Construction of authentication codes with arbitration from alternate matrices over finite fields
YU Hua-feng, You Gao · Journal of Natural Science of Heilongjiang University · 2012
Let Fq be the finite field with q elements,where q is a power of a prime.Suppose the set of source S is a cogradient normal form of all the n×n alternate matrices over Fq,the set of encoding rules ET and decoding rules ER is all of the n×n nonsingular matrices over Fq,and the set of messages M is all of the n×n alternate matrices over Fq.Construct the map f:S×ET|→M,(K′(ν,n),P)→PK′(ν,n) PT g:M×ER|→S∪{reject}(A,Q)|→K′(ν,n) if QKAKTQT=K′(ν,n),rankA=2ν{reject} otherwise That the six triple(S,ET,ER,M;f,g) is an authentication code with arbitration is proved,and the parameters of the code are computed.Moreover,assume that the encoding and decoding rules are chosen according to a uniform probability distribution,the largest probabilities of all kinds successful attack are computed.