关于不可表示的多部秘密共享拟阵

一直以来,理想的存取结构具有的特性是秘密共享领域中主要的开放性问题之一,并且该问题与拟阵论有着密切的联系.由于每个拟阵都是多部的且有一个对应的离散多拟阵,通过对离散多拟阵的秩函数进行研究,给出并证明了一个新的多部拟阵为不可表示的多部拟阵的必要条件,并且将这一结论分别应用于m部拟阵(m≤2)和Vamos拟阵.此结论对于解决哪些拟阵是可表示的、哪些是不可表示的(因为与可表示的拟阵相关联的存取结构均为理想的存取结构)这一开放性问题将是一个新的贡献.     

异或视觉密码的理想存取结构研究

该文给出异或视觉密码的理想存取结构的定义,分析了其特征,研究了理想存取结构的共享份构造方法。在此基础上,提出将通用存取结构划分为若干个理想存取结构的算法,设计了通用存取结构的秘密分享与恢复流程。与现有的方案相比,该方案实现了秘密图像的完全恢复,且明显地减小了共享份的规模。     

理想的多密门限体制的拟阵结构

门限体制是秘密共享体制中最基本的一类,其特点是简洁而实用．本文讨论了门限体制的拟阵结构,得到理想的多密门限体制存在的条件．     

理想同态密钥共享体制的判别算法

对于m阶循环群G和给定的存取结构 A,利用适合A 的拟阵在环Z_m上的良好表示,给出了 A 为G-理想同态的判别算法.     

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.     

含至多四个参与者的量子秘密共享方案的最优信息率

信息率是衡量量子秘密共享方案性能的一个重要指标.在本文中,我们利用超图的相关理论刻画了量子存取结构.然后,利用超图和量子存取结构间的关系给出了参与者人数至多为4的所有13个量子存取结构,并基于量子信息论研究了其最优信息率及所对应的完善的量子秘密共享方案.对其中的5种存取结构的最优信息率的准确值进行了计算,并讨论了达到此信息率的方案的具体构造;对余下的8种存取结构的最优信息率的上界进行了计算.     

基于网络流上的秘密共享体制

给定一个通道结构,使它的极小通道结构对应于一个网络的极小割集族,那么存在一个实现它的理想秘密共享体制。而每一个密钥的子密钥正好构成该网络的一个流,反之亦然。给出的实现这些体制的方法极其有效。     

基于ECO的可公开验证的多秘密共享方案

基于椭圆曲线密码体制，提出了一个新的可公开验证的多秘密共享方案。该方案中，参与者和分发者可同时产生各参与者的秘密份额，可同时防止分发者和参与者进行欺骗。在秘密恢复过程中，任何个体都能验证参与者是否拥有有效的子秘密，秘密恢复者可验证参与者是否提供了正确的秘密份额。每个参与者只需要维护一个秘密份额，就可以实现对多个秘密的共享。方案的安全性是基于椭圆曲线密码体制以及（t，n）门限秘密共享体制的安全性。     

基于压缩算法的存取式多秘密视觉密码

依据多幅秘密图像的像素组合与基矩阵之间的映射关系,该文分析了目前存取式多秘密视觉密码存在的冗余基矩阵问题,提出了一种减小基矩阵规模的压缩算法.该算法以一列像素为处理单元,且满足秘密图像的整体对比性.在此基础上,设计了新的存取式多秘密视觉密码的秘密分享与恢复流程.与现有的方案相比,该方案能够有效减小共享份的尺寸,且对于简单图像的压缩效果更加明显.     

双负材料对多层介质的传输特性影响研究

基于传输线等效方法给出了包含双负、单负和双正材料的任意多层结构的传输系数和反射系数计算公式;研究了双负材料对实心、双层和A夹层等天线罩壁形式的传输特性的影响规律,并分析了单负材料的传输特性和双负材料的透镜效应.结果表明:双正与双负混合双层板和A夹层板在参数选择恰当时可达到(准)理想匹配状态,双负材料电磁参数的虚部为正时具有透波增强特性.     

Multipartite Secret Sharing by Bivariate Interpolation

Given a set of participants that is partitioned into distinct compartments, a multipartite access structure is an access structure that does not distinguish between participants belonging to the same compartment. We examine here three types of such access structures: two that were studied before, compartmented access structures and hierarchical threshold access structures, and a new type of compartmented access structures that we present herein. We design ideal perfect secret sharing schemes for these types of access structures that are based on bivariate interpolation. The secret sharing schemes for the two types of compartmented access structures are based on bivariate Lagrange interpolation with data on parallel lines. The secret sharing scheme for the hierarchical threshold access structures is based on bivariate Lagrange interpolation with data on lines in general position. The main novelty of this paper is the introduction of bivariate Lagrange interpolation and its potential power in designing schemes for multipartite settings, as different compartments may be associated with different lines or curves in the plane. In particular, we show that the introduction of a second dimension may create the same hierarchical effect as polynomial derivatives and Birkhoff interpolation were shown to do in Tassa (J. Cryptol. 20:237–264, 2007). A preliminary version of this paper appeared in The Proceedings of ICALP 2006.     

Ideal Multipartite Secret Sharing Schemes

Multipartite secret sharing schemes are those having a multipartite access structure, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. In this work, the characterization of ideal multipartite access structures is studied with all generality. Our results are based on the well-known connections between ideal secret sharing schemes and matroids and on the introduction of a new combinatorial tool in secret sharing, integer polymatroids .     

Strongly ideal secret sharing schemes

We define strongly ideal secret sharing schemes to be ideal secret sharing schemes in which certain natural requirements are placed on the decoder. We prove an information-theoretic characterization of perfect schemes, and use it to determine which access structures can be encoded by strongly ideal schemes. We also discuss a hierarchy of secret sharing schemes that are more powerful than strongly ideal schemes.     

Multipartite Secret Sharing Based on CRT

Secure communication has become more and more important for system security. Since avoiding the use of encryption one by one can introduce less computation complexity, secret sharing scheme (SSS) has been used to design many security protocols. In SSSs, several authors have studied multipartite access structures, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. Access structures realized by threshold secret sharing are the simplest multipartite access structures, i.e., unipartite access structures. Since Asmuth–Bloom scheme based on Chinese remainder theorem (CRT) was presented for threshold secret sharing, recently, threshold cryptography based on Asmuth–Bloom secret sharing were firstly proposed by Kaya et al. In this paper, we extend Asmuth–Bloom and Kaya schemes to bipartite access structures and further investigate how SSSs realizing multipartite access structures can be conducted with the CRT. Actually, every access structure is multipartite and, hence, the results in this paper can be seen as a new construction of general SSS based on the CRT. Asmuth–Bloom and Kaya schemes become the special cases of our scheme.     

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     

具有传递性质的接入结构上的秘密分享方案的构造

引入了具有传递性质的接入结构的概念,并给出一种构造具有这类接入结构的秘密分享方案的通用方法,该方法简捷易行.对要分享的一个秘密,不管一个参与者属于多少个最小合格子集,他只需保存一个秘密份额.而且用于分享多个秘密时,不需要增加分享者额外的信息保存量.因而优于已有的其他许多方法.文中还给出了实例以说明如何具体地构造具有这类接入结构的秘密分享方案.     

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 classification of ideal secret sharing schemes

In a secret sharing scheme a dealer has a secret key. There is a finite set P of participants and a set of subsets of P. A secret sharing scheme with as the access structure is a method which the dealer can use to distribute shares to each participant so that a subset of participants can determine the key if and only if that subset is in . The share of a participant is the information sent by the dealer in private to the participant. A secret sharing scheme is ideal if any subset of participants who can use their shares to determine any information about the key can in fact actually determine the key, and if the set of possible shares is the same as the set of possible keys. In this paper we show a relationship between ideal secret sharing schemes and matroids.This work was performed at the Sandia National Laboratories and was supported by the U.S. Department of Energy under Contract No. DE-AC04-76DP00789.     

Secret sharing schemes from three classes of linear codes

Secret sharing has been a subject of study for over 20 years, and has had a number of real-world applications. There are several approaches to the construction of secret sharing schemes. One of them is based on coding theory. In principle, every linear code can be used to construct secret sharing schemes. But determining the access structure is very hard as this requires the complete characterization of the minimal codewords of the underlying linear code, which is a difficult problem in general. In this paper, a sufficient condition for all nonzero codewords of a linear code to be minimal is derived from exponential sums. Some linear codes whose covering structure can be determined are constructed, and then used to construct secret sharing schemes with nice access structures.