Posted on Categories:Cryptography, 密码学, 数学代写

# 数学代写|密码学代写Cryptography Theory代考|Homophonic encoding

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 数学代写|密码学Cryptography Theory代考|Homophonic encoding

An alternative means of defeating single letter frequency analysis is to tackle the letter frequencies head on. The idea behind homophonic encoding is to encrypt plaintext letters by a number of different ciphertext characters in order to directly confuse the ciphertext symbol frequency statistics (we say symbol rather than letter here because, after homophonic encoding has been applied, there are many more ciphertext symbols than there are letters in the alphabet). This technique is best explained by means of an example.
EXAMPLE OF HOMOPHONIC ENCODING
The aim of homophonic encoding is to design a cryptosystem whose ciphertext alphabet histogram is close to being ‘flat’ (in other words, every ciphertext symbol occurs approximately equally often). We achieve this by increasing the ciphertext alphabet.

A possible homophonic code for use with English plaintexts can be devised from Table 2.1 of English letter frequencies, as follows. Suppose we choose a ciphertext alphabet of 1000 symbols. This means that instead of 26 letters, each ciphertext character is one of these 1000 symbols. We then secretly divide the 1000 ciphertext symbols into 26 groups. Each group is then associated with one specific plaintext letter. From Table 2.1 we see that:

• Plaintext letter A occurs approximately $8.2 \%$ of the time, so we assign 82 ciphertext symbols for encrypting A.
• Plaintext letter B occurs approximately $1.5 \%$ of the time, so we assign 15 ciphertext symbols for encrypting B.
• Plaintext letter $\mathrm{C}$ occurs approximately $2.8 \%$ of the time, so we assign 28 ciphertext symbols for encrypting $\mathrm{C}$.

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

The last historical cryptosystem we will look at is the famous Vigenère Cipher, which was for a significant period in history regarded as being such a secure cryptosystem that it was regularly used for protecting sensitive political and military information and referred to as the ‘indecipherable cipher’. The Vigenère Cipher is of interest to us because it illustrates the use of positional dependency to defeat single letter frequency analysis.
ENCRYPTION USING THE VIGENÈRE CIPHER
The Vigenère Cipher is fairly straightforward to understand. The key of the Vigenère Cipher consists of a string of letters that form a keyword. Associating the letters $\mathrm{A}, \mathrm{B}, \ldots, \mathrm{Z}$ with the numbers $0,1, \ldots, 25$, respectively, the encryption process proceeds as follows:

1. Write out the keyword repeatedly underneath the plaintext until every plaintext letter has a keyword letter beneath it.
2. Encrypt each plaintext letter using a Caesar Cipher, whose key is the number associated with the keyword letter written beneath it.
Figure 2.5 provides an example of the Vigenère Cipher with keyword DIG, where the plaintext appears in the top row and the ciphertext appears in the bottom row. Thus, for example, the first plaintext letter A is shifted using a Caesar Cipher with shift 3 (corresponding to keyword letter D) to obtain the ciphertext letter D. The second plaintext letter, which is also A, is shifted using a Caesar Cipher with shift 8 (corresponding to keyword letter I) to obtain ciphertext letter I. The third plaintext letter, which is R, is shifted using a Caesar Cipher with shift 6 (corresponding to keyword letter G) to obtain ciphertext letter $\mathrm{X}$. The rest of the ciphertext is produced in a similar way. Decryption is just the reverse process.

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

vigen密码相当容易理解。vigenires密码的密钥由一串字母组成，这些字母组成一个关键字。将字母$\mathrm{A}， \mathrm{B}， \ldots， \mathrm{Z}$分别与数字$0,1，\ldots, 25$相关联，加密过程如下:

## 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。