  We present the implementation of Grover's algorithm in a quantum simulator to
perform a quantum search for preimages of two scaled hash functions, whose
design only uses modular addition, word rotation, and bitwise exclusive or. Our
implementation provides the means to assess with precision the scaling of the
number of gates and depth of a full-fledged quantum circuit designed to find
the preimages of a given hash digest. The detailed construction of the quantum
oracle shows that the presence of AND gates, OR gates, shifts of bits and the
reuse of the initial state along the computation, require extra quantum
resources as compared with other hash functions based on modular additions, XOR
gates and rotations. We also track the entanglement entropy present in the
quantum register at every step along the computation, showing that it becomes
maximal at the inner core of the first action of the quantum oracle, which
implies that no classical simulation based on Tensor Networks would be of
relevance. Finally, we show that strategies that suggest a shortcut based on
sampling the quantum register after a few steps of Grover's algorithm can only
provide some marginal practical advantage in terms of error mitigation.
