International Association
for Cryptologic Research

We introduce four constructions of systematic authentication codes. The first two are built over finite fields using resilient functions and they provide optimal impersonation and substitution probabilities. The 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. For the special case of characteristic $p^2$, those maps are bent indeed, and this case is subsumed by our general construction of characteristic $p^s$, with $s\\geq 2$.