion of collision resistance (N"-resistance) properties. We present a discussion that supports the idea of quantum hashing oriented for cryptographical purposes. We propose a quantum setting of a classical digital signature scheme do demonstrate a theoretical possibilities and restrictions of (delta, N")-hashing. The assumption we use is that a set of qubits (quantum hash) we generate, send, and receive during the execution of a protocol can be stored for a certain (a large enough) amount of time; next, the scheme requires the high degree of entanglement between the qubits which makes such a quantum hash. These properties make quantum hash cryptographically efficient.