Authentication codes based on resilient Boolean maps

We introduce new constructions of systematic authentication codes over finite fields and Galois rings. One code is built over finite fields using resilient functions and it provides optimal impersonation and substitution probabilities. Other two proposed codes are defined over Galois rings, one is based on resilient maps and it attains optimal probabilities as well, while the other uses maps whose Fourier transforms get higher values. Being the finite fields special cases of Galois rings, the first code introduced for Galois rings apply also at finite fields. For the special case of characteristic p, the maps used at the second case in Galois rings are bent indeed, and this case is subsumed by our current general construction of characteristic p, with s ≥ 2.