Construction of Cartesian authentication code from alternate matrices over finite fields
Ya-Yuan Tao · 2007
Let F_qbe the finite field with q elements,where q is a power of a prime.Suppose the set of source states S is a cogradient normal form of all the n×n alternate matrices over F_q,the set of encoding rules E is all of the n×n nonsingular matrices over F_q,and the set of messages Mis all of the n×n alternate matrices over F_q.Construct the map f:S×E→M,(K′_((v,n)),g)→gK′_((v,n))_g~T. In the present paper,that the four tuple(S,E,M;f) is a Cartesian authentication code is proved, and the parameters of the code are computed.Moreover,assume that the encoding rules are chosen according to a uniform probability distribution,and P_I and P_S,which denote the largest probabilities of a successful impersonation attack and of a successful substitution attack respectively,of the code are computed.