两类组合设计及其在认证码中的应用

W．Ogata等定义了两种新的组合设计：外差族（EDF）与外平衡不完全区组设计（E-BIBD）．本文首先用有限域中的分圆类给出EDF的一个构造；接着用EBIBD构造出具有完善保密性的最优分裂A-码，然后证明了由满足一定条件的两个EBIBD通过上述方法构造出的两个认证码是同构的.     

Splitting balanced incomplete block designs with block size 3 × 2

Splitting balanced incomplete block designs were first formulated by Ogata, Kurosawa, Stinson, and Saido recently in the investigation of authentication codes. This article investigates the existence of splitting balanced incomplete block designs, i.e., (v, 3k, λ)‐splitting BIBDs; we give the spectrum of (v, 3 × 2, λ)‐splitting BIBDs. As an application, we obtain an infinite class of 2‐splitting A‐codes. © 2004 Wiley Periodicals, Inc.     

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…     

On Balanced Optimal Optical Orthogonal Codes

Variable‐weight optical orthogonal codes (OOCs) were introduced by G.‐C. Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirement. In this paper, by using incomplete difference matrices and perfect relative difference families, a balanced ‐OOC is obtained for every positive integer .     

Combinatorial Classification of Optimal Authentication Codes with Arbitration

Unconditionallysecure authentication codes with arbitration ( A ²-codes)protect against deceptions from the transmitter and the receiveras well as that from the opponent. We first show that an optimalA ²-code implies an orthogonal array and an affine-resolvable design. Next we define a new design,an affine -resolvable + BIBD,and prove that optimal A ²-codes are equivalentto this new design. From this equivalence, we derive a conditionon the parameters for the existence of optimal A ²-codes.Further, we show tighter lower bounds on the size of keys thanbefore for large sizes of source states which can be consideredas an extension of the bounds on the related designs.     

Some (17q, 17, 2) and (25q, 25, 3) BIBD Constructions

We give the explicit construction of a regular (17q, 17, 2)-BIBD for any prime power q 17 (mod 32) such that 2 is not a 4th power in GF(q) and the explicit construction of a regular (25q, 25, 3)-BIBD for any prime power q 25 (mod 48) such that and +3 are non-squares in GF(q).     

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.     

Combinatorial Bounds on Authentication Codes with Arbitration

Unconditionallysecure authentication codes with arbitration ( A²-codes)protect against deceptions from the transmitter and the receiveras well as that from the opponent. In this paper, we presentcombinatorial lower bounds on the cheating probabilities andthe sizes of keys of A²-codes. These bounds areall tight. Our main technique is a reduction of an A²-codeto a splitting A-code.     

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.     

Cyclic Designs with Block Size 4 and Related Optimal Optical Orthogonal Codes

We prove the existence of a cyclic (4p, 4, 1)-BIBD—and hence, equivalently, that of a cyclic (4, 1)-GDD of type 4 ^p —for any prime such that (p–1)/6 has a prime factor q not greater than 19. This was known only for q=2, i.e., for . In this case an explicit construction was given for . Here, such an explicit construction is also realized for .We also give a strong indication about the existence of a cyclic (4p 4, 1)-BIBD for any prime , p>7. The existence is guaranteed for p>(2q ³–3q ²+1)²+3q ² where q is the least prime factor of (p–1)/6.Finally, we prove, giving explicit constructions, the existence of a cyclic (4, 1)-GDD of type 6 ^p for any prime p>5 and the existence of a cyclic (4, 1)-GDD of type 8 ^p for any prime . The result on GDD's with group size 6 was already known but our proof is new and very easy.All the above results may be translated in terms of optimal optical orthogonal codes of weight four with =1.     

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     

利用有限仿射几何构作Cartesian认证码

设 0 相似文献   

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.     

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.     

Constructing difference families through an optimization approach: Six new BIBDs

In this paper we formulate the construction of difference families as a combinatorial optimization problem. A tabu search algorithm is used to find an optimal solution to the optimization problem for various instances of difference families. In particular, we construct six new difference families which lead to an equal number of new balanced incomplete block designs with parameters: (49, 98, 18, 9, 3), (61, 122, 20, 10, 3), (46, 92, 20, 10, 4), (45, 90, 22, 11, 5), (85, 255, 24, 8, 2) and (34, 85, 30, 12, 10). © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 261–273, 2000     

一种构造多水平超饱和设计的新方法

超饱和设计在搜索试验中有重要应用.自上世纪九十年代迄今, 超饱和设计的研究取得了丰硕成果,研究的设计从二水平发展到多水平, 进而到混合水平;构造方法从巧妙的构思到利用组合理论进行系统构造,进而到各种算法的开发; 对于超饱和设计的评优准则也有更深入的认识.本文介绍一种构造多水平超饱和设计的新方法. 这种方法简单易行,很容易构造出具有优良性质的多水平超饱和设计, 有很强的实用性.     

多项式剩余类环上循环码新的表示

在编码理论中，多项式剩余类环是非常有意义的，它已经用来构造最优频率希望序列。本文，定义了多项式剩余类环上循环码的离散傅立叶变换及Mattson-Solomon（MS）多项式，证明了多项式剩余类环上的循环码同构于多项式剩余类环的Galois扩张的理想。     

Realizations for direct constructions of resolvable Steiner 2‐designs with block size 5

We consider direct constructions due to R. J. R. Abel and M. Greig, and to M. Buratti, for ({ν},5,1) balanced incomplete block designs. These designs are defined using the prime fields F_p for certain primes p, are 1‐rotational over G ⊕ F_p where G is a group of order 4, and are also resolvable under certain conditions. We introduce specifications to the constructions and, by means of character sum arguments, show that the constructions yield resolvable designs whenever p is sufficiently large. © 2000 John Wiley & Sons, Inc. J Combin Designs 8:207–217, 2000     

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.     

利用有限局部环Z/pkZ上的幂等矩阵的标准型构作认证码

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 au- thentication 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.