A shift register construction of unconditionally secure authentication codes

In English We consider the authentication problem, using the model described by Simmons. Several codes have been constructed using combinatorial designs and finite geometries. We introduce a new way of constructing authentication codes using LFSR-sequences. A central part of the construction is an encoding matrix derived from these LFSR-sequences. Necessary criteria for this matrix in order to give authentication codes that provides protection aginst impersonation and substitution attacks will be given. These codes also provide perfect secrecy if the source states have a uniform distribution. Moreover, the codes give a natural splitting of the key into two parts, one part used aginst impersonation attacks and a second part used against substitution attacks and for secrecy simultaneously. Since the construction is based on the theory of LFSR-sequences it is very suitable for implementation and a simple implementation of the construction is given.