黑龙江大学自然科学学报
黑龍江大學自然科學學報
흑룡강대학자연과학학보
JOURNAL OF NATURAL SCIENCE OF HEILONGJIANG UNIVERSITY
2010年
1期
54-59,68
,共7页
带仲裁的认证码%有限域%矩阵标准形
帶仲裁的認證碼%有限域%矩陣標準形
대중재적인증마%유한역%구진표준형
authentication codes with arbitration%finite field%normal form of matrix
设F_q是q元有限域,q是素数的幂.令信源集S为F_q上所有的n×n矩阵的等价标准型,编码规则集E_T和解码规则集E_R为F_q上所有的n×n非奇异矩阵对,信息集为F_q上所有的n×n非零的奇异矩阵,构造映射f:S×E_T→M g:M×E_R→S∪{欺诈}(S_r,(P,Q))|→PS_rQ,(A,(X,Y))|→{S_r,如果 XKAKY=S_r,秩A=r 欺诈,其他 其中K=(I_(n-1) 0 0 0).证明了该六元组(S,ET,ER,M;f,g)是一个带仲裁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P_I,P_S,P_T,P_(R0),P_(R1).
設F_q是q元有限域,q是素數的冪.令信源集S為F_q上所有的n×n矩陣的等價標準型,編碼規則集E_T和解碼規則集E_R為F_q上所有的n×n非奇異矩陣對,信息集為F_q上所有的n×n非零的奇異矩陣,構造映射f:S×E_T→M g:M×E_R→S∪{欺詐}(S_r,(P,Q))|→PS_rQ,(A,(X,Y))|→{S_r,如果 XKAKY=S_r,秩A=r 欺詐,其他 其中K=(I_(n-1) 0 0 0).證明瞭該六元組(S,ET,ER,M;f,g)是一箇帶仲裁Cartesian認證碼,併計算瞭該認證碼的參數.進而,噹收方與髮方的編碼規則按照等概率均勻分佈選取時,計算齣該碼的概率P_I,P_S,P_T,P_(R0),P_(R1).
설F_q시q원유한역,q시소수적멱.령신원집S위F_q상소유적n×n구진적등개표준형,편마규칙집E_T화해마규칙집E_R위F_q상소유적n×n비기이구진대,신식집위F_q상소유적n×n비령적기이구진,구조영사f:S×E_T→M g:M×E_R→S∪{기사}(S_r,(P,Q))|→PS_rQ,(A,(X,Y))|→{S_r,여과 XKAKY=S_r,질A=r 기사,기타 기중K=(I_(n-1) 0 0 0).증명료해륙원조(S,ET,ER,M;f,g)시일개대중재Cartesian인증마,병계산료해인증마적삼수.진이,당수방여발방적편마규칙안조등개솔균균분포선취시,계산출해마적개솔P_I,P_S,P_T,P_(R0),P_(R1).
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.
