有限域上最优码的一种新的构造方法

基于域F_p^m上一类特殊的矩阵,定义了环R(_p^m,k)=F_p^m[u]/k>到F_p^p_mj的一个新的Gray映射,其中u^k=0、p为素数、j为正整数且p^j－1+1≤k≤p^j.得到了环R(_p^m,k)上码长为任意长度N的(1+u)常循环码的Gray象是F_p^m上长为p^jN的保距线性循环码,并给出了Gray象的生成多项式,构造了F₃,F₅和F₇上的一些最优线性循环码.     

几类指标为2的不可约拟循环码的重量分布

少重量线性码在认证码、结合方案以及秘密共享方案的构造中有着重要的应用。如何构造少重量线性码一直是编码理论研究的重要内容。该文通过选取特殊的定义集,构造了有限域上指标为2的不可约拟循环码,利用有限域上的高斯周期确定了几类指标为2的不可约拟循环码的重量分布,并且得到了几类2-重量线性码和3-重量线性码。结果表明,由该文构造的3类2-重量线性码中有两类是极大距离可分(MDS)码,另一类达到了Griesmer界。     

一类四重和六重线性码的构造

低重线性码在结合方案、认证码以及秘密共享方案等方面有着极其重要的作用,因而低重线性码的设计一直是线性码的重要研究方向。该文通过选取恰当的定义集,构造了有限域${F_p}$(p为奇素数)上的一类四重和六重线性码,利用高斯和确定了码的重量分布,并编写Magma程序进行了验证。结果表明,构造的码中存在关于Singleton界的几乎最佳码。     

两类极小二元线性码的构造

线性码在数据存储、信息安全以及秘密共享等领域具有重要的作用。而极小线性码是设计秘密共享方案的首选码,设计极小线性码是当前密码与编码研究的重要内容之一。该文首先选取恰当的布尔函数,研究了函数的Walsh谱值分布,并利用布尔函数的Walsh谱值分布构造了两类极小线性码,确定了码的参数及重量分布。结果表明,所构造的码是不满足Ashikhmin-Barg条件的极小线性码,可用作设计具有良好访问结构的秘密共享方案。     

基于极小线性码上的秘密共享方案

从理论上说,每个线性码都可用于构造秘密共享方案,但是在一般情况下,所构造的秘密共享方案的存取结构是难以确定的.本文提出了极小线性码的概念,指出基于这种码的对偶码所构造的秘密共享方案的存取结构是容易确定的.本文首先证明了极小线性码的缩短码一定是极小线性码.然后对几类不可约循环码给出它们为极小线性码的判定条件,并在理论上研究了基于几类不可约循环码的对偶码上的秘密共享方案的存取结构.最后用编程具体求出了一些实例中方案的存取结构.     

VI-2类5维q元线性码的汉明重量谱的确定

上 线性码c的汉明重量谱为序列 ,其中,dr是c的r维子码的最小支撑重量。第VI类5维q元线性码的汉明重量谱,按照新的必要条件可以分成6个子类。运用有限射影几何方法研究VI-2类的5维q元线性码的汉明重量谱,确定VI-2类5维q元线性码的几乎所有汉明重量谱。     

环Fp+vFp+v2Fp上线性码的各种重量计数器及其MacWilliams恒等式

首先给出了环R=F_p+vF_p+v²F_p上线性码及其对偶码的结构及其Gray象的性质.定义了环R上线性码的各种重量计数器并讨论了它们之间的关系,特别的,确定了该环上线性码与其对偶码之间关于完全重量计数器的MacWilliams恒等式,利用该恒等式,进一步建立了该环上线性码与其对偶码之间的一种对称形式的MacWilliams恒等式.最后,利用该对称形式的MacWilliams恒等式得到了该环上的Hamming重量计数器和Lee重量计数器的MacWilliams恒等式,利用不同的方法推广了文献[7]中的结果.     

一种新的无可信中心门限DSS签名方案

利用"乘法型共享技术",Langford给出了一种无可信中心的(t2-t 1,n)门限DSS签名方案。结合"加法型共享技术"和"乘法型共享技术"的思想,文中提出了一种新的无可信中心门限DSS签名方案,与(t2-t 1,n)门限签名方案相比较,该方案只需2t-1个签名者。     

Ideal secret sharing schemes with multiple secrets

We consider secret sharing schemes which, through an initial issuing of shares to a group of participants, permit a number of different secrets to be protected. Each secret is associated with a (potentially different) access structure and a particular secret can be reconstructed by any group of participants from its associated access structure without the need for further broadcast information. We consider ideal secret sharing schemes in this more general environment. In particular, we classify the collections of access structures that can be combined in such an ideal secret sharing scheme and we provide a general method of construction for such schemes. We also explore the extent to which the results that connect ideal secret sharing schemes to matroids can be appropriately generalized.The work of the second and third authors was supported by the Australian Research Council.     

On the size of shares for secret sharing schemes

A secret sharing scheme permits a secret to be shared among participants in such a way that only qualified subsets of participants can recover the secret, but any nonqualified subset has absolutely no information on the secret. The set of all qualified subsets defines the access structure to the secret. Sharing schemes are useful in the management of cryptographic keys and in multiparty secure protocols.We analyze the relationships among the entropies of the sample spaces from which the shares and the secret are chosen. We show that there are access structures with four participants for which any secret sharing scheme must give to a participant a share at least 50% greater than the secret size. This is the first proof that there exist access structures for which the best achievable information rate (i.e., the ratio between the size of the secret and that of the largest share) is bounded away from 1. The bound is the best possible, as we construct a secret sharing scheme for the above access structures that meets the bound with equality.This work was partially supported by Algoritmi, Modelli di Calcolo e Sistemi Informativi of M.U.R.S.T. and by Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo of C.N.R. under Grant Number 91.00939.PF69.     

An Advanced Threshold Secret Sharing Scheme for Identifying Cheaters

1　Introduction(k ,n) thresholdschemesare proposedbyBlakley[1 ] andShamir[2 ] respectively .Assoonastheywereproposed ,theywerepaidattentiontobe causeoftheirimportantusesinmanyaspectssuchaskeymanagementinsecrecycommunication ,securitycalculation ,datasecurity ,securitymanagementoffinancenet,etc .[3～ 1 0 ] A (k,n) thresholdsecrecysharingschemeisasfollows:Dividingagivensecretsintonsharessuchthat( 1 )knowingkormoresharesonecanobtains;and( 2 )knowingk- 1orfewsharesonecannotde termines.LetP ={P…     

一个建立在整数环上的秘密共享方案

自A.Shamir和G.R.Blakley于1979年各自独立地提出“秘密共享”的思想及方法以后,现已出现了多种秘密共享方案。这些方案可适应不同的环境要求,然而,这些方案都是在域上建立的,当所面临问题的背景结构不构成域时会遇到麻烦。本文提出了一种新的秘密共享方案,该方案直接在整数环Z上实现,不需要对环Z作任何扩张,因而具有较高的有效性。其安全性基于Hash函数的安全性和大整数分解的难解性。     

On Matroid Characterization of Ideal Secret Sharing Schemes

A characterization of ideal secret sharing schemes with an arbitrary number of keys is derived in terms of balanced maximum-order correlation immune functions. In particular, it is proved that a matroid is an associated matroid for a binary ideal secret sharing scheme if and only if it is representable over the binary field. Access structure characterization of connected binary ideal schemes is established and a general method for their construction is pointed out. Received 16 April 1993 and revised 10 October 1996     

The Size of a Share Must Be Large

A secret sharing scheme permits a secret to be shared among participants of an n-element group in such a way that only qualified subsets of participants can recover the secret. If any nonqualified subset has absolutely no information on the secret, then the scheme is called perfect. The share in a scheme is the information that a participant must remember. In [3] it was proved that for a certain access structure any perfect secret sharing scheme must give some participant a share which is at least 50\percent larger than the secret size. We prove that for each n there exists an access structure on n participants so that any perfect sharing scheme must give some participant a share which is at least about times the secret size.^1 We also show that the best possible result achievable by the information-theoretic method used here is n times the secret size. ^1 All logarithms in this paper are of base 2. Received 24 November 1993 and revised 15 September 1995     

基于线性码的可验证秘密分享方案

论文基于线性码提出了一个非交互的可验证秘密分享方案,利用线性码的一致校验矩阵来验证每一个秘密分享者从秘密分配者Dealer处所获得子秘密的合法性,各子秘密拥有者独立验证,无须合作。