Using normal form of matrices over finite fields to construct authentication codes with arbitration
Jizhu Nan · Journal of Natural Science of Heilongjiang 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 formed by all equivalent normal forms of n×n matrices over Fq,the set of encoding rules ET and decoding rules ER are formed by all pairs of the n×n nonsingular matrix over Fq,and the set of messages M is formed by all n×n both nonzero and singular matrices over Fq.Construct the mapsf:S×ET→Mg:M×ER→S∪{reject}(Sr,(P,Q))|→PSrQ,(A,(X,Y))|→Sr,if XKAKY=Sr,rank(A)=r,reject,otherwise,where K=In-1000.The six tuple(S,ET,ER,M;f,g),which is a Cartesian authentication code with arbitration,is constructed,and the associated parameters are calculated.Moreover,the encoding rules obey a uniform probability distribution,and PI,PS,PT,PR0 and PR1 are computed.