Efficient Branching Programs for Quantum Hash Functions Generated by Small-Biased Sets

In the paper we consider quantum ( δ , ϵ )-hash functions in so called phase form (phase quantum ( δ , ϵ )-hash function). It is known that ϵ -biased sets generate phase quantum ( δ , ϵ )- hash function. We show that the construction is invertible, that is, phase quantum ( δ , ϵ )-hash function defines ϵ -biased sets. Next, we present an efficient (in the sense of time and qubits needed) Branching program construction for phase quantum ( δ , ϵ )-hash function.