## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|CS171

statistics-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography & Cryptanalysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写密码学Cryptography & Cryptanalysis代写方面经验极为丰富，各种代写密码学Cryptography & Cryptanalysis相关的作业也就用不着说。

• 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|Columnar Cipher

The columnar cipher is an intriguing type of transposition cipher. In this cipher, the text you want to encrypt is written in rows usually of a specific length and determined by some keyword. For example, if the keyword is falcon, which is six characters long, you would write out your messages in rows of six characters each. So, you would write out
At tack
thebea
chat su
nriseq
Notice the added $q$ at the end. That was added because the last row is only five characters long. In a regular columnar cipher, you pad the last row so that all rows are of equal length.

If you leave the blank spaces intact, this would be an irregular columnar cipher, and the order of columns would be based on the letters in the keyword as they appear in the alphabet. So, if the keyword is falcon, the order is 314265 as $f$ is the third lowest letter in the alphabet, $a$ is the lowest, $l$ is the fourth lowest, and so on. So, if we apply 314265 to encrypt the message, we first write out the letters down column 3 , then column 1 , then column 4 , then column 2 , then column 6 , and then column 5. So, the message.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Four-Square Cipher

As you can probably surmise, the four-square cipher takes the Playfair model and expands it to use four squares. This cipher was invented by Felix Marie Delastelle. Delastelle was a Frenchman who lived from 1840 until 1902 and invented several ciphers including the bifid, trifid, and four square (Aishwarya et al. 2014).

Delastelle contributions to cryptography during the 1800 s extend well beyond the four-square cipher. He also developed the bifid and trifid ciphers, which will be covered a bit later in this chapter. He finished work on a book on cryptography entitled ité Élémentaire de Cryptographie, just 11 months before he died in April 1902. His book was published 3 months after his death. What is most remarkable was that Delastelle was an amateur cryptographer with no formal training in math. Given the state of cryptography in the 1800s, this was possible, though uncommon. However, with modern cryptography, it is simply impossible to do any substantive work in cryptography without a strong mathematics background.

The four-square works by first generating four squares of $5 \times 5$ letters, often either the $\mathrm{Q}$ is omitted, or $\mathrm{I} / \mathrm{J}$ are combined in order to account for the 26 letters in the alphabet. Notice that in the matrices shown below, in some cases I have omitted the Q, in others combined I and $\mathrm{j}$. Also note that the letters may or may not be in alphabetical order. It should also be noted that the two upper case matrices are going to be ciphertext, the two lower case matrices are for plaintext. This should also explain why it is the two upper case matrices that are not in alphabetical order.

At tack
thebea
chat su
nriseq

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Four-Square Cipher

Delastelle 在 1800 年代对密码学的贡献远远超出了四方密码。他还开发了 bifid 和 trifid 密码，本章稍后将对此进行介绍。在他于 1902 年 4 月去世前 11 个月，他完成了一本名为 ité Élémentaire de Cryptographie 的密码学书籍的工作。他的书在他去世 3 个月后出版。最引人注目的是，Delastelle 是一名业余密码学家，没有接受过正规的数学训练。鉴于 1800 年代的密码学状态，这是可能的，尽管并不常见。但是，在现代密码学中，如果没有强大的数学背景，根本不可能在密码学方面做任何实质性的工作。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|CS709

statistics-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography & Cryptanalysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写密码学Cryptography & Cryptanalysis代写方面经验极为丰富，各种代写密码学Cryptography & Cryptanalysis相关的作业也就用不着说。

• 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|Polybius Cipher

The Polybius cipher (also known as the Polybius square) was invented by the Greek historian Polybius (c. 200-118 BCE). Obviously, his work used the Greek alphabet, but we will use it with English here. As shown in the following grid, in the Polybius cipher, each letter is represented by two numbers (Mollin 2000). Those two numbers being the $\mathrm{x}$ and $\mathrm{y}$ coordinates of that letter on the grid. For example, $A$ is $11, T$ is 44 , $C$ is 13 , and $K$ is 25 . Thus, to encrypt the word attack, you would use 114444111325 . You can see this in Fig. 1.1.

Despite the use of two numbers to represent a single letter, this is a substitution cipher and still maintains the letter and word frequencies found in the underlying language of the plaintext. If you used the standard Polybius square, which is a widely known cipher, it would be easily cracked, even without any frequency analysis. If you wanted to use a different encoding for letters in the square, that would require that the sending and receiving parties share the particular Polybius square in advance, so that they could send and read messages.

It is interesting to note that the historian Polybius actually established this cipher as a means of sending codes via torches. Messengers standing on hilltops could hold up torches to represent letters, and thus send messages. Establishing a series of such messengers on hilltops, each relaying the message to the next, allowed communications over a significant distance, much faster than any messenger on foot or horseback could travel.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Scytale Cipher

The Scytale cipher is one such ancient cypher. Often mispronounced (it actually rhymes with “Italy”), this cipher used a cylinder with a strip of parchment wrapped around it. If you had the correct diameter cylinder, then when the parchment was wrapped around it, the message could be read (Dooley 2018). You can see the concept shown in Fig. 1.3.

If you did not have the correct size of cylinder, however, or if you simply found the parchment and no cylinder, the message would appear to be a random string of letters. This method was first used by the Spartans and later throughout Greece. The earliest mention of Scytale was by the Greek poet Archilochus in the seventh century BC. However, the first mention of how it actually worked was by Plutarch in the first century BCE, in his work The Parallel Lives:
The dispatch-scroll is of the following character. When the ephors send out an admiral or a general, they make two round pieces of wood exactly alike in length and thickness, so that each corresponds to the other in its dimensions, and keep one themselves, while they give the other to their envoy. These pieces of wood they call “scytale.” Whenever, then, they wish to send some secret and important message, they make a scroll of parchment long and narrow, like a leather strap, and wind it round their “scytale,” leaving no vacant space thereon, but covering its surface all round with the parchment. After doing this, they write what they wish on the parchment, just as it lies wrapped about the “scytale;” and when they have written their message, they take the parchment off, and send it, without the piece of wood, to the commander. He, when he has received it, cannot other get any meaning of it-since the letters have no connection, but are disarranged-unless he takes his own “scytale” and winds the strip of parchment about it, so that, when its spiral course is restored perfectly, and that which follows is joined to that which precedes, he reads around the staff, and so discovers the continuity of the message. And the parchment, like the staff, is called “scytale,” as the thing measured bears the name of the measure. ${ }^{9}$

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Scytale Cipher

Scytale 密码就是这样一种古老的密码。经常发音错误（它实际上与“意大利”押韵），这个密码使用了一个圆柱体，周围有一条羊皮纸。如果您有正确直径的圆柱体，那么当将羊皮纸包裹在它周围时，可以读取消息（Dooley 2018）。您可以看到如图 1.3 所示的概念。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|CS127

statistics-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography & Cryptanalysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写密码学Cryptography & Cryptanalysis代写方面经验极为丰富，各种代写密码学Cryptography & Cryptanalysis相关的作业也就用不着说。

• 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|Affine Ciphers

Affine ciphers are any single-substitution alphabet ciphers (also called mono-alphabet substitution) in which each letter in the alphabet is mapped to some numeric value, permuted with some relatively simple mathematical function, and then converted back to a letter. For example, using the Caesar cipher, each letter is converted to a number, shifted by some amount, and then converted back to a letter.
The basic formula for any affine cipher is
$$\mathrm{ax}+\mathrm{b}(\bmod \mathrm{m})$$
$M$ is the size of the alphabet-so in English that would be 26. The $x$ represents the plaintext letter’s numeric equivalent, and the $b$ is the amount to shift. The letter $a$ is some multiple-in the case of the Caesar cipher, $a$ is 1 . So, the Caesar cipher would be
$$1 x+3(\bmod 26)$$
What has been presented thus far is rather simplified. To actually use an affine cipher, you need to pick the value a so that it is coprime with $\mathrm{m}$. We will explore coprime in more detail later in this book. However, for now simply understand that two numbers are coprime if they have no common factors. For example, the number 8 has the factors 2 and 4 . The number 9 has the factor 3 . Thus, 8 and 9 have no common factors are coprime. If you don’t select $a$ and $m$ that are coprime, it may not be possible to decrypt the message.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Homophonic Substitution

Over time, the flaws in single-substitution ciphers became more apparent. Homophonic substitution was one of the earlier attempts to make substitution ciphers more robust by masking the letter frequencies, as plaintexı letters were mapped to more than one ciphertext symbol, and usually the higher frequency plaintext letters were given more ciphertext equivalents. For example, $a$ might map to either $x$ or $y$. This had the effect of disrupting frequencies, making analysis more difficult. It was also possible to use invented symbols in the ciphertext and to have a variety of mappings. For example, $a$ maps to $x$, but $z$ maps to $¥$. The symbol $¥$ is one I simply created for this example.

There are variations of this cipher, and one of the most notable versions is called the nomenclator cipher, which used a codebook with a table of homophonic substitutions. Originally, the codebook used only the names of people, thus the term nomenclator. So, for example, Mr. Smith might be $X X$ and Mr. Jones would be $X Y Z$. Eventually, nomenclators were created that used a variety of words rather than just names. The codes could be random letters, such as those already described, or code words. Thus, Mr. Jones might be enciphered as poodle and Mr. Smith enciphered as catfish. Such codebooks with nomenclator substitutions where quite popular in espionage for a number of years. The advantage of a nomenclator is that it does not provide any frequencies to analyze. However, should the codebook become compromised, all messages encoded with it will also be compromised.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Affine Ciphers

$$a x+b(\bmod m)$$
$M$ 是字母的大小一一所以在英语中是 26。 $x$ 表示明文字母的等效数字，并且 $b$ 是要转移的数量。信 $a$ 是一些倍数-在 凯撒密码的情况下， $a$ 是 1 。所以，凯撒密码是
$$1 x+3(\bmod 26)$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|CISS3341

statistics-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography & Cryptanalysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写密码学Cryptography & Cryptanalysis代写方面经验极为丰富，各种代写密码学Cryptography & Cryptanalysis相关的作业也就用不着说。

• 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|Mathematical Notation of the Caesar Cipher

With the various ancient ciphers, we will be using, the math is trivial. However, it is a good idea for you to become accustomed to mathematical notation, at least with those algorithms where such notation is appropriate. It is common to use a capital letter $P$ to represent plaintext and a capital letter $C$ to represent ciphertext. We can also use a capital letter $K$ to represent the key. This gives us the following mathematical description of a Caesar cipher:
$$\mathrm{C} \equiv \mathrm{P}+\mathrm{K}(\bmod 26)$$
Here we see a symbol some readers may not be acquainted with, the $\equiv$. This is not a misprint of the $=$ sign, rather it is the symbol for congruence. Do not be overly concerned about the $\equiv 26$. We will explore modulus operations and congruence in detail in Chap. 4. For now, I just use the modulus operation to denote dividing by a given number (in this case, 26 , because there are 26 letters in the alphabet) and listing only the remainder. That is not a rigorous mathematical explanation, but it will suffice for now.
Decryption can also be represented via mathematical symbols:
$$\mathrm{P} \equiv \mathrm{C}-\mathrm{K}(\bmod 26)$$
The mathematical representation of Caesar’s method of shifting three to the right is
$$\mathrm{C} \equiv \mathrm{P}+3(\bmod 26)$$

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Atbash Cipher

Hebrew scribes copying the biblical book of Jeremiah used the Atbash substitution cipher. Applying the Atbash cipher is fairly simple: just reverse the order of the letters of the alphabet. This is, by modern standards, a very primitive cipher that is easy to break. For example, in English, $a$ becomes $z, b$ becomes $y, c$ becomes $x$, and so on. Of course, the Hebrews used the Hebrew alphabet, with aleph being the first letter and tav the last letter. However, I will use English examples to demonstrate the cipher:
Attack at dawn
becomes
Zggzxp zg wzdm
As you can see, the $A$ (the first letter in the alphabet) is switched with $Z$ (the last letter), and the $t$ is the 19th letter (or 7th from the end) and gets swapped with $g$, the 7th letter from the beginning. This process is continued until the entire message is enciphered.

To decrypt the message, you simply reverse the process so that $z$ becomes $a, b$ becomes $y$, and so on. This is obviously a simple cipher and is not used in modern times. However, like the Caesar cipher example, it illustrates the basic concept of cryptography – to perform some permutation on the plaintext to render it difficult to read by those who don’t have the key to “unscramble” the ciphertext. The Atbash cipher, like the Caesar cipher, is a single-substitution cipher (each letter in the plaintext has a direct, one-to-one relationship with each letter in the ciphertext). The same letter and word frequency issues that can be used to crack the Caesar cipher can be used to crack the Atbash cipher.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Mathematical Notation of the Caesar Cipher

$$\mathrm{C} \equiv \mathrm{P}+\mathrm{K}(\bmod 26)$$

$$\mathrm{P} \equiv \mathrm{C}-\mathrm{K}(\bmod 26)$$

$$\mathrm{C} \equiv \mathrm{P}+3(\bmod 26)$$

Attack at Dawn

Zggzxp zg wzdm

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|CS6260

statistics-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography & Cryptanalysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写密码学Cryptography & Cryptanalysis代写方面经验极为丰富，各种代写密码学Cryptography & Cryptanalysis相关的作业也就用不着说。

• 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|Digital Signatures

In this book, we will deal with digital signatures as well. A digital signature represents a cryptographic primitive that is fundamental in the process of authentication, authorization, and non-repudiation. The goal of a digital signature is to offer a way for an entity to map its identity with a piece of information. The process of signing implies the transforming of the message and a part known as secret information that is held by the entity into a tag known as the signature.
A general description is as follows:

• $\mathcal{M}$ represents the set of messages that have the possibility to be signed.
• $\mathcal{S}$ represents the set of elements known as signatures. The signatures can be binary strings with a fixed length.
• $\mathcal{S}{A}$ is defined as a transformation from the set of messages $\mathcal{M}$ to the set of signatures $\mathcal{S}$, known as a signing transformation for entity $A$ (Alice). The $\mathcal{S}{A}$ is stored as a secret by $A$ and is used to create signatures for the messages from $\mathcal{M}$.$V_{A}$ represents a transformation from the set $\mathcal{M} \times \mathcal{S}$ to the set ${$ true, false $} . \mathcal{M} \times \mathcal{S}$ consists of all pairs $(m, s)$ where $m \in \mathcal{M}$ and $s \in \mathcal{S}$, known as the Cartesian product of $\mathcal{M}$ and $\mathcal{S} . V_{A}$ is a transformation that can be used as a verification process for the signatures of $A$, is known as public, and is used by different entities in order to verify the signatures created by $A$.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Public-Key Cryptography

Public-key cryptography plays an important role in .NET and when we need to implement related algorithms. There are several important commercial libraries that implement public-key cryptography solutions for developers, such as [21-30].
To understand better how public-key cryptography works, let’s consider a of encryption transformations defined as $\left{E_{e}: e \in \mathcal{K}\right}$ and a set of matching decryption transformations defined as $\left{D_{d}: d \in \mathcal{K}\right}$, where $\mathcal{K}$ represents the key space. Take into consideration the following pair association of encryption/decryption transformations $\left(E_{e} D_{d}\right)$ and let’s suppose that each pair has the property of knowing $E_{e}$ that is computationally unrealizable, having a random ciphertext $c \in \mathcal{C}$ to manage to identify the message $m \in \mathcal{M}$ in such way that $E_{e}(m)=c$. The property defined involves that for any given $e$ it is unrealizable to determine the corresponding decryption key $d$.

Having the assumptions made above, let’s consider a two-party communication between Alice and Bob as illustrated in Figure 1-6.

• Bob will select a key pair $(e, d)$.
• Bob will send the encryption key $e$, known as the public key, to Alice over any channel and will keep the decryption key, $d$, known as the private key, secure and secret.
• Alice, afterwards, will send a message $m$ to Bob by applying the encryption transformation that is computed and determined by Bob’s public key in order to get $c=E_{e}(m)$. Bob will decrypt the ciphertext $c$ by using the inverse transformation $D_{d}$ which is determined uniquely by $d$.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Permutations

$$p(1)=2, p(2)=5, p(3)=4, p(4)=2, p(5)=1$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|CIS556

statistics-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography & Cryptanalysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写密码学Cryptography & Cryptanalysis代写方面经验极为丰富，各种代写密码学Cryptography & Cryptanalysis相关的作业也就用不着说。

• 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|Trapdoor One-Way Functions

Definition 1.16. A trapdoor one-way function is defined as a one-way function $f: A \rightarrow B$ with the additional property that by having extra information (known as trapdoor information) it will become feasible to find and identify any given $b \in \operatorname{Im}(f)$, with an $a \in A$ in such way that $f(a)=b$.

In Example 1.15, we show the concept of a trapdoor one-way function. With extra information about the factors of $n=2957524163$ it will become much easier to invert the function. The factors of 2957524163 are large enough that finding them by hand computation would be difficult. With the help of any computer software we can find the factors quite quickly. If, for example, we have very large distinct prime numbers (each number having around 200 decimal digits), $p$ and $q$, with today’s technologies, it’s quite difficult even with the most powerful computers to find $p$ and $q$ from $n$. This is the wellknown problem entitled as integer factorization problem, which for quantum computers will not represent an issue.

One-way and trapdoor one-way functions represent the basic foundation for publickey cryptography. These concepts are very important and they will become much clearer later when their application to cryptographic techniques are implemented and discussed. It is quite important to keep these abstract concepts from this section in mind as the concrete methods and the main foundation for the cryptography algorithms that will be implemented later within this book.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Permutations

Permutations represent functions that are in cryptographic constructs.
Definition 1.17. Consider $S$ to be a finite set formed of elements. A permutation $p$ on $S$ represents a bijection as defined in Definition 1.8. The bijection is represented from $S$ to itself as $p: S \rightarrow S$.

Example 1.18. This example represents a permutation example. Let’s consider the following permutation: $S={1,2,3,4,5}$. The permutation $p: S \rightarrow S$ is defined as follows:
$$p(1)=2, p(2)=5, p(3)=4, p(4)=2, p(5)=1$$
A permutation can be described in different ways. It can be written as above or as an array as
$$p=\left(\begin{array}{lllll} 1 & 2 & 3 & 4 & 5 \ 3 & 5 & 4 & 2 & 1 \end{array}\right)$$
in which the top row of the array is represented by the domain and the bottom row is represented by the image under $p$ as mapping.
As the permutations are bijections, they have inverses. If the permutation is written as an away (second form), its inverse will be very easily to find by interchanging the rows in the array and reordering the elements from the new top row and the bottom row. In this case, the inverse of $p$ is defined as follows:
$$p^{-1}=\left(\begin{array}{ccccc} 1 & 2 & 3 & 4 & 5 \ 5 & 4 & 1 & 3 & 2 \end{array}\right)$$
Example 1.19. This example represents a permutation example. Let’s consider $A$ to be the set of integers ${0,1,2, \ldots, p \cdot q-1}$ where $p$ and $q$ represent two distinct large primes. We need to suppose also that neither $p-1$ nor $q-1$ can be divisible by 3 . The function $p(a)=r_{a}$, in which $r_{a}$ represents the remainder when $a^{3}$ is divided by $p q$ can be demonstrated and shown as being the inverse perumutation. The inverse permutation is computationally infeasible by computers nowadays, unless $p$ and $q$ are known.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Permutations

$$p(1)=2, p(2)=5, p(3)=4, p(4)=2, p(5)=1$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|CS171

statistics-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography & Cryptanalysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写密码学Cryptography & Cryptanalysis代写方面经验极为丰富，各种代写密码学Cryptography & Cryptanalysis相关的作业也就用不着说。

• 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|(One-to-One) Functions

Definition 1.6. We can say that a function or transformation is $1-1$ (one-to-one) if each of the elements found within the codomain $B$ are represented as the image of at most one element in the domain $A$.

Definition 1.7. We can say that a function or transformation is onto if each of the elements found within the codomain $B$ represents the image of at least one element that can be found in the domain. At the same time, a function $f: A \rightarrow B$ is known as being onto if $\operatorname{Im}(f)=B$.
Definition 1.8. If function $f: A \rightarrow B$ is to be considered $1-1$ and $\operatorname{Im}(f)=B$, and then the function $f$ is called bijection.
Conclusion 1.9. If $f: A \rightarrow B$ is considered $1-1$, then $f: A \rightarrow \operatorname{Im}(f)$ represents the bijection. In special cases, if $f: A \rightarrow B$ is represented as $1-1$, and $A$ and $B$ are represented as finite sets with the same size, then $f$ represents a bijection.
Based on the scheme and its representation, if $f$ represents a bijection, then each element from $B$ has exactly one line that is incidental with it. The function shown and described in Examples $1.3$ and $1.4$ does not represent bijections. As you can see in Example 1.3, element 3 doesn’t have the image of any other element that can be found within the domain. In Example 1.4, each element from the codomain is identified with two preimages.
Definition 1.10. If $f$ is a bijection from $A$ to $B$, then it is a quite simple matter to define a bijection $g$ from $B$ to $A$ as follows: for each $b \in B$ we will define $g(b)=a$ where $a \in A$ and $f(a)=b$. The function $g$ is obtained from $f$ and it is called an inverse function of $f$ and is denoted as $g=f^{-1}$.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|One-Way Functions

In cryptography, there are a certain types of functions that play an important role. Due to the rigor, a definition for one-way function is given as follows.
Definition 1.12. Let’s consider function $f$ from set $A$ to set $B$ that is called a oneway function if $f(a)$ proves to be simple and easy to be computed for all $a \in A$ but for “essentially all” elements $b \in \operatorname{Im}(f)$ it is computationally infeasible to manage to find any $a \in A$ in such way that $f(a)=b$.
Note 1.13. This note represents some additional notes and clarifications of the terms used in Definition1.12.

1. For the terms easy and computationally infeasible a rigorous definition is necessary but it will distract the attention from the general idea that is being agreed. For the goal of this chapter, the simple and intuitive meaning is sufficient.
2. The phrase “essentially all” refers to the idea that there are a couple of values $b \in B$ for which it is easy to find an $a \in A$ in such way that $b=f(a)$. As an example, one may compute $b=f(a)$ for a small number of $a$ values and then for these, the inverse is known by a table look-up. A different way to describe this property of a one-way function is as follows: for any random $b \in \operatorname{Im}(f)$, it is computationally feasible to have and find any $a \in A$ in such way that $f(a)=b$.

The following examples show the concept behind a one-way function.
Example 1.14. (one-way function) Consider $A={1,2,3, \ldots, 16}$ and let’s define $f(a)=r_{a}$ for all the elements $a \in A$ where $r_{a}$ represents the remainder when $3^{x}$ will be divided with 17 .

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|One-Way Functions

1. 对于简单且在计算上不可行的术语，需要严格定义，但这会分散人们对正在商定的一般概念的注意力。对于 本章的目标，简单直观的含义就足够了。
2. 短语“基本上全部”指的是有几个值的想法 $b \in B$ 很容易找到 $a \in A$ 以这样的方式 $b=f(a)$. 例如，可以计算 $b=f(a)$ 对于少数 $a$ 值，然后对于这些值，通过查表可以知道倒数。描述单向函数的这一性质的另一种方法 如下: 对于任何随机 $b \in \operatorname{Im}(f)$ ，在计算上是可行的 $a \in A$ 以这样的方式 $f(a)=b$.
以下示例显示了单向函数背后的概念。
示例 1.14。(单向函数) 考虑 $A=1,2,3, \ldots, 16$ 让我们定义 $f(a)=r_{a}$ 对于所有元素 $a \in A$ 在哪里 $r_{a}$ 表示余 数时 $3^{x}$ 将除以 17 。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Improving Visual Quality for Share Images

statistics-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography & Cryptanalysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写密码学Cryptography & Cryptanalysis代写方面经验极为丰富，各种代写密码学Cryptography & Cryptanalysis相关的作业也就用不着说。

• 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|Basic Extended VC

Ordinary VC produces meaningless and noise-like shares, which makes it difficult to manage the shares if more than one shares need to be stored. It is difficult for the share manager to determine which share belongs to which secret image. Furthermore, during transmission, these meaningless shares may arouse the suspicions from potential attackers.

An extended visual cryptography (extended VC), as proposed in [8], produces meaningful shares (also called shadows). By using a tag image as the cover image, the meaningful shares are easier to store or manage. Furthermore, the meaningful shares may also act as a steganographic mechanism in visual cryptography and try to hide the fact that the transmitted image is a share from visual cryptography. As a result, the shares in extended VC are less likely to arouse suspicion from attackers if their quality is high enough. For this purpose, the share should be perceptually as close to the cover image as possible.

A $(2,2)$-threshold extended VC was first introduced in Naor and Shamir’s 1994 seminal paper [8]. Let $\mathbf{S}$ be a secret image and $\mathbf{C}{1}$ and $\mathbf{C}{2}$ be two cover images. The secret $\mathbf{S}$ is split into the two shares $\mathbf{B}{1}$ and $\mathbf{B}{2}$, where $\mathbf{B}{i}$ has the appearance of corresponding cover image $\mathbf{C}{i}$, respectively. In Naor and Shamir’s scheme, each secret pixel is expanded to a $2 \times 2$ block. Let’s focus on one secret pixel $S[i, j]$. Let $\left(c_{1}, c_{2}\right)$ be the two corresponding pixels on the cover images. To encode a white secret pixel $S[i, j]=0$, the encoder uses one of the following four basis matrices:

\begin{aligned} &\mathbf{M}{00}^{0}=\left[\begin{array}{llll} 0 & 0 & 1 & 1 \ 1 & 0 & 1 & 0 \end{array}\right], \quad \mathbf{M}{01}^{0}=\left[\begin{array}{llll} 0 & 0 & 1 & 1 \ 1 & 0 & 1 & 1 \end{array}\right] \ &\mathbf{M}{10}^{0}=\left[\begin{array}{llll} 1 & 0 & 1 & 1 \ 0 & 0 & 1 & 1 \end{array}\right], \quad \mathbf{M}{11}^{0}=\left[\begin{array}{llll} 1 & 0 & 1 & 1 \ 1 & 0 & 1 & 1 \end{array}\right] \end{aligned}
where the basis matrix $\mathbf{M}{c{1} c_{2}}^{s}$ is for the case when the secret pixel equals to $s$ and the two corresponding cover pixels equal to $c_{1}$ and $c_{2}$, respectively. Similarly, to encode a black secret pixel $S[i, j]=1$, the encoder uses one of the following four basis matrices:
$$\begin{array}{ll} \mathbf{M}{00}^{1}=\left[\begin{array}{llll} 0 & 0 & 1 & 1 \ 1 & 1 & 0 & 0 \end{array}\right], & \mathbf{M}{01}^{1}=\left[\begin{array}{llll} 0 & 0 & 1 & 1 \ 1 & 1 & 1 & 0 \end{array}\right], \ \mathbf{M}{10}^{1}=\left[\begin{array}{llll} 1 & 1 & 1 & 0 \ 0 & 0 & 1 & 1 \end{array}\right], & \mathbf{M}{11}^{1}=\left[\begin{array}{llll} 0 & 1 & 1 & 1 \ 1 & 1 & 1 & 0 \end{array}\right], \end{array}$$
After a basis matrix is chosen by the combination of $S[i, j]=s, C_{1}[i, j]=c_{1}$ and $C_{2}[i, j]=c_{2}$, the columns of this matrix are permuted. Then, the first row is reorganized into a $2 \times 2$ block and assigned to share $\mathbf{B}{1}$, while the second row is re-organized into a $2 \times 2$ block and assigned to share $\mathbf{B}{2}$. By stacking two rows of matrices $\mathbf{M}{c{1}, c_{2}}^{0}$, the blackness is 3 , while stacking two rows of matrices $\mathbf{M}{c{1}, c_{2}}^{1}$ produces blackness 4 . So, the target image will reveal the secret image. Furthermore, for $c_{i}=1$, the $i$-th row of corresponding $\mathbf{M}^{s}$ contains three black pixels, while for $c_{i}=0$, the $i$-th row of corresponding $\mathbf{M}^{s}$ contains two black pixels. So, the shares will resemble corresponding cover images.

Using the images in Fig.4.1 as secret and cover images, we get the experimental result in Fig. 4.2. While this algorithm shows acceptable result for binary cover images, it is not directly applicable to halftone image.

The binary secret image and two halftone cover images are shown in Fig. 4.3. The two share images and recovered target image are shown in Fig. 4.4. The share images show reduced contrast. Some low contrast details are also lost.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|User-Friendly Random Grid

Naor and Shamir’s scheme is not size-invariant, because the size of the shares is four times of the size of the secret and cover images. Chen proposed a random grid based scheme, friendly random grid visual secret sharing (FRGVSS), which is size-invariant [1].

Note that in an extended VC, each share has to carry two type of pixels: the secret pixels and the cover pixels. The FRGVSS algorithm uses a probabilistic approach to determine which pixel on a share is to carry the secret pixel and which pixel to carry the corresponding cover pixel. With probability $\beta$, the share pixel carries a secret pixel. When a secret pixel is chosen, an ordinary random grid algorithm is used to generate two share pixels on two share images. With probabilities $\frac{1-\beta}{2}$, a cover pixel is chosen (assuming $(2,2)$-threshold VC), then the corresponding share pixel will reflect this cover pixel, and the other share will generate a black pixel to ensure that the stacking result is black.

The parameter $0<\beta<1$ controls the tradeoff between the quality of the share images and the quality of the target image. Using a small $\beta$, only a small number of pixels on a share are used to carrier the secret pixel, and a large number of pixels are used to carry the corresponding cover pixels. So, we may expect that the share images have a good quality (higher fidelity with the cover image), while the target image has a worse quality.
Chen’s algorithm is summarized in Algorithm 10 .
The experimental results for share images and target images are shown in Fig. $4.5$ and Fig.4.6, respectively, for different $\beta$. Obviously, we observe improved quality for the share images for a smaller $\beta$. But this comes with the price of a lower contrast in target image.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Pixel Swapping Algorithm

Another effort in improving the quality of share image is Lou’s pixel swapping algorithm [7]. This algorithm is block-based and tries to re-arrange the locations

of black pixels within a small block to make the target block as close to the secret block as possible. If the secret block is a black block (i.e., containing only black pixels), then among the two corresponding share blocks, we choose the one having more black pixels to modify. The black pixels in this block is re-arranged, so that the stacking result contains as many black pixels as possible. If the secret block is a white block (i.e., containing only white pixels), then among the two corresponding share blocks, we choose the one having more black pixels to modify. The black pixels in this block is re-arranged, so that the stacking result contains as many white pixels as possible. Ōbviously, this re-arrangement only guarantees best-effort approximation, so the target image is only partially reconstructed.

The pixels are only moved around in a small block and the proportion of black pixels is not changed, so the share image has a good visual quality. However, only the secret block with all black pixels and the secret block with all white pixels are approximated with best effort. From the stacking result, we may see interferences from the cover image. Lou’s algorithm is summarized in Algorithm $11 .$

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Basic Extended VC

[8] 中提出的扩展视觉密码学（扩展 VC）产生有意义的共享（也称为影子）。通过使用标签图像作为封面图像，有意义的共享更易于存储或管理。此外，有意义的共享也可以作为视觉密码学中的一种隐写机制，并试图隐藏传输的图像是视觉密码学的共享的事实。因此，扩展 VC 中的份额如果质量足够高，则不太可能引起攻击者的怀疑。为此，分享应该在感知上尽可能接近封面图像。

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|User-Friendly Random Grid

Naor 和 Shamir 的方案不是大小不变的，因为共享的大小是秘密和覆盖图像大小的四倍。Chen 提出了一种基于随机网格的方案，友好的随机网格视觉秘密共享 (FRGVSS)，它是大小不变的 [1]。

Chen 的算法总结在算法 10 中。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Digital Halftoning

statistics-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography & Cryptanalysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写密码学Cryptography & Cryptanalysis代写方面经验极为丰富，各种代写密码学Cryptography & Cryptanalysis相关的作业也就用不着说。

• 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|Ordered Dithering

Considering the fact that the HVS is a low-pass system that only perceives the result of local average, one can design a distributed multilevel quantizer in a small region. For example, using a $2 \times 2$ block, we may design a five-level quantizer with thresholds $(1 / 8,3 / 8,5 / 8,7 / 8)$ and reconstruction points $(0,1 / 4,2 / 4,3 / 4,1)$. Then the thresholds are placed in a $2 \times 2$ block as:
$$\mathbf{T}=\left[\begin{array}{lll} 3 / 8 & 5 / 8 \ 7 / 8 & 1 / 8 \end{array}\right]$$
Suppose that the input value is a constant $2 \times 2$ block $\mathbf{x}$ :
$$\mathbf{x}=\left[\begin{array}{ll} c & c \ c & c \end{array}\right]$$
then we perform sample-wise quantization as in (3.2) as:
$$y[i, j]= \begin{cases}1, & \text { if } c>T[i, j], \ 0, & \text { otherwise }\end{cases}$$
So, the number of black pixels in $y$ will be approximately proportional to the value of $c$ in $\mathbf{x}$. Or, one can think of the proportion of black pixels in $\mathbf{y}$ as representing the reconstruction levels $(0,1 / 4,2 / 4,3 / 4,1)$. Thus, by arranging the quantization levels in a small block of thresholds, we get a distributed multi-level quantizer. The reconstruction levels are the proportion of black pixels in the output block. This is usually referred to as Ordered Dithering since we can consider the thresholds in $\mathbf{T}$ as dithering of the constant threshold $1 / 2$.

In general, for ordered dithering, the thresholds are specified by an index matrix. For a $L \times L$ block, the index matrix contains a list of all the $L^{2}$ integer numbers $\left{0, \ldots, L^{2}-1\right}$. For example, for $L=2$, the index matrix can be
$$\mathbf{I}=\left[\begin{array}{ll} 3 & 0 \ 2 & 1 \end{array}\right]$$
which specifies the sequence of turning on the corresponding pixels to black. From it, the threshold matrix can be determined:

$$T[i, j]=\frac{I[i, j]+1 / 2}{L^{2}}$$
which gives the threshold matrix:
$$\mathbf{T}=\left[\begin{array}{lll} 7 / 8 & 1 / 8 \ 5 / 8 & 3 / 8 \end{array}\right]$$
In general, the size of the image is larger than the size of the threshold matrix. So, the image is segmented into blocks having the same size of the threshold matrix, and then we use the threshold matrix to quantize each block.
$$y[i, j]= \begin{cases}1, & \text { if } x[i, j]>T[i \bmod L, j \bmod L], \ 0, & \text { otherwise. }\end{cases}$$
The size of the threshold matrix is usually much larger than $2 \times 2$, such as $8 \times$ $8,16 \times 16$ or even the size of the image to be processed. For such a large size, the arrangement of thresholds is not a trivial issue. Different arrangements of the quantization levels lead to different halftoning effects. If nearby quantization levels are spatially close to each other, then we have clustered dot dithering. If nearby quantization levels are located far away from each other, then we have dispersed dot dithering.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Clustered Dot Dithering

The term ‘clustered dot’ comes from the fact that when using this dithering, the black dots are clustered together when the image pixels are smoothly varying. For this reason, changing the input gray level is equivalent to changing the size of the whole clustered dot, and is usually called Amplitude Modulation (AM) [9].

To construct the index matrix, we start from the center of the matrix, and put the integers from 0 to $L^{2}-1$ into it, by following a spiral curve with increasing radius. This is shown in Fig.3.2.
Similarly, we can get index matrix for $L=8$ :

which is shown as an image in Fig.3.3
Using this index matrix, we halftone a test image having continuous varying gray scale, as shown in Fig.3.4. Visually, the size of the marco-dot is changing with incrcasing blackncss.

Onc drawback of clustcred dot dithcring, duc to the dot-sizc modulation, is that the halftone result has reduced resolution. The larger the size of the block, the lower the resolution. This drawback can be remedied by dispersed dot dithering.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Dispersed Dot Dithering

For dispersed dot dithering, such as Bayer’s dithering, adjacent thresholds are separated as far as possible from each other. Bayer’s index matrix is defined recursively [2], starting from trivial $2 \times 2$ index matrix
$$\mathbf{I}{2}=\left[\begin{array}{ll} 1 & 2 \ 3 & 0 \end{array}\right]$$ and $$\mathbf{I}{2 n}=\left[\begin{array}{lc} 4 \mathbf{I}{n}+1 & 4 \mathbf{I}{n}+2 \ 4 \mathbf{I}{n}+3 & 4 \mathbf{I}{n} \end{array}\right]$$
for $n=2,4, \ldots$ The $8 \times 8$ threshold matrix for dispersed dot dithering is shown in Fig. 3.5a, and the halftone result for the grayscale image in Fig.3.4a is shown in Fig. 3.5b. Since the thresholds are separated from each other, different blackness corresponds to different frequency of black dots. The resolution is significantly improved.

X=[CC CC]

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考| Security Issue in Visual Cryptography

statistics-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography & Cryptanalysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写密码学Cryptography & Cryptanalysis代写方面经验极为丰富，各种代写密码学Cryptography & Cryptanalysis相关的作业也就用不着说。

• 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|Strong Security and Weak Security

As a cryptography scheme, the security requirement is usually mandatory. So, when designing a VC algorithm, one usually tries to maximize the contrast, under the constraint of security. Some researchers also suggest that there are tradeoffs between security, contrast and pixel expansion. If we relax the requirement on one aspect, then maybe it is possible to improve the performance of the other two. For example, if we relax requirement on security, then it is possible to improve contrast and reduce pixel expansion $[6,10,12]$.

For a VC scheme in its strict sense, the shares are usually printed on transparencies and decoding is realized by stacking, and no computation is required for decoding. In the definition of VC (Definition 2.1), for $q<k$ shares, the two sets of sub-matrices $\hat{\mathrm{C}}{0}$ and $\hat{\mathrm{C}}{1}$ are equivalent. So, an attacker, after obtaining $\hat{\mathrm{C}}{0}$ and $\hat{\mathrm{C}}{1}$, cannot tell if

$s=0$ or $s=1$, no matter the computational abilities he may have at his disposal. This is called strict sense security or unconditional security [6, 10]. For this security, we assume that the attacker has infinite computational abilities.

However, considering the media of the shares and the decoding mechanism, it is reasonable to assume that if the attacker only uses his vision system to find clue of secret from the $q<k$ shares, then the ‘computation’ devices are stacking operation and HVS. Then if from the stacking result of the $q<k$ rows of the matrices, one cannot infer $s$, our algorithm is safe under these assumptions. We call this the weak security.

Weak security was proposed by Liu [12] and Iwamoto [10] independently for different types of VC systems. Liu’s work focuses on block encoding approach to size-invariant VC, while Iwamoto’s works focus on size-expanded VC (deterministic VC) for color image. A key conclusion from their work is that, by relaxing the security level to weak security, it is possible to improve the quality of the target image and reduce the pixel expansion.
In what follows, we introduce three security issues:

1. Iwamoto’s weak security.
2. Liu’s weak security.
3. Replacement attack.
In order to introduce the concept of weak security, we need to formalize some operations on the basis matrices: row restriction and row stacking, and introduce the concept of equivalence between two sets of matrices [10].

For $(k, n)$-threshold scheme, a set of participants can be represented by $\mathrm{P}=$ $\left{i_{1}, \ldots, i_{q}\right} \subset{1, \ldots, n}$. Given a basis matrix $\mathbf{B} \in \mathbb{Z}{2}^{n \times m}$, one can make another matrix by restricting the rows of $\mathbf{B}$ to the rows specified in set $P$. This operation is denoted by $$\hat{\mathbf{B}}=\mathbf{B} \llbracket \mathrm{P} \rrbracket$$ with $$\hat{B}[\ell, j]=B\left[i{\ell}, j\right],$$
where $\ell \in{1, \ldots, q}, i_{\ell} \in \mathrm{P}$, and $j \in{1, \ldots, n}$.
Another formal operation introduced by Iwamoto is stacking of rows of a matrix. Let a matrix $\mathbf{B}$ be partitioned as
$$\mathbf{B}=\left[\begin{array}{c} \mathbf{b}{1} \ \vdots \ \mathbf{b}{n} \end{array}\right] \in \mathbb{Z}{2}^{n \times m}$$ Then, the stacking of rows of $\mathbf{B}$ is denoted as $$\eta(\mathbf{B})=\mathbf{b}{1} \vee \ldots \vee \mathbf{b}_{n},$$

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Introduction to Digital Halftoning

Most printing devices and some display devices can only render limited number of colors [9]. For example, a typical laser printer can only output a black dot or ‘no dot’ at a time. In order to print grayscale images, we must quantize the input color to coarser scales, such that the perceived color is still similar to the original color when observed by human eyes.

In this chapter, we assume that the input image is a grayscale image and each pixel is normalized to the range $[0,1]$. If the pixel is quantized, 8-bit quantization is assumed. The printer is assumed to be able to produce only two colors: black (black dot) and white (no dot).

The image quantization problem then can be stated as follows: Given an input grayscale image $x[i, j]$, the quantizer produces a binary image $y[i, j] \in{0,1}$ such that it is visually similar to the input image $x[i, j]$ when viewing from sufficient distance. Let $\mathcal{H}$ be a system representing the human visual perception, then the digital halftoning problem can be formulated as an optimization problem:
$$\min {\mathbf{y} \in \mathbb{Z}{2}^{M \times N}} \mathcal{H}{\mathbf{x}-\mathbf{y}}$$
where the images are of size $M \times N$. Solving this optimization problem directly is usually impractical due to the high dimensional searching space that has $2^{M \times N}$ feasible solutions.

Many heuristic approaches are proposed for solving the halftoning problem in (3.1), including constant threshold bi-level quantization, ordered dithering, error diffusion and direct binary search (DBS).

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Bi-level Quantization

The simplistic approach is to quantize each sample independently using a bi-level quantizer [6]:
$$y[i, j]= \begin{cases}1, & \text { if } x[i, j]>T, \ 0, & \text { otherwise }\end{cases}$$
where $T$ is a constant threshold. For this quantizer, the two reconstruction levels are $\left(y_{0}, y_{1}\right)=(0,1)$ and the decision boundaries are $\left(d_{0}, d_{1}, d_{2}\right)=(0, T, 1)$. The threshold $T$ can be designed by minimizing the mean-squared error:
$$\operatorname{MSE}(T)=\sum_{i=0}^{1} \int_{d_{i}}^{d_{i+1}}\left(x-y_{i}\right)^{2} p_{X}(x) d x$$
where $p_{X}(x)$ is the PDF of the samples of the input image $x$. It can be modeled as uniform distribution over the interval $[0,1]$, considering the wide varieties of the histogram of natural images. By solving $\frac{\partial \mathrm{MSE}(T)}{\partial T}=0$, one can easily find that $T=1 / 2$.

A halftoning result using bi-level quantizer on Lena image is shown in Fig. 3.1. As can be seen, only some high contrast edges and textures are preserved, a lot of low contrast details are lost. The halftone image is not visually similar to the original grayscale image.

Several important properties of the grayscale images and halftone images are not utilized in simple bi-level quantization halftoning. First, a grayscale image usually consists of smooth regions separated by edges. Second, the HVS can only perceive a local average of the halftone image in a small region, or equivalently, the HVS is a low-pass system. One way to utilize these properties is to use a distributed multilevel quantizer, where the quantization levels are spatially distributed in a small region. This idea leads to ordered dithering.

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Strong Security and Weak Security

s=0或者s=1，无论他可能拥有的计算能力如何。这称为严格意义上的安全性或无条件安全性 [6, 10]。对于这种安全性，我们假设攻击者具有无限的计算能力。

Liu [12] 和 Iwamoto [10] 分别针对不同类型的 VC 系统提出了弱安全性。Liu 的工作侧重于尺寸不变 VC 的块编码方法，而 Iwamoto 的工作侧重于彩色图像的尺寸扩展 VC（确定性 VC）。他们工作的一个关键结论是，通过将安全级别放宽到弱安全，可以提高目标图像的质量并减少像素扩展。

1. 岩本的弱安全性。
2. 刘的弱安全。
3. 替换攻击。
为了引入弱安全性的概念，我们需要形式化一些基于矩阵的操作：行限制和行堆叠，并引入两组矩阵之间的等价概念[10]。

Iwamoto 介绍的另一个正式操作是矩阵行的堆叠。让一个矩阵乙被划分为

## 数学代写|密码学作业代写Cryptography & Cryptanalysis代考|Bi-level Quantization

MSE⁡(吨)=∑一世=01∫d一世d一世+1(X−是一世)2pX(X)dX

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。