利用有限域上交错矩阵构造带仲裁的认证码

设Fq是q元有限域,q是素数的幂。令信源集S是Fq上所有的n×n交错矩阵的合同标准形,编码规则集ET及解码规则集ER为Fq上所有的n×n非奇异矩阵,信息集M为Fq上所有的n×n交错矩阵,构造映射f:S×ET|→M,(K’(ν,n),P)→PK’(ν,n)PTg:M×ER|→S∪{欺诈}(A,Q)|→K’(ν,n)若QKAKTQT=K’(ν,n),其中A的秩为2ν{欺诈}{其他证明该六元组(S,ET,ER,M;f,g)是一个带仲裁的认证码,并计算它的参数。进而,假定编码规则和解码规则按均匀的概率分布选取,计算了该码的参数和各种攻击成功的概率。

Construction of authentication codes with arbitration from alternate matrices over finite fields

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.