2 Email: lincy@iim.nctu.edu.tw; 4 Email: jjhwang@cc.nctu.edu.tw
ABSTRACT
The authors propose **a** novel **generalized** **secret** **sharing** **scheme** that realizes an **ordered** **access** structure, in which the participants of **a** qualified subset can reconstruct the shared **secret** only if they follow the sequence of share/

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Hsinchu, Taiwan 300, R.O.C.
E-mail: ssp@csie.nctu.edu.tw
**A** perfect **secret** **sharing** **scheme** allows **a** **secret** K to be shared among **a** set of partici- pants in such **a** way that only qualified subsets of participants can recover the **secret**, and unqualified subsets of participants obtain no information regarding the **secret**. In this paper, we propose **a** construction of perfect **secret** **sharing** schemes with uniform, **generalized** ac- cess **structures** of rank 3. Compared with other constructions, our construction has some improved lower bounds on the information rate. In addition, we also generalize the con- struction to perfect **secret** **sharing** schemes with uniform, **generalized** **access** **structures** of constant rank.

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The experimental results showed that the proposed **scheme** is fea- sible and that it also can achieve both the high visual quality of the shadow images and high embedding capacity.
It would be worthwhile to conduct research to determine how to construct an efﬁcient **secret** **sharing** **scheme** for every given ac- cess structure. However, the problem of setting up **secret** image **sharing** schemes with **generalized** **access** **structures** has been lar- gely ignored by researchers in this area. We hope that some inno- vative and ingenious approaches will be found by investigating and studying this problem.

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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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一、 、 、 、簡介 簡介 簡介 簡介
隨著網路的蓬勃發展，人們愈來愈依賴網路 來傳播資訊，但在傳遞機密資料的過程中，機密 資料若被惡意的攻擊者所擷取，則會導致企業嚴 重的損失或是國家安全遭受威脅。因此，資料傳 輸的安全性也愈來愈受重視。為了保護機密資料 洩漏的問題，機密資料的擁有者常事先將資料進 行加密，再傳送之。之後，即使傳送中的資料被 竊取，仍無法得知機密資料的任何相關資訊。在 1979 年， Blakley [2] 和 Shamir [7] 兩學者分別 以 不 同 的 方 法 提 出 秘 密 分 享 機 制 ( **Secret** **sharing** **scheme** )，使得機密資料能分散地保管。

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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**

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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]

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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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0287@sun.epa.gov.tw, gbhorng@cs.nchu.edu.tw
Received 15 October 2007; Revised 1 December2007; Accepted 8 January 2008
Abstract. With the progress of the mobile communication technology and the popularity of the handheld de- vices, mobile commerce is of great importance today. We can use these devices to conduct business, such as to purchase books, and stocks, and digital goods (videos, audios, codes), and to play games, receive email, and even **access** various network resources. When the requested services need to be verified, the authentica- tion of users and the non-repudiation of transactions become very important. Completing these tasks in wire- less environments is **a** challenge for mobile devices that have limited computational capabilities. In this paper, we propose **a** server-aided signature **scheme** based on **secret** **sharing** for mobile commerce. Through one-time password authentication and **secret** **sharing** technology, we generate the cooperative signature of the server and the handheld device to satisfy the issues of security, non-repudiation, simplicity, validity, and mobility.

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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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In the paper [Ift06], the compartmented **access** structure was studied where the users are as- signed to diﬀerent groups and share the **secret** in two levels, the ﬁrst level is global level and the second, compartment level. The **secret** has been separated into **a** global share and **a** set of com- parment shares. There have two shares for each user which are the global **secret** shares and the compartment shares. The **secret** can only be reconstructed when the number of qualiﬁed users greater than or equal to the threshold of the global level and also the compartment level. Here the **secret** **sharing** appeared twice and we can call it as two-level SSS for applying the compartmented **access** structure which considers **a** more complicated **access** structure.

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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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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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Abstract - **A** copyright protection **scheme** for gray- level images based on image **secret** **sharing** and wavelet transformation is proposed in this paper.
The **scheme** contains **a** **secret** image generation phase and **a** watermark retrieval phase. In the generation phase, the proposed **scheme** extracts the features from **a** host image using the discrete wavelet transformation (DWT), and then employs the features and the watermark, **a** visually recognizable pattern, to generate the **secret** image using the image **secret** **sharing** (ISS). In the retrieval phase, the watermark is retrieved by combining the **secret** image and the features obtained from the suspect image. The retrieved watermark is then compared with the original watermark for copyright verification. The experiment shows that the proposed **scheme** can withstand 5 kinds of common image processing operations, including JPEG compression, blurring, sharpening, scaling, and cropping.

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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]

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摘要: Noar and Shamir presented the concept of visual cryptography. Many researches following it go down the same track: to expand the **secret** pixels to blocks. As **a** result, the size of the **secret** image becomes larger, and the quality of the expanded **secret** image becomes worse. In order to prevent the pixels from expanding, Yang has proposed his probability-based visual **secret** **sharing** **scheme**, where the concept of probability is employed to pick out pixels from the black or white sets. In this paper, we shall propose **a** new **scheme** that is **a** modified version of Yang?s **scheme**. Our experimental results show that we can

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日期: 2009-11
上傳時間: 2009-12-17T06:57:24Z 出版者: Asia University
摘要: In this paper, we propose **a** novel (2,2) verifiable **secret** **sharing** (VSS) **scheme**, which not only protects **a** **secret** image but also allows users to verify the restored **secret** image in the revealing and verifying phase, for all binary, grayscale and color images. Error diffusion and image

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Based on the commutative property of encryption, Saied Hosseini Khayat [7]
considered the following situation. Suppose that Alice wants to transfer **a** **secret** to Bob securely such that bob cannot decrypt the **secret** unless **a** group of trustees agree.
Though all involved parties can be trusted to follow **a** prescribed protocol, the com- munication channels are insecure. Furthermore, the **secret** must be protected not to be revealed to the trustees, nor to anyone but Bob. This situation often arises in many practical applications in commercial or military environments. At the first thought,

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LQ WKLV VWXG\ 7KH PHGLFDO LPDJH DQG WKH ZDWHUPDUN. VKRZQLQ)LJVDDQGDUHVSHFWLYHO\ZHUHXVHGLQWKH[r]

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A share spanning tree that connects the root node (the user that recreates the secret under consideration) to some other nodes such that its vertices hold all [r]

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