摘要
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。
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.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2012年第1期42-50,55,共10页
Journal of Natural Science of Heilongjiang University
基金
国家自然科学基金资助项目(61179026)
关键词
有限域
交错矩阵
具有仲裁的认证码
finite fields
ahernate matrix
authentication codes with arbitration
