对一种多重密钥共享认证方案的分析和改进

在(t,n)密钥共享方案中,密钥管理者将一个秘密密钥分成n个子密钥,然后让n个成员中的每个成员保存一个子密钥.当需要恢复秘密密钥时,任意t个成员拿出他们持有的子密钥后,就可以按既定的公开算法恢复出所需密钥.而多重密钥共享使得密钥管理者可以安全且有效地共享多个密钥.Shi给出了一种高效率的多重密钥共享认证方案.在其方案中,不仅成员持有的子密钥能够重复使用,而且管理者分发的子密钥和成员提供的影子子密钥也都是可认证的.对Shi方案的安全性进行了分析:首先指出该方案的一个设计错误;然后给出两个攻击,以表明该方案中的子密钥和影子子密钥认证方法实际上都是不安全的.准确地说,利用所提出的攻击,不诚实的管理者可以将假的子密钥分发给成员;而不良成员可以很容易地伪造假的但能满足认证等式的影子子密钥,从而欺骗诚实成员,使得诚实成员误以为他们恢复出的密钥是正确的.另外,还给出了改进方法,以避免上述设计错误和攻击.     

无存储器冲突的并行快速排序算法*

本文在一个EREW PRAM(exclusive read exclusive write paralled random accessmachine)上提出一个并行快速排序算法，这个算法用k个处理器可将n个项目在平均O((n/k+logn)logn)时间内排序．所以平均来说算法的时间和处理器数量的乘积对任何k≤n/logn是 O(nlogn)．     

不需要可信任方的门限不可否认签名方案

在1992年澳大利亚密码会议上, Harn and Yang 第一次提出了(t,n)门限不可否认签名的概念.其中,只有成员个数不少于t的子集才能代表群体产生、确认和否认签名.随后,一些研究者又提出了几个方案,但这些方案都是不安全的.因此,到目前为止,怎样设计一个安全的(t,n)门限不可否认签名方案仍然是个公开问题.提出了一个基于离散对数密码系统的(t,n)门限不可否认签名方案.该方案不仅安全、高效,而且不需要可信任方.另外,方案还具有一个很好的性质,即成员的诚实性是可以验证的.这是由于在分发密钥时,采用了Schoenmakers在1999年美洲密码会议上提出的可公开验证秘密共享方案和两个用来提供正确性证据的离散对数恒等式协议.     

矩阵条件数及高斯算法平滑分析的进一步研究

算法的复杂度平滑分析是对许多算法在实际应用中很有效但其最坏情况复杂度却很糟这一矛盾给出的更合理的解释.高性能计算机被广泛用于求解大规模线性系统及大规模矩阵的分解.求解线性系统的最简单且容易实现的算法是高斯消元算法(高斯算法).用高斯算法求解n个方程n个变量的线性系统所需要的算术运算次数为O(n³).如果这些方程中的系数用m位表示,则最坏情况下需要机器位数mn位来运行高斯算法.这是因为在消元过程中可能产生异常大的中间项.但大量的数值实验表明,在实际应用中,需要如此高的精度是罕见的.异常大的矩阵条件数和增长因子是导致矩阵A病态,继而导致解的误差偏大的主要根源.设-A为任意矩阵,A是-A受到微小幅度的高斯随机扰动所得到的随机矩阵,方差σ²≤1.Sankar等人对矩阵A的条件数及增长因子进行平滑分析,证明了Pr[K(A)≥α]≤(3.64n(1+4√log(α)))/ασ.在此基础上证明了运行高斯算法输出具有m位精度的解所需机器位数的平滑复杂度为m+71og₂(n)+3log₂(1/σ)+log₂log₂n+7.在上述结果的证明过程中存在错误,将其纠正后得到以下结果:m+71og₂n+3log₂(1/σ)+4√2+log₂n+log₂(1/σ)+7.367.通过构造两个分别关于矩阵范数和随机变量乘积的不等式,将关于矩阵条件数的平滑分析结果简化到Pr[K(A)≥α]≤(6√2n²)/α·σ.部分地解决了Sankar等人提出的猜想:Pr[K(A)≥α]≤O(n/α·σ).并将运行高斯算法输出具有m位精度的解所需机器位数的平滑复杂度降低到m+81og₂n+3log₂(1/σ)+7.实验结果表明,所得到的平滑复杂度更好.     

无向图的边极大匹配并行算法及其应用*

在EREW PRAM(exclusive-read and exclusive-write parallel random access machine)并行计算模型上,对范围很广的一类无向图的边极大匹配问题,给出时间复杂性为O(logn),使用O((n+m)/logn)处理器的最佳、高速并行算法.     

任意多边形顶点凸、凹性判别的简捷算法

给出了一种确定任意多边形顶点凸、凹性的简捷算法.该算法只需要2n+4次乘法,5n+10次加、减法及2n+3次比较即可完成(n是多边形顶点的个数).同时,给出了任意简单多边形走向的充要条件.     

资源独立工作流可满足性的最小增量模式回溯

工作流可满足性是业务安全规划的基本问题, 正在面临高资源配比(资源数n显著大于步骤数k)造成的性能挑战. 在资源独立约束下, 其最高效求解途径是模式空间上的增量回溯法IPB. 为克服结点真实性验证的性能瓶颈, 它增量计算模式k指派(二部)图及其(左完备)匹配, 分别需要O(kn)和O(k²)时间. 利用父子模式的原子差异增量计算完全指派图, 只需O(n)时间, 特别是其实际性能, 将随模式块规模增长迅速提高. 但该图的O(kn)规模导致了同样的增量匹配时间. 进而引入完备k核心匹配概念, 证明其存在性等价于左完备匹配, 且其增量计算时间为O(k²). 由此, 建立了时间复杂度更低的最小增量模式回溯法. 在含互斥和两种全局值势约束而授权比例约为1/4的扩展公开实例集上进行实验, 结果表明: 当n/k=10(及n/k=100), 而k变化时, 该方法较IPB有平均超过2(及5)倍、最低1.5(及2.9)倍的性能优势; 当k=18(及k=36), 而n/k=2~4096(及n/k=2~2048)时, 该方法有平均超过2.6(及3.6)倍优势; 而较2021年Minizinc挑战赛的冠军求解器Google OR-Tools CP-SAT, 该方法最低有超过3倍优势.     

有Mate-Pairs的个体单体型MSR问题的参数化算法

个体单体型MSR(minimum SNP removal)问题是指如何利用个体的基因测序片断数据去掉最少的SNP(single-nucleotide polymorphisms)位点,以确定该个体单体型的计算问题.对此问题,Bafna等人提出了时间复杂度为O(2^kn²m)的算法,其中,m为DNA片断总数,n为SNP位点总数,k为片断中洞(片断中的空值位点)的个数.由于一个Mate-Pair片段中洞的个数可以达到100,因此,在片段数据中有Mate-Pair的情况下,Bafna的算法通常是不可行的.根据片段数据的特点提出了一个时间复杂度为O((n-1)(k₁-1)k₂2^2h+(k₁+1)^2h+nk₂+mk₁)的新算法,其中,k₁为一个片断覆盖的最大SNP位点数(不大于n),k₂为覆盖同一SNP位点的片段的最大数(通常不大于19),h为覆盖同一SNP位点且在该位点取空值的片断的最大数(不大于k₂).该算法的时间复杂度与片断中洞的个数的最大值k没有直接的关系,在有Mate-Pair片断数据的情况下仍然能够有效地进行计算,具有良好的可扩展性和较高的实用价值.     

分布式存储的并行串匹配算法的设计与分析

并行串匹配算法的研究大都集中在PRAM(parallel random access machine)模型上,其他更为实际的模型上的并行串匹配算法的研究相对要薄弱得多.该文采用将最优串行算法并行化的技术,利用模式串的周期性质,巧妙地将改进的KMP(Knuth-Morris-Pratt)算法并行化,提出了一个简便、高效且具有良好可扩放性的分布式串匹配算法,其计算复杂度为O(n/p+m),通信复杂度为O(ulogp相似文献   

背包类问题的并行O(25n/6)时间-空间-处理机折衷

将串行动态二表算法应用于并行三表算法的设计中,提出一种求解背包、精确的可满足性和集覆盖等背包类NP完全问题的并行三表六子表算法.基于EREW-PRAM模型,该算法可使用O(2^n/8)的处理机在O(2^7n/16)的时间和O(2^13n/48)的空间求解n维背包类问题,其时间-空间-处理机折衷为O(2^5n/6).与现有文献的性能对比分析表明,该算法极大地提高了并行求解背包类问题的时间-空间-处理机折衷性能.由于该算法能够破解更高维数的背包类公钥和数字水印系统,其结论在密钥分析领域具有一定的理论和实际意义.     

基于Hash函数的秘密共享方案安全研究

分析了当前几种秘密共享方案的不足，且给出了一个基于单向Hash函数的动态秘密共享方案的改进算法，它的特性如下：更新系统密钥时，无须更改每个子密钥；当某个子密钥泄密时，不对其它子密钥的安全构成威胁；系统为新共享者分配子密钥时，其它子密钥不受任何影响；子密钥可无限制地多次使用；具有很强的防欺诈和欺诈识别功能,该算法已在计算机上进行模拟，该文将给出一些实验数据，并对算法性能进行分析。     

A general (k, n) scalable secret image sharing scheme with the smooth scalability

A novel (k, n) scalable secret image sharing (SSIS) scheme was proposed to encrypt a secret image into n shadow images. One can gradually reconstruct a secret image by stacking k or more shadows, but he/she cannot conjecture any information from fewer than k shadows. The advantage of a (k, n)-SSIS scheme is that it provides the threshold property (i.e., k is a threshold value necessary to start in to reveal the secret) as well as the scalability (i.e., the information amount of a reconstructed secret is proportional to the number of shadows used in decryption). All previous (k, n)-SSIS schemes did not have the smooth scalability so that the information amount can be “smoothly” proportional to the number of shadows. In this paper, we consider the smooth scalability in (k, n)-SSIS scheme.     

A novel two-in-one image secret sharing scheme based on perfect black visual cryptography

Perfect black visual cryptography scheme (PBVCS) shares a binary secret image into n shadows. Stacking any \(k(k<n)\) shadows can reveal a vague secret image, and the black area of the secret image is recovered as perfect black. Two-in-one image secret sharing (TiOISS) scheme is a secret image sharing method with two decoding options. It can not only decode a vague secret image by stacking any k shadows, but also reveal the original grayscale secret image with k shadows by computation. Researchers proposed some TiOISS schemes, which are based on visual cryptography and polynomial-based image secret sharing (PISS). Since PISS reveals the secret image by Lagrange’s interpolation, these TiOISS schemes need complex computation. In this paper, we proposed a novel TiOISS scheme based on PBVCS using exclusive OR operation. Compared with literature TiOISS schemes, our scheme does not need complex computation in revealing process, and it can be used in real-time application. The grayscale secret image can be recovered quickly with a few Boolean operations.     

A secret sharing scheme based on (t, n) threshold and adversary structure

The existing secret sharing schemes cannot be applied directly if the threshold and the adversary structures are both needed to meet. A secret sharing scheme which can meet the requirements of both the (t, n) threshold and the adversary structure is proposed basing on the existing (t, n) threshold schemes and the knowledge of set theory, and the validity of the proposed scheme is proved perfectly. The scheme does not need to traverse the whole set of participants to get the qualified or unqualified subsets, and can distribute the shadows according to the requirements of threshold and adversary structure directly. The scheme can prevent the participants from cheating, and does not need the participants to provide their real shadows when the shared secret is reconstructed. The shadows do not need to be renewed when the shared secret is changed. The comparisons to the existing schemes show that, the proposed scheme is more efficient when the threshold and the adversary structure are both required.     

Sharing and hiding secret images with size constraint

This paper presents a method for sharing and hiding secret images. The method is modified from the (t,n) threshold scheme. (Comput.Graph. 26(5)(2002)765) The given secret image is shared and n shadow images are thus generated. Each shadow image is hidden in an ordinary image so as not to attract an attacker's attention. Any t of the n hidden shadows can be used to recover the secret image. The size of each stego image (in which a shadow image is hidden) is about 1/t of that of the secret image, avoiding the need for much storage space and transmission time (in the sense that the total size of t stego images is about the size of the secret image). Experimental results indicate that the qualities of both the recovered secret image and the stego images that contain the hidden shadows are acceptable. The photographers who work in enemy areas can use this system to transmit photographs.     

XOR-ed visual secret sharing scheme with robust and meaningful shadows based on QR codes

Quick response (QR) codes are becoming increasingly popular in various areas of life due to the advantages of the error correction capacity, the ability to be scanned quickly and the capacity to contain meaningful content. The distribution of dark and light modules of a QR code looks random, but the content of a code can be decoded by a standard QR reader. Thus, a QR code is often used in combination with visual secret sharing (VSS) to generate meaningful shadows. There may be some losses in the process of distribution and preservation of the shadows. To recover secret images with high quality, it is necessary to consider the scheme’s robustness. However, few studies examine robustness of VSS combined with QR codes. In this paper, we propose a robust (k, n)-threshold XOR-ed VSS (XVSS) scheme based on a QR code with the error correction ability. Compared with OR-ed VSS (OVSS), XVSS can recover the secret image losslessly, and the amount of computation needed is low. Since the standard QR encoder does not check if the padding codewords are correct during the encoding phase, we replace padding codewords by initial shadows shared from the secret image using XVSS to generate QR code shadows. As a result, the shadows can be decoded normally, and their error correction abilities are preserved. Once all the shadows have been collected, the secret image can be recovered losslessly. More importantly, if some conventional image attacks, including rotation, JPEG compression, Gaussian noise, salt-and-pepper noise, cropping, resizing, and even the addition of camera and screen noises are performed on the shadows, the secret image can still be recovered. The experimental results and comparisons demonstrate the effectiveness of our scheme.

     

Sharing a quantum secret without a trusted party

In a conventional quantum (k, n) threshold scheme, a trusted party shares a secret quantum state with n participants such that any k of those participants can cooperate to recover the original secret, while fewer than k participants obtain no information about the secret. In this paper we show how to construct a quantum (k, n) threshold scheme without the assistance of a trusted party, who generates and distributes shares among the participants. Instead, each participant chooses his private state and contributes the same to the determination of the final secret quantum state.     

Advanced image steganography based on exploiting modification direction and neutrosophic set

A new variant of image steganography based on exploiting modification directions (EMD) named advanced EMD (AEMD) is introduced. In this method the secret digits in mⁿ -ary notional systems are embedded into a group of n pixels of the cover image. To increase data hiding capacity, edge masking characteristics of human visual system is exploited to embed more bits at image edge pixels than non-edge pixels. To do this, a neutrosophic set edge detector, named as MNSED is also introduced to classify cover image into 2?×?2 non-overlapping edge and non-edge blocks without any overhead information. Hence the secret digits in two different bases are embedded into the edge and non-edge blocks. Experimental results show that the proposed method provides higher embedding capacity and better quality compared to the existing schemes, while its resistance to steganographic attack is still higher.

     

Efficient visual secret sharing scheme for color images

A k-out-of-n visual secret sharing scheme (VSSS) resolves the visual variant of the k-out-of-n secret sharing problem where only k or more out of n participants can reveal the secret by human visual system without any cryptographic computation. The best pixel expansion of the general k-out-of-n VSSS for c-colored images was c×m by Yang and Laih [New colored visual secret sharing schemes, Des Codes Cryptogr. 24 (2000) 325-335] where m is the pixel expansion of an existing binary k-out-of-n VSSS. Regarding the c-colored n-out-of-n scheme, the best pixel expansion is (c-1)2^n-1-c+2 and c(c-1)2^n-2-c when n is odd and even, respectively, by Blundo et al. [Improved schemes for visual cryptography, Des Codes Cryptogr. 24 (2001) 255-278]. In this paper, we propose a new c-colored k-out-of-n VSSS by using a pixel expansion of that is more efficient than ever.     

A high quality and small shadow size visual secret sharing scheme based on hybrid strategy for grayscale images

Many secret sharing schemes for digital images have been developed in recent decades. Traditional schemes typically must deal with the problem of computational complexity, and other visual secret sharing schemes come with a higher transmission cost and storage cost; that is, each shadow size is m times as big as the original secret image. The new (2,n) secret sharing scheme for grayscale images proposed in this paper is based a combination of acceptable image quality using block truncation coding (BTC), high compression ratio discrete wavelet transform (DWT) and good subjective performance of the vector quantization (VQ) technique. Experimental results confirm that our proposed scheme not only generates a high quality reconstructed original image but also generates small, random-like grayscale shadows.