利用有限域上反对称矩阵的标准型构作卡氏认证码

利用有限域上反对称矩阵的标准型构作了一个迪卡尔认证码并计算出该码的所有参数. 进而,假定编码规则按照统一的概率分布所选取,该码的成功伪造与成功替换的最大概率PI与PS亦被计算出来.     

利用有限域上2-幂零矩阵构作Cartesian认证码

给出 2 -幂零矩阵的Jordan标准型在相似变换下的稳定群的结构 ,利用有限域上 2 -幂零矩阵构作了一个Cartesian认证码 ,计算出了该认证码的参数 .在假定编码规则按等概率分布选取的条件下 ,计算出了该认证码被成功的模仿攻击的最大概率PI 及被成功的替换攻击的最大概率PS.     

利用有限域上对合阵构作认证码

本文利用有限域上ｎ阶对合阵给同了构作Ｃａｒｔｅｓｉｏｎ认证码的一种新方案,计算了这类认证码的参数,在编码规则等概率分布选取的假设下,给出了这类认证码被被成功地模仿攻击的最大概率Ｐ１和被成功地替换攻击的最大概率Ｐｓ     

构作正交空间中的一类Cartesian认证码

利用正交几何构作出一类Cartesian认证码,并且计算了它们的参数.假定信源和编码规则都按等概率分布选取,求出了认证码的成功的模仿攻击概率PI和成功的替换攻击概率PS.本文构作的Cartesian认证码的成功的模仿攻击概率PI均达到了其下界.     

利用奇、偶特征的正交几何构作的最优Cartesian认证码

利用奇、偶特征有限域上的正交几何构作出一类C artesian认证码,并且计算了它们的参数.并在假定按照等概率分布来选择编码规则下,求出了认证码的成功的模仿攻击概率和成功的替换攻击概率.作为一个推论,还得到了一些最优的C artesian认证码.     

Construction of Cartesian Authentication Codes from Pseudo Symplectic Geometry of Even Dimension

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＳ,ＥａｎｄＭｂｅｔｈｒｅｅｎｏｎ－ｅｍｐｔｙｆｉｎｉｔｅｓｅｔｓａｎｄｌｅｔｆ：Ｓ×Ｅ→Ｍｂｅａｍａｐ．Ｔｈｅｆｏｕｒｔｕｐｌｅ（Ｓ,Ｅ,Ｍ;ｆ）ｉｓｃａｌｅｄａｎａｕｔｈｅｎｔｉｃａｔｉｏｎｃｏｄｅ（ｓｅｅ［１...     

基于2-Jordan型幂零阵的Cartesian认证码的构造

利用群在集合上的共轭作用,给出了一种由2 -Jordan型幂零矩阵构造Cartesian认证码的新方案,计算了相关参数,并在假定编码规则按等概率分布选取时分析了模仿攻击和替换攻击成功的概率.     

利用有限域上一类幂零阵的标准形构造Cartesian认证码

Let Fq be a finite field. In this paper, a construction of Cartesian au-thentication codes from the normal form of a class of nilpotent matrices over the field Fq is presented. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the probabilities PI and PS, of a successful im-personation attack and of a successful substitution attack respectively, of these codes are also computed.     

利用有限域上矩阵的标准型构作卡氏认证码

本文利用有限域上长方矩阵的等价标准型构作了一个笛卡尔认证码并计算出该码的所有参数．进而，假定编码规则按照统一的概率分布所选取，该码的成功伪造与成功替换的最大概率Ｐ_Ｉ与Ｐ_Ｓ亦被计算出来．     

Construction of Cartesian authentication codes from unitary geometry

In the present paper several constructions of Cartesian authentication codes from unitary geometry over finite fields are presented and their size parameters are computed. Assuming that the encoding rules are chosen according to a uniform probability distribution, the probabilities P _I and P _S of a successful impersonation attack and a successful substitution attack, respectively, of these codes are also computed. Moreover, those codes so constructed, for which P _I and P _S are nearly optimal, are also determined.     

利用辛对合矩阵构造Cartesian认证码

利用辛对合矩阵构作了一个C artesian认证码,并且计算了其参数.假设编码规则是按均匀概率分布选取时,计算了模仿攻击成功的概率PI和替换攻击成功的概率PS.     

利用辛几何构作两类Cartesian认证码

本文利用辛几何构作了两类 Cartesian认证码 ,计算了码的参数 .当编码规则按等概率分布选取时 ,计算出敌方成功的模仿攻击概率和成功的替换攻击概率     

利用有限域上特征为2的正交几何构作一类Cartesian认证码

利用了有限域上的特征为2的正交几何构造了一类Cartesian认证码,并且计算了其参数及模仿攻击成功的概率PI和替换攻击成功的概率PS.     

Two constructions of optimal cartesian authentication codes from unitary geometry over finite fields

Two constructions of cartesian authentication codes from unitary geometry are given in this paper. Their size parameters and their probabilities of successful impersonation attack and successful substitution attack are computed. They are optimal under some cases.     

利用有限域上酉几何构作两类Cartesian认证码

本文利用有限域上的酉几何构作了两类Ｃａｒｔｅｓｉａｎ认证码，并且计算了它们的参数及成功的模仿攻击概率和成功的替换攻击概率。     

利用有限域上伪辛几何构作两类Cartesian认证码

本文利用有限域上的伪辛几何构作了两类Cartesian认证码，并且计算了它们的参数及成功的模仿攻击概率和成功的替换攻击概率．     

利用SLn(Fq)的BN对分解构造Cartesian认证码

In the present paper,a construction of Cartesian authentication codes by using the BN pair decomposition of special linear group is presented.Moreover,under the case that the encoding rules are chosen according to a uniform probability distribution,the probability of a successful impersonation attack and the probability of a successful substitution attack of the code are computed.     

基于酉几何的具有仲裁的认证码的构造

具有仲裁的认证码即要防止敌手的欺骗,又要防止收方和发方的互相欺骗．本文给出一种由酉几何构造具有仲裁的认证码的方法,并计算了有关参娄,分析了各种攻击成功的概率。     

Authentication codes and bipartite graphs

In this paper, a characterization of authentication codes in terms of bipartite graphs is given. By using such a characterization, two necessary and sufficient conditions for a minimal authentication code with perfect secrecy are derived. The probabilities of a successful impersonation and of a successful substitution attack are discussed. As a result, some (optimal) minimal authentication codes with perfect secrecy are constructed from association schemes, from finite groups or from known authentication codes no matter whether the known ones are with or without secrecy.     

Quasi-cyclic codes with cyclic constituent codes

Ling and Solé [S. Ling, P. Solé, On the algebraic structure of quasi-cyclic codes I: Finite fields, IEEE Trans. Inform. Theory 47 (2001) 2751–2760] showed that every quasi-cyclic code C is constructed from shorter linear codes which are called the constituent codes of C. Given a quasi-cyclic code C of length ℓm and index ℓ with m being pairwise coprime to ℓ and the order of the field C is over, if all its constituent codes are cyclic with their zeroes having full multiplicity, C is then shown to be equivalent to a cyclic code whose zeroes with their multiplicities are fully described in terms of the nonzeroes of the cyclic constituent codes. The general transformation to obtain the above-mentioned equivalent cyclic code is also explicitly given. The approach adopted here follows the approach used by A.M.A. Natividad [A.M.A. Natividad, PhD thesis, Department of Mathematics, University of Philippines Diliman, The Philippines, 2004] and uses the generalized discrete Fourier transform on the algebraic structure of the class of quasi-cyclic codes developed by Ling and Solé [S. Ling, P. Solé, On the algebraic structure of quasi-cyclic codes I: Finite fields, IEEE Trans. Inform. Theory 47 (2001) 2751–2760].