【作者】 贾星星；

【导师】 伍渝江； 王道顺；

【作者基本信息】 兰州大学 ， 应用数学， 2010， 博士

【摘要】 密钥管理是密码学的核心问题之一。线性阈值方案和可视分存方案是实现密钥管理的两种主要方法。本文对密钥管理中的相关问题进行了研究,主要工作如下：(1)在(k,n)秘密共享方案中,假设管理者不在线,若有t(t≥1)个新用户欲共享秘密,存在给新用户分发秘密的问题。本文采用由k个原有参与者联合担任管理者的角色,基于Lagrange插值多项式给出了由(k,n)方案到(k,n+t)方案的构造,该方案可完成对t个新用户的密钥分发,从n+t个分存中任选k个可重构秘密,少于k个得不到秘密的任何信息。(2)典型的公共可验证秘密共享方案需要管理者分发秘密,而在秘密分发过程中,可能存在管理者欺骗问题。为防止管理者欺骗,本文分别基于中国剩余定理和Lagrange多项式插值提出了不需要管理者,由参与者联合来生成共享密钥并分发相应的分存。通过使用ElGamal公钥密码对传输信息进行加密,应用零知识证明实现公共可验证性。(3)已有的多门限多秘密共享方案在传输信息时需要私密信道,用户不能自己选择分存,方案的可验证性不能检测管理者的欺骗。由于私有信道维护成本高,应用范围受限,本文提出了改进的算法。利用RSA公钥密码对传输信息进行加密,使得信息传输不需要私密信道,而是使用广泛可用的公开信道,每个参与者可以自己选择分存,使用指数运算给出验证信息,能够在管理者,参与者和组合者之间进行验证,改进了已有的方案。(4)在可视分存方案中存在像素膨胀的问题,概率可视分存方案利用白色像素在重构图像中黑色区域和白色区域出现的频率来区分黑和白,构造出没有像素膨胀的方案。本文基于图像缩小算法,提出了一种新的方法来降低可视分存方案中的像素膨胀。该方法的关键是如何在缩小过程中保持图像的形状和拓扑结构。采用人眼视觉系统和连通性分类,提出了两种图像缩小算法,以此来解决可视分存方案中的像素膨胀问题。更多还原

【Abstract】 Key management is one of the important cryptographic problems. Linear threshold scheme and visual cryptography scheme provide two different methods to solve problem of secret sharing. This dissertation devotes to the related problems of secret sharing and the main contributions are listed as follows:(1) While the dealer is not on-line in a (k, n)-threshold scheme, assume t(t≥1) new participants want to share the secret, there exists a problem to distribute shares to new participants. This paper adopts the (k,n+t) scheme transformed from old (k,n) scheme based on Lagrange interpolation in which k out of n old participants will function as the dealer to distribute new shares to t new participants. The scheme achieves the distribution of searet to t new participants. k out of n+t shares can reconstruct the secret and less than k shares will get no information about the secret.(2) Typical publicly verifiable secret sharing schemes rely on a dealer to distribute shares. However, there may be cheating action from the dealer which distributes an inconsistent secret to participants. In order to prevent cheating action from the dealer, two publicly verifiable secret sharing are presented based on the Chinese Remainder Theorem and Lagrange interpolation separately without the dealer substituded by n participants to jointly generate shared secret and to distribute their shares. ElGamal cryptosystem is used to encrypt transmitted information. The public verification is realized by utilizing zero-knowledge proof.(3) Existing multi-threshold multi-secret sharing schemes need private channel to transmit information. Their shares can not be selected by the dealer instead of participants. The verification can not preventing the cheating action from the dealer distributing an inconsistent secret to participants. Because of the high cost to protect private channel, an improved scheme is proposed in this paper. The information is encrypted using the RSA cryptosystem so that the public channels can be used to transmit data and participants can choose their shares by themselves in the proposed scheme. The new scheme is provided with verification which ulilizes exponentional opreations among the dealer, participants and secrets combiner.(4) Visual secret sharing scheme has disadvantage of pixel expansion since each original pixel is encoded into m subpixels per shadow image. Probabilistic visual secret sharing scheme uses the frequency of white pixels in the black and white areas of the recoverd image for interpreting black and white pixels by human visual system to present non-expansible scheme. We propose a new method to reduce the pixel expansion based on image shrinking algorithm. The main problem of the shrinking algorithm is how to preserve the shape and topology of the image during the shrinking. We propose two image shrinking algorithms to preserve shape and topology utilizing human visual system and connectivity classification.更多还原