Three Authentication Schemes Based on Finite Fields and Galois Rings

We give three new systematic authentication schemes, two using Gray map, finite fields and Galois rings, and one using only Galois rings. In the first scheme, we increase the size and simplify the scheme’s source space in [9]. In the second scheme, we reduce the key space of the first scheme. Finally, by not considering Gray map, used in the previous schemes, we give a third scheme on Galois rings, which generalizes the scheme over finite fields given in [8]. The introduced schemes obtain optimal impersonation and substitution probabilities.