TWO NEW CONSTRUCTIONS OF CARTESIAN AUTHENTICATION CODES FROM SYMPLECTIC GEOMETRY

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利用奇异酉几何构造新的带仲裁的认证码

带仲裁的认证码既要防止敌人的欺骗,又要防止收方和发方的相互欺骗.文章利用有限域上奇异酉几何构造了一个新的带仲裁的认证码,计算了这个码的各种参数.当收方和发方的编码规则按等概率分布选取时,计算出了各种攻击成功的概率.     

Construction of codes from Arakelov geometry

We give a construction of the codes from Hermitian vector bundles on an arithmetic curve generalizing the number field codes introduced by Guruswami and Lenstra. Using Arakelov geometry, we give an estimate of the parameters of these codes.     

利用有限域上交错矩阵构造Cartesian认证码

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交错矩阵的合同标准形,编码规则集E为Fq上所有的n×n非奇异矩阵,信息集M为Fq上所有的n×n交错矩阵,构造映射f:S×E→M,(K'(v,n),g)→gK'(v,n)gT.证明了该四元组(S,E,M;f)是一个Cartesian认证码,并计算了它的参数.进而,假定编码规则按照均匀的概率分布所选取,计算出了该码的成功模仿攻击概率PI和替换攻击概率Ps.     

Combinatorial characterizations of authentication codes

In this paper, we prove two new combinatorial characterizations of authentication codes. Authentication codes without secrecy are characterized in terms of orthogonal arrays; and general authentication codes are characterized in terms of balanced incomplete block designs. In both of these characterizations, it turns out that encoding rules must be equiprobable; in the second characteriztion, the source states must also be equiprobable.A preliminary version of this paper appeared in Advances in Cryptology—CRYPTO '91 Proceedings Lecture Notes in Computer Science 576 (1992) 62–73, Springer-Verlag.Research supported by NSERC grant A9287.     

On the hyperbolic unitary geometry

Hans Cuypers (Preprint) describes a characterisation of the geometry on singular points and hyperbolic lines of a finite unitary space—the hyperbolic unitary geometry—using information about the planes. In the present article we describe an alternative local characterisation based on Cuypers’ work and on a local recognition of the graph of hyperbolic lines with perpendicularity as adjacency. This paper can be viewed as the unitary analogue of the second author’s article (J. Comb. Theory Ser. A 105:97–110, 2004) on the hyperbolic symplectic geometry.     

Universal hashing and authentication codes

In this paper, we study the application of universal hashing to the construction of unconditionally secure authentication codes without secrecy. This idea is most useful when the number of authenticators is exponentially small compared to the number of possible source states (plaintext messages). We formally define some new classes of hash functions and then prove some new bounds and give some general constructions for these classes of hash functions. Then we discuss the implications to authentication codes.A preliminary version of this paper was presented at CRYPTO '91 and appeared in Lecture Notes in Computer Science, vol. 576, pp. 74–85, Springer-Verlag, 1992.     

Integral geometry of unitary area measures

The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is shown to have the structure of a co-product. In the case of the unitary group the algebra associated to this co-product is described explicitly in terms of generators and relations. As a consequence, a simple algorithm that yields explicit kinematic formulas for unitary area measures is obtained.     

Affine geometry over free unitary modules

In this paper we consider systems (P,L,,), where P is an arbitrary non-empty set, L a set of subsets of p and resp. a relation on PxP resp. LxL. In successive stages adding geometrical axioms, we characterize the class of those structures (P,L, ,), which coincides — up to isomorphisms — with the class of all Affine Barbilian-Spaces.     

Systematic authentication codes using additive polynomials

Using additive polynomials related to some curves over finite fields, we construct two families of systematic authentication codes. We use tight bounds for the number of rational points of these curves in estimating the probabilities of the systematic authentication codes. We compare their parameters with some existing codes in the literature. We observe that the parameters are better than the existing ones in some cases.     

A class of authentication codes with secrecy

We study a class of authentication codes with secrecy. We determine the maximum success probabilities of the impersonation and the substitution attacks on these codes and the level of secrecy. Therefore we give an answer to an open problem stated in Ding et al. (J Pure Appl Algebra 196:149–168, 2005). Our proofs use the number of rational places of a certain class of algebraic function fields. We determine this number by extending the corresponding results of E. Çakçak and F. Özbudak (Finite Fields Appl 14(1):209–220, 2008). Our authentication codes use a map which is not perfect nonlinear in certain subcases. We give an extended and unified approach so that the parameters of our authentication codes are good also when the corresponding map is not perfect nonlinear.     

A construction of fully diverse unitary space-time codes

Fully diverse unitary space-time codes are useful in multiantenna communications, especially in multiantenna differential modulation. Recently, two constructions of parametric fully diverse unitary space-time codes for three antennas system have been introduced. We propose a new construction method based on the constructions. In the present paper, fully diverse codes for systems of odd prime number antennas are obtained from this construction. Space-time codes from present construction are found to have bet...     

Partial permutation decoding for codes from affine geometry designs

We find explicit PD-sets for partial permutation decoding of the generalized Reed-Muller codes from the affine geometry designs of points and lines in dimension 3 over the prime field of order p, using the information sets found in [8]. This work was supported by the DoD Multidisciplinary University Research Initiative (MURI) program administered by the Office of Naval Research under Grant N00014-00-1-0565.     

Difference packing arrays and systematic authentication codes

In this paper, a type of combinatorial design (called difference packing array) is proposed and used to give a construction of systematic authentication codes. Taking advantage of this construction, some new series of systematic authentication codes are obtainable in terms of existing difference packing arrays.     

GOB designs for authentication codes with arbitration

Combinatorial characterization of optimal authentication codes with arbitration was previously given by several groups of researchers in terms of affine α-resolvable + BIBDs and α-resolvable designs with some special properties, respectively. In this paper, we revisit this known characterization and restate it using a new idea of GOB designs. This newly introduced combinatorial structure simplifies the characterization, and enables us to extend Johansson’s well-known family of optimal authentication codes with arbitration to any finite projective spaces with dimension greater than or equal to 3.     

On the construction of authentication and secrecy codes

We present several recursive constructions for authentication and secrecy codes using t-designs. These constructions are based on combinatorial structures called authentication perpendicular arrays, introduced by Stinson. As a by-product we obtain a method for constructing sets of permutations which are uniform and t-homogeneous for arbitrarily large t. A table of parameters for codes whose existence is known is included.     

带仲裁的认证码的一个新构造

基于群在集合上的作用和非线性函数构造了一类新的带仲裁的认证码,计算了该码的各种参数,并在假定收方和发方编码规则服从均匀概率分布的情况下,计算了该码受到的五种攻击成功的概率.