### 数学代写|密码学作业代写Cryptography & Cryptanalysis代考| Remark and Introduction to Chapters

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Remark and Introduction to Chapters

In this book, we focus on VC algorithms satisfying strong security and no pixel expansion. The secret image is a grayscale image, whereas the shares are meaningless. Under these conditions, we review important efforts in improving the visual quality of the reconstructed secret image.
This book consists of seven chapters and the topics are arranged as follows.
In Chap. 2, after introducing the basic framework of visual cryptography, we review the three basic VC schemes, the classic deterministic VC, the probabilistic $\mathrm{VC}$ and the random grid VC. The security issue including the weak security and replacement attacks will also be briefly reviewed.

In Chap. 3, we introduce the problem of digital halftoning and important halftoning schemes, including simple bi-level quantization, ordered dithering, error diffusion and direct binary search. The quality measures for halftone image are also reviewed. Furthermore, we introduce the residual variance measure that will be used to evaluate the quality of recovered secret image in VC. The purpose of this chapter is to introduce to the reader a self-contained background for digital halftoning. For the VC algorithms we are focusing to, the secret images and/or cover images are grayscale images.

In Chap. 4, we introduce important algorithms in improving visual quality for the share images in extended VC, i.e., VC with meaningful shares. For binary cover image, we introduce three important algorithms, the basic extended VC, user-friendly random grid, and pixel swapping algorithm. For halftone shares, we introduce error diffusion based algorithms, and an improvement of this algorithm by including a hidden watermark, for authentication purpose.

In Chap. 5, we introduce the VC problem for grayscale secret image. Then the efforts in improving size-invariant VC are reviewed. For probabilistic VC, Wang’s size-invariant algorithm and our analysis-by-synthesis algorithms will be introduced. For random grid VC, we introduce the blue noise approach and our analysis-bysynthesis approach.

In Chap. 6, the vector VC approach will be comprehensively reviewed. For halftone secret image, we introduce Hou’s block encoding algorithm, Lee’s block

encoding algorithm, and our local blackness preserving algorithm. From Lee’s work, we formally define the vector VC scheme, which is then improved by a vector VC in the analysis-by-synthesis framework.

The Chap. 7 concludes this book with a short summary and discussion of future works.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Framework of Visual Secret Sharing

In a $(k, n)$-threshold visual cryptography (visual secret sharing) problem [13], a secret image $\mathbf{s}$ is shared between $n$ parties, called participants. Each participant obtains one share image. If less than $k$ shares are obtained, it is not possible to infer s from them. But. if $k$ or more than $k$ shares are obtained. then the secret $s$ can be revealed by stacking these shares, producing different average brightnesses for the white secret pixels and black secret pixels. For visual cryptography, the shares are usually printed on transparencies, and decoding corresponds to stacking the shares. The stacking result is called the target image.

The above threshold schemes can be extended to more general access structure [1]. There are two sets of participants, the forbidden set $\Gamma_{\text {Forb }}$, and the qualified set $\Gamma_{\text {Qual }}$. For a group of participants $P$, if $P \in \Gamma_{\text {Forb }}$, then it should be impossible to infer $s$ from the shares owned by these participants. If $P \in \Gamma_{\text {Qual }}$, then by stacking all the shares owned by these participants, the content of the secret should be recovered with sufficient contrast.
For example, for a $(3,3)$-threshold scheme, we have
\begin{aligned} &\Gamma_{\text {Qual }}={{1,2,3}}, \ &\Gamma_{\text {Forb }}={{1},{2},{3},{1,2},{1,3},{2,3}} \end{aligned}

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|A Note on Color Convention

For monochrome, there are two conventional ways of numerical representation of colors. For the first approach, the axis is lightness, where larger value corresponds to brighter color. Such a convention is widely used in digital image processing and digital display. For the second approach, the axis represents the amount of absorption

of light, where larger value corresponds to darker color. Such a convention is adopted in printing, visual cryptography and QR (Quick Response) code.

Visual cryptography, in its strict sense, needs to print its shares on transparencies. So, larger value should correspond to higher darkness. In this book, we adopt this convention. If an image is normalized to the range $[0,1]$, then ‘ 0 ‘ corresponds to the brightest color (White) and ‘ 1 ‘ (for normalized image) or ‘ $255^{\text {‘ }}$ (for 8 -bit representation) corresponds to the darkest color (Black). In summary, we use the following numerical representation of pixels:
\begin{aligned} &\square \leftrightarrow 1, \ &\square \leftrightarrow 0 . \end{aligned}Deterministic VC is the type of VC proposed by Naor and Shamir [13]. The prefix ‘deterministic’ is used here to distinguish it from the probabilistic schemes. Please note that deterministic doesn’t mean that every step of the algorithm is deterministic. For deterministic VC, each secret pixel is represented by a block on share images. Usually, the shape of the block is a square, in order to preserve the aspect ratio of objects in the secret image onto the target image.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Framework of Visual Secret Sharing

Γ哪一个 =1,2,3, Γ福布 =1,2,3,1,2,1,3,2,3

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|A Note on Color Convention

↔1, ↔0.确定性 VC 是 Naor 和 Shamir [13] 提出的 VC 类型。此处使用前缀“确定性”将其与概率方案区分开来。请注意，确定性并不意味着算法的每一步都是确定性的。对于确定性 VC，每个秘密像素都由共享图像上的一个块表示。通常，块的形状是正方形，以保持秘密图像中对象在目标图像上的纵横比。

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## MATLAB代写

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