Using Ⅱ-Jordan Nilpotent Matrices Over Finite Fields To Construct Cartesian Authentication Codes

Some results about the authentication codes are involved in this dissertation, In which the concepts of the authentication codes and the relative knowledge of construction of Cartesian authentication codes are introduced in the first section;On the basis of the explanation ,the definition of â…¡-Jordan nilpotent matrices is defined and its transmission to a simpler form is discussed in the second section;In the third section ,one construction of Cartesian authentication codes from â…¡-Jordan nilpotent matrices over finite fields is presented and its size parameters are computed . And assuming that the encoding rules are chosen according to a uniform probability distribution , the probabilities P_I and P_S, of a successful impersonation attack and of a successful substitution attack respectively ,of these codes are also computed .