Some Constructions of Cartesian Authentication Codes from Pseudo－symplectic Geometry

ＳｏｍｅＣｏｎｓｔｒｕｃｔｉｏｎｓｏｆＣａｒｔｅｓｉａｎＡｕｔｈｅｎｔｉｃａｔｉｏｎＣｏｄｅｓｆｒｏｍＰｓｅｕｄｏ－ｓｙｍｐｌｅｃｔｉｃＧｅｏｍｅｔｒｙＧａｏＹｏｕ（高有）（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉｃＳｃｉｅｎｃｅ，ＮｏｒｔｈｅａｓｔＩｎｓｔ...     

A Note on Authentication Codes with Arbitration

1.IntroductionInthemodelofunconditionallysecureauthenticationcode(A-code),therearethreepar-ticipants;atransmitter,areceiverandanopponent.Theopponentwantstodeceivethembytheso-calledspoofingattack.Aninformation-theoreticlowerboundsfortheprobabilityofsuc-cessfuldeceptionforasPOofingattackoforderrisgivenby[lj.Inthismodel,thetransmitterandthereceivertrusteachother.Howeveritisnotalwaysthecasethatthetransmitterandthereceiverwanttrusteachother.Inspiredbythisproblem,Simmonshasintroducedanextendedaut…     

Using Normal Form of Idempotent Matrices over Finite Local Ring Z/p^kZ to Construct Cartesian Authentication Codes

In this paper, we determine the normal forms of idempotent matrices for similarity over finite local rings Z/p^kZ, from which we construct a Cartesian authentication code and compute its size parameters and the probabilities of successful impersonation and substitution attack under the hypothesis that the cecoding rules are chosen according to a uniform probability distribution.     

Ternary Code Construction of Unimodular Lattices and Self-Dual Codes over ℤ6

We revisit the construction method of even unimodular lattices using ternary self-dual codes given by the third author (M. Ozeki, in Théorie des nombres, J.-M. De Koninck and C. Levesque (Eds.) (Quebec, PQ, 1987), de Gruyter, Berlin, 1989, pp. 772–784), in order to apply the method to odd unimodular lattices and give some extremal (even and odd) unimodular lattices explicitly. In passing we correct an error on the condition for the minimum norm of the lattices of dimension a multiple of 12. As the results of our present research, extremal odd unimodular lattices in dimensions 44, 60 and 68 are constructed for the first time. It is shown that the unimodular lattices obtained by the method can be constructed from some self-dual ₆-codes. Then extremal self-dual ₆-codes of lengths 44, 48, 56, 60, 64 and 68 are constructed.     

Construction of Extremal Type II Codes over ℤ4

In this paper, we give a pseudo-random method to construct extremal Type II codes overℤ₄ . As an application, we give a number of new extremal Type II codes of lengths 24, 32 and 40, constructed from some extremal doubly-even self-dual binary codes. The extremal Type II codes of length 24 have the property that the supports of the codewords of Hamming weight 10 form 5−(24,10,36) designs. It is also shown that every extremal doubly-even self-dual binary code of length 32 can be considered as the residual code of an extremal Type II code over ℤ₄.     

Packing Superballs from Codes and Algebraic Curves

In the present paper, we make use of codes with good parameters and algebraic curves over finite fields with many rational points to construct dense packings of superballs. It turns out that our packing density is quite reasonable. In particular, we improve some values for the best-known lower bounds on packing density.     

A Construction of Cryptogroups

Abstract In this paper, a cryptogroup is constructed by a band and a family of groups and homomorphisms satisfying some conditions.     

A Simple Proof for a Property of the Vector Space Ⅴ Over the Field F

<正> In this paper we'll prove a fundameutal property of the vector space by means of the ex-tension field,i.e.the numbers of the elements of a basis of the vector space V over the field Fequal to the d imensions(V:F).     

A Construction of Co-H Spaces

ＡＣｏｎｓｔｒｕｃｔｉｏｎｏｆＣｏ－ＨＳｐａｃｅｓＷａｎｇＸｕ（王旭）（Ｉｎｓｔ．ｏｆＭａｔｈ．，ＡｃａｄｅｍｉｃａＳｉｎｉｃａ，北京，１０００８０）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＳｈｅｎＸｉｎｙａｏＲｅｃｅｉｖｅｄＯｃｔ．１３，１９９４ＡＣｏｎｓｔｒ...     

Basic Sequences in the Dual of a Fréchet Space

In this paper we study some properties of basic sequences in the dual of a Fréechet space. As a consequence we obtain that if E is a Fréechet space with the property that for each closed subspace F of E and each bounded subset B of E/F there is a bounded subset A of E with φ(A) = B, where φ denotes the canonical surjection of E onto E/F, then one of the following conditions is at least satisfied: 1. E is a Banach space, 2. E is a Schwartz space, 3. E is the product of a Banach space by ω. Finally, we also obtain some results concerning totally reflexive spaces.     

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...     

Another Construction of Cartesian Authentication Codes from Geometry of Classical Groups

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

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.     

New Combinatorial Bounds for Authentication Codes and Key Predistribution Schemes

This paper provides new combinatorial bounds and characterizations of authentication codes (A-codes) and key predistribution schemes (KPS). We first prove a new lower bound on the number of keys in an A-code without secrecy, which can be thought of as a generalization of the classical Rao bound for orthogonal arrays. We also prove a new lower bound on the number of keys in a general A-code, which is based on the Petrenjuk, Ray-Chaudhuri and Wilson bound for t-designs. We also present new lower bounds on the size of keys and the amount of users' secret information in KPS, the latter of which is accomplished by showing that a certain A-code is hiding inside any KPS.     

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.     

利用有限域上的向量空间构作一种新的A~2-码

利用有限域上的向量空间的子空间作了一个A~2-码,并计算了该码的参数.在假定发方编码规则和收方解码规则按等概率分布选取时,计算了各种攻击成功的概率.     

利用有限仿射几何构作Cartesian认证码

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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     

利用有限域上的向量空间构作带仲裁的认证码

This paper is devoted to constructing an authentication code with arbitration using subspaces of vector spaces over finite fields.Moreover,if we choose the encoding rules of the transmitter and the decoding rules of the receiver according to a uniform probability distribution,then some parameters and the probabilities of successful attacks are computed.