Three constructions of authentication codes from power function over finite fields with perfect secrecy. (Q2846638)

The paper presents algebraic constructions of authentication codes with secrecy and without splitting, related to the authentication model introduced in [\textit{G. J. Simmons}, Advances in cryptology, Proc. Workshop, Santa Barbara/Calif. 1984, Lect. Notes Comput. Sci. 196, 411--431 (1985; Zbl 0575.94011)]. Two kinds of attacks are considered: the impersonation attack, when an opponent inserts his message into the channel, and the substitution attack, when the opponent replaces a message with his own one. The codes defined by two of the three constructions are optimal. One of the constructions leads to the class of codes that consists of optimal codes as well as the codes that are merely asymptotically optimal. All authentication codes from the three classes provide perfect secrecy.