Two eminent specialists on quasigroups, Dénes and Keedwell, onced augured the advent of a new era in cryptology, consisting in the application of non-associative algebraic systems. Nevertheless, at present, very few researchers use these tools and in many cases it seems unreasonable and reckless. For example, constructing one-way functions, algorithms are usually designed, in which computations are performed using regular algebraic systems as groups, rings and fields, simple boolean operations, modular arithmetic, and cyclic permutations. Such an approach may simplify cryptanalysis. However, computations of the value of cryptographic one-way function should be easy, but taking into account the security, an algorithm describing the hash function should involve rather an algebraic system, which is strongly recalcitrant, and the behaviour of which is unforeseeable. A quasigroup field, as an algebraic system, has such favorable properties. Thus quasigroup fields can be easily applied in designing both unkeyed and keyed hash functions, iterated or not-iterated as well, that is why in this contribution it will be shown how to do it.