利用等价矩阵标准形构造带仲裁的认证码(英文)

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。

Using normal form of matrices over finite fields to construct authentication codes with arbitration

Let F_q 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 F_q, the set of encoding rules Er and decoding rules E_R are formed by all pairs of the n×n nonsingular matrix over F_q, and the set of messages M is formed by all n×n both nonzero and singular matrices over F_q. Construct the maps f:S×E_T→M g:M×E_R→S∪{reject}(S_r,(P,Q))|→PS_rQ,(A,(X,Y))|→{(S_r,if XKAKY=S_r,rank(A) =r) reject,otherwise, where K=(I_(n-1 0 0 0). The six tuple (S,E_T,E_R,M;f,g) whieh is a Cartesian authentieation code with arbitration, is constructed, and the associated parameters are calculated. Moreover, the encoding rules obey a uniform probability distribution, and P_I,P_S ,P_T,P_(R0) and P_(R1) are computed.