Abstract
A class of bent functions on a Galois ring is introduced and based on these functions systematic authentication codes are presented. These codes generalize those appearing in [4] for finite fields.
Highlights
On a public communication channel there is a risk that an intruder can deliberately observe and even cause a disturbance in the communication
A class of bent functions on a Galois ring of characteristic p2 is given by Proposition 2 Let R = GR(p2, m), r ≥ 1 be an integer such that (r, pm−1) = 1 and let f (x) = xpr+1+αxp where α ∈ R
The transmitter wishes to send a piece of information, s ∈ S, called the source state, to the receiver
Summary
On a public communication channel there is a risk that an intruder can deliberately observe and even cause a disturbance in the communication. An authentication code provides a method for insuring the integrity of the information to be sent through this channel. These codes, first introduced by Gilbert, MacWilliams and Sloane, have since received attention by several authors and may be with secrecy and without secrecy; a subclass of the latter is the Systematic Authentication Codes (SACs). Several types of SACs have been constructed using various concepts such as highly nonlinear functions over finite fields or non-degenerated and rational functions on a Galois ring. By introducing a class of bent functions over a Galois ring of characteristic p2, (p a prime) and using the Gray map on such ring, a class of SACs is presented and an example is given to illustrate the main results
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