Using alternation matrices to construct cartesian authentication codes with arbitration
Kong De-bao · Journal of Liaoning Normal University · 2010
Let Fq be the finite field with q elements,where q is a power of a prime.Suppose the set of source states S is a cogredient normal form of all the n × n alternate matrices over Fq,the set of encoding rules ET and decoding rules ER are all of the n × n nonsingular matrices over Fq,and the set of messages M is all of the n × n singular alternate matrices over Fq.Construct the mapsf:S×ET→M g:M×ER→S∪{reject}K'(ν,n),PPK'(ν,n)Pt,(A,X)K'(ν,n)if XKAKXt=K'(ν,n),rank(A)=2νreject,otherwise.where K=[In-1000].In this paper,we prove that the sets(S,ET,ER,M;f,g)is a Cartesian authentication code and the associated parameters are calculated.When the encoding rules obey a uniform probability distribution,we calculate PI,PS,PT,PR0 and PR1,which denote the largest probabilities of a successful impersonation attacks by the opponent,a successful substitution attacks by the opponent,a successful impersonation attacks by the transmitter,a successful impersonation attacks by the receiver and a successful substitution attacks by the receiver,respeetively.