Abstract
**The** concept of **visual** **secret** **sharing** (VSS) scheme was first proposed by Noar and Shamir in 1994. This is a technique to divide a **secret** image into several meaningless images, called shadows, such that certain qualified subsets of shadows can recover **the** **secret** image by “eyes”. **The** main characteristic of VSS **schemes** is that its decoding process can be perceived directly by **the** human **visual** system without **the** knowledge of cryptography and cryptographic computations. It possesses a special meaning and effect that “**the** **secret** codes are visible”.

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cryptography - **Visual** **secret** **sharing** - **Visual** **secret** **sharing** **schemes** Classification code:943 Mechanical and Miscellaneous Measuring Instruments - 942 Electric and Electronic Measuring Instruments - 941 Acoustical and Optical Measuring Instruments - 903 Information Science - 742.**2** Photographic Equipment - 944 Moisture, Pressure and Temperature, and Radiation Measuring Instruments - 723.5 Computer Applications - 722.**2** Computer Peripheral Equipment - 718 Telephone Systems and Related Technologies; Line Communications - 717 Optical Communication - 716 Telecommunication; Radar, Radio and Television - 723 Computer Software, Data Handling and

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Young-Chang Hou 於 2003 年根據 以往視覺密碼的研究，加上半色調技術及 分色原理 C、M、Y 顏料三原色，再對其 子影像做處理，提出灰階影像和彩色影像 的視覺密碼作法[8]，和傳統上的黑白影像 視覺密碼模型一樣，將機密影像上的每一 個像素擴展至分享影像上的 **2**×**2** 區塊，而 區塊中皆保持 **2** 個色點的狀態。它不但延 續了黑白視覺密碼直接利用視覺系統解 密，無須大量運算的優點，利用在他的方 法上，亦可應用於灰階及彩色影像的製作 上。

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DEFINITION **2**. A (k, n) NEVSS scheme can be shown as two collections C 0 and C 1 consisting of n λ
and n γ n × 1 matrices, respectively. When **sharing** a white (resp. black) pixel, **the** dealer first randomly chooses one column matrix in C 0 (resp. C 1 ), and then randomly selects one row of this column matrix to a relative shadow. **The** chosen matrix defines **the** gray level of one sub pixel in every one of **the** n shadows. A NEVSS Scheme is considered valid if **the** following conditions are met :

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to simplify **the** proposed scheme, we used a simple 3-LSB substitu- tion to embed shadow data into **the** cover image. Since **the** corre- sponding shadow data are real numbers, we divided these shadow data into two parts: **the** integral part and **the** decimal part, to deal with. Meanwhile, correcting **the** shadow data to 1 decimal place is able to effectively ensure that **the** **secret** image can be reconstructed losslessly. Of course, many variations based **on** LSB substitution also can be utilized to embed shadow data. It may be possible for these steganographic methods to improve **the** vi- sual quality of shadow images and enlarge **the** embedding capac- ity. However, it is beyond **the** scope of this paper to provide all of **the** details associated with this issue.

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Brickell and Stinson [5] studied a perfect secret sharing scheme for graph-based access structure F where the monotone-increasing access structure F contains the pairs of partic[r]

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名: A Scheme for Threshold **Multi**-**Secret** **Sharing** 作者: Chan, C. W.;Chang, C. C
關鍵詞: Access structure;Basis of access structure;**The** Chinese remainder theorem;Distinctness;Entropy;Idealness;**Multi**-**secret** **sharing** scheme;Perfectness;**The** Shamir (t, n)-threshold **secret** **sharing** scheme;(t, n)-threshold access structure;Threshold **multi**-**secret** **sharing** scheme

5. Conclusion
Taken no attention of how to calculate **the** minimum heating and cooling requirements for a heat- exchanger network, this study presents a **sharing** strategy for **the** design of **multi**-period heat-exchanger network where **the** required heat exchanger area are known. For a fixed match in different periods, **the** required heat-exchanger areas are not same. Within **the** overall objective of investment cost optimization of a **multi**-period industrial process, it is of great importance to improve **the** efficiency of recombining heat-exchanger network. This work gives a mathematical programming approach to automatically generate **the** best equipment **sharing** structure when there are significant changes in **the** environment of a plant. This paper shows **the** several criteria to discern **the** feasible heat-exchanger network to be recombined. Based **on** **the** extensive case studies performed so far, it can be observed that this proposed approach is especially effective for **multi**-period HEN design problems in which **the** process conditions vary significantly.

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Morillo et al. [19] considered **the** weighted threshold **secret**-**sharing** **schemes**. This is **the** case when every participant is given a weight depending **on** his or her position in an organization. A set of participants is in **the** access structure if and only if **the** sum of **the** weights of all participants in **the** set is not less than **the** given threshold. Morillo et al. characterized weighted threshold access structures based **on** graphs and studied their optimal information rate. Since these access struc- tures are more applicable in real-life situation, an in-depth investigation can have a signiﬁcant contribution to **the** applica- tion of **secret** **sharing**. We are motivated to construct better **secret**-**sharing** **schemes** for them and have a more detailed analysis of **the** average information rate of our **schemes**.

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Shiuh-Pyng Shieh ( ) received **the** M.S. and Ph.D.
degrees in electrical engineering from **the** University of Maryland, College Park, in 1986 and 1991, respectively. He is currently a professor with **the** Department of Computer Science and Informa- tion Engineering, National Chiao Tung University. From 1988 to 1991, he participated in **the** design and implementation of **the** B**2** Secure XENIX for IBM, Federal Sector Division, Gaithersburg, Maryland, USA. He is also **the** designer of **the** SNP (Secure Net- work Protocols). Since 1994, he has been a consultant for **the** Com- puter and Communications Laboratory, Industrial Technology Re- search Institute, Taiwan, in **the** area of network security and dis- tributed operating systems. He is also a consultant for **the** National Security Bureau, Taiwan.

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Abstract
Lin and Wu [IEE Proc. Comput. Digit. Tech. 146 (1999) 264] have proposed an eﬃcient ðt; nÞ threshold veriﬁable **multi**-**secret** **sharing** (VMSS) scheme based **on** **the** factorization problem and **the** discrete logarithm modulo a large composite problem. In their scheme, **the** dealer can arbitrarily give any set of multiple secrets to be shared, and only one reusable **secret** shadowis to be kept by every participant. **On** **the** other hand, they have claimed that their scheme can provide an eﬃcient solution to **the** cheating problems between **the** dealer and any participant. However, He and Wu [IEE Proc.

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current technology, **the** same set of shares can be embedded with many sets of **secret** messages after one of **the** shares is rotated at different degrees. However, **the** used share is rectangle so that only four kinds of angle variation exist when stacking shares. Thus, when intending to embed many sets of confidential messages by using these shares, **the** angle variation of rotating **the** shares is limited. This paper proposes an improved (**2**, **2**)-**visual** **secret** **sharing** scheme that adapts circular shares to deal with **the** limitation of rotating angles in traditional **visual**

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摘要: In this paper, we propose a novel scheme called a self-verifying **visual** **secret** **sharing** scheme, which can be applied to both grayscale and color images. This scheme uses two halftone images. **The** first, considered to be **the** host image, is created by directly applying a halftoning technique to **the** original **secret** image. **The** other, regarded as **the** logo, is generated from **the** host image by exploiting **the** interpolation and error diffusion techniques. Because **the** set of shadows and **the** reconstructed **secret** image are generated by simple Boolean operations, no computational complexity and no pixel

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reconstructed grayscale image quality than Wang et al.'s scheme without significantly increasing computational complexity, we apply the voting strategy and the least significant bits a[r]

Brick- ell and Stinson studied a perfect secret sharing scheme for a graph-based structure where the monotone-increasing access structure F contains the pairs of p[r]

Abstract A perfect **secret**-**sharing** scheme is a method of distributing a **secret** among a set of participants such that only qualified subsets of participants can recover **the** **secret** and **the** joint shares of **the** participants in any unqualified subset is statistically independent of **the** **secret**. **The** set of all qualified subsets is called **the** access structure of **the** scheme. In a graph-based access structure, each vertex of a graph G represents a participant and each edge of G represents a minimal qualified subset. **The** information ratio of a perfect **secret**-**sharing** scheme is defined as **the** ratio between **the** maximum length of **the** share given to a participant and **the** length of **the** **secret**. **The** average information ratio is **the** ratio between **the** average length of **the** shares given to **the** participants and **the** length of **the** **secret**. **The** infimum of **the** (average) information ratios of all possible perfect **secret**-**sharing** **schemes** realizing a given access structure is called **the** (average) information ratio of **the** access structure. Very few exact values of **the** (average) information ratio of infinite families of access structures are known. Csirmaz and Tardos have found **the** information ratio of all trees. Based **on** their method, we develop our approach to determining **the** exact values of **the** average information ratio of access structures based **on** trees.

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Abstract―Multiple **secret** images **sharing** scheme deals with **the** problem that how to secretly distribute several **secret** images among a group of participants at **the** same time, and reconstruct these **secret** images by collecting **the** shared images or **the** shares held in qualified subsets. Many studies explore **the** technique about **the** **secret** image **sharing**, but most of them only can be applied in special access structure or distributed single gray-level image. Shyu and Chen proposed multiple **secret** images **sharing** scheme for general access structure in 2008, but there may exists an unqualified subset which can reconstruct **the** **secret** images that should not be reconstructed by them in their scheme. Hence, Lee and Juan solved this insecure situation. In **the** mean time, they also reduced **the** time complexity, and **the** sizes of **the** public image are smaller than those for Shyu and Chen’s scheme. However, **the** computation of Shyu and Chen’s scheme and Lee and Juan’s scheme still can be reduced, and they both do not achieve **the** property of **multi**-use.

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We now present an attack **on** **the** Hwang–Chen **schemes**. Let **the** proxy sign- er P 1 be malicious throughout this section. We will show how P 1 can forge a **multi**-proxy **multi**-signature for a **secret** message M 0 while participating with **the** other proxy signers in signing another message M.

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weight 160, 64, 24, 8, 134, 12, and 3, respectively. Figure 4 is **the** image revealed by Figs. 3 共a兲 –3 共d兲 , and **the** revealed image is identical to Fig. 1.
Figure 5 compares **the** execution time in **the** weighted **secret** image–**sharing** phase using Thien and Lin’s 共t=256, n = w i 兲 threshold scheme 3 and our 共t=256, n=1兲 threshold scheme. **The** two **schemes** are both tested **on** an AMD Ath- lon 3500 ⫹ computer with 3GB of RAM. Notably, **the** ex- ecution time of our **sharing** algorithm is 7 ⫾3 ms for each of these 255 sets of weights, whereas **the** execution time increases linearly as **the** weight value increases in Thien and Lin’s direct and repeated application 共using multiple shadows to simulate weighted feature兲.

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Birkhoff interpolation. In their scheme, **the** **secret** is shared by a set of participants partitioned into several levels, and **the** **secret** data can be reconstructed by satisfying a sequence of threshold require- ments (e.g., it has at least t 0 participants from **the** highest level, as well as at least t 1 > t 0 participants from **the** two highest levels and so forth). There are many real-life examples of hierarchical thresh- old **schemes**. Consider **the** following example. According to a grad- uate school’s policy, a graduate who wants to apply for a postgraduate position must have letters of recommendation. As- sume that **the** graduate school’s policy concerning such recom- mendations is that **the** candidate must have at least two recommendations from professors and at least ﬁve recommenda- tions from a combination of professors and associate professors.

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