摘要
设Fq是q元有限域,q是素数的幂。令信源集S为Fq上所有的n×n矩阵的等价标准型,编码规则集ET和解码规则集ER为Fq上所有的n×n非奇异矩阵对,信息集为Fq上所有的n×n非零的奇异矩阵,构造映射f:S×ET→M g:M×ER→S∪{欺诈}(Sr,(P,Q))|→PSrQ,(A,(X,Y))|→Sr,如果XKAKY=Sr,秩A=r欺诈,其他其中K=In-100 0。证明了该六元组(S,ET,ER,M;f,g)是一个带仲裁的Cartesian认证码,并计算了该认证码的参数。进而,当收方与发方的编码规则按照等概率均匀分布选取时,计算出该码的概率PI,PS,PT,PR0,PR1。
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.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2010年第1期54-59,68,共7页
Journal of Natural Science of Heilongjiang University
基金
Supported by the Natural Science Foundation of China(10771023)
关键词
带仲裁的认证码
有限域
矩阵标准形
authentication codes with arbitration
finite field
normal form of matrix