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

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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|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

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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。