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# 数学代写|密码学代写Cryptography Theory代考|Caesar Cipher

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## 数学代写|密码学Cryptography Theory代考|Caesar Cipher

The Caesar Cipher tends to be the first example in any introduction to cryptography. Although it is a very straightforward cryptosystem, there are basic lessons to be learnt from studying it. The cryptosystem we describe is sometimes referred to as the Shift Cipher, with the name ‘Caesar Cipher’ occasionally used in a more restricted way to describe the Shift Cipher when the particular shift of three is used.
DESCRIPTION OF THE CAESAR CIPHER
The idea of the Caesar Cipher is to encrypt each letter of the alphabet by the letter obtained by ‘shifting’ the alphabet a secret number of positions. One way of visualising this is to:

1. Write out the plaintext letters of the alphabet A to $\mathrm{Z}$, in order, twice (one after the other).
2. Imagine a ‘sliding ruler’ consisting of one copy of the ciphertext letters of the alphabet A to $\mathrm{Z}$, in order. This ‘sliding ruler’ can be shifted to any position underneath the plaintext letters.
3. Sender Alice and receiver Bob both agree on a secret shift, which is represented by a number between 0 and 25 .
In order to encrypt a plaintext letter, Alice positions the sliding ruler underneath the first set of plaintext letters and slides it to the left by the number of positions of the secret shift. The plaintext letter is then encrypted to the ciphertext letter underneath it on the sliding ruler.

The result of this process is depicted in Figure 2.1 for an agreed shift of three positions. In this case, plaintext HOBBY is encrypted to ciphertext KREEB.

## 数学代写|密码学Cryptography Theory代考|Simple Substitution Cipher

Our next example is the Simple Substitution Cipher, which is a considerable improvement on the Caesar Cipher. Like the Caesar Cipher, however, we will see that this cryptosystem is also fundamentally flawed. We start with a useful definition.
PERMUTATIONS
A permutation of a set of objects is an arrangement of the objects in some order. For example, $(A, B, C),(B, C, A)$, and $(C, A, B)$ are all permutations of the letters $A, B$, and $C$. The total number of possible permutations of $A, B$, and $C$ is:
$$3 \times 2 \times 1=6$$
A permutation of all the letters of the alphabet is the 26 letters of the alphabet arranged in some order. The most natural permutation is $(A, B, C, \ldots, Z)$, but $(Z, Y, X, \ldots, A)$ is also a permutation, and so is any arrangement such as $(G, Y, L, \ldots, X, B, N)$. The total number of such permutations is:
$$26 \times 25 \times 24 \times \cdots \times 3 \times 2 \times 1$$
which is such a big number that we normally write it using the notation 26 ! (which is read as 26 factorial). In general, if we have $n$ objects, then the total number of possible permutations is:
$$n !=n \times(n-1) \times(n-2) \times \cdots \times 3 \times 2 \times 1$$

## 数学代写|密码学Cryptography Theory代考|Simple Substitution Cipher

$$3 \times 2 \times 1=6$$

$$26 \times 25 \times 24 \times \cdots \times 3 \times 2 \times 1$$

$$n !=n \times(n-1) \times(n-2) \times \cdots \times 3 \times 2 \times 1$$

## 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。