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数学代写|密码学代写Cryptography Theory代考|CS355 A Revolutionary Cryptologist

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数学代写|密码学Cryptography Theory代考|A Revolutionary Cryptologist

During the American Revolutionary War, James Lovell attempted to deal with the problem within the context of a cipher system of his own creation. ${ }^1$ His system was similar to the Vigenère cipher and is best explained through an example. Suppose our message is I HAVE NOT YET BEGUN TO FIGHT and the key is WIN. We form three alphabets by continuing from each of the three key letters like so:

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline 1 & $\mathrm{~W}$ & I & $\mathrm{N}$ & 15 & $\mathrm{~J}$ & W \
\hline . & $\mathrm{X}$ & J & 0 & 16 & K & $\mathrm{X}$ \
\hline 3 & $\mathrm{Y}$ & $\mathrm{K}$ & P & 17 & $\mathrm{~L}$ & $\mathrm{Y}$ \
\hline 4 & Z & $\mathrm{L}$ & Q & 18 & M & Z \
\hline 5 & $\&$ & M & R & 19 & $\mathrm{~N}$ & $\&$ \
\hline 6 & A & $\mathrm{N}$ & S & 20 & 0 & A \
\hline 7 & B & 0 & $\mathrm{~T}$ & 21 & P & B \
\hline & C & $\mathrm{P}$ & U & 22 & Q & $\mathrm{C}$ \
\hline & D & Q & $\mathrm{V}$ & 23 & R & D \
\hline 10 & $\mathrm{E}$ & $\mathrm{R}$ & W & 24 & S & $E$ \
\hline 11 & $\mathrm{~F}$ & $S$ & $X$ & 25 & $\mathrm{~T}$ & $\mathrm{~F}$ \
\hline 12 & G & $\mathrm{T}$ & $Y$ & 26 & U & G \
\hline 1 & $\mathrm{H}$ & $\mathrm{U}$ & Z & 27 & $\mathrm{~V}$ & $\mathrm{H}$ \
\hline 14 & I & $\mathrm{V}$ & $\&$ & & & \
\hline
\end{tabular}

Notice that Lovell included $\&$ as one of the characters in his alphabet.
The first letter of our message is $I$, so we look for $I$ in the column headed by $W$ (our first alphabet). It is found in position 14 , so our ciphertext begins with 14. Our next plaintext letter is $\mathrm{H}$. We look for $\mathrm{H}$ in the column headed by I (our second alphabet) and find it in position 27. Thus, 27 is our next ciphertext number. Then we come to plaintext letter A. Looking at our third alphabet, we find $A$ in position 15 . So far, our ciphertext is $1427 \quad 15$. We’ve now used all three of our alphabets, so for the fourth plaintext letter we start over with the first alphabet, in the same manner as the alphabets repeat in the Vigenère cipher. The complete ciphertext is $\begin{array}{lllll}14 & 27 & 15 & 27\end{array}$ $\begin{array}{lllllllllllllllllll}24 & 1 & 20 & 12 & 12 & 10 & 12 & 16 & 10 & 26 & 8 & 19 & 12 & 2 & 11 & 1 & 21 & 13 & 12 .\end{array}$

Lovell explained this system to John Adams and Ben Franklin and attempted to communicate with them using it. He avoided having to agree on keys ahead of time by prefacing his ciphertexts with clues to the key, such as “You begin your Alphabets by the first 3 letters of the name of that family in Charleston, whose Nephew rode in Company with you from this City to Boston.” 2 Thus, for every message Lovell sent using this scheme, if a key hadn’t been agreed on ahead of time, he had to think of some bit of knowledge that he and the recipient shared that could be hinted at without allowing an interceptor to determine the answer. This may have typically taken longer than enciphering! Also, Lovell’s cipher seems to have been too complicated for Adams and Franklin even without the problem of key recovery, as both failed to read messages Lovell sent. Abigail Adams was even moved to write Lovell in 1780, “I hate a cipher of any kind.”

数学代写|密码学Cryptography Theory代考|Diffie–Hellman Key Exchange

In order to find a satisfactory solution to the problem of key exchange, we must jump ahead from the Revolutionary War to America’s bicentennial. ${ }^4$ The early (failed) attempt to address the problem was presented first to give a greater appreciation for the elegance of the solutions that were eventually discovered.

In 1976, Whitfield Diffie (Figure 14.1) and Martin Hellman (Figure 14.2) presented their solution in a wonderfully clear paper titled “New Directions in Cryptography.” Neal Koblitz, whom we will meet later in this book, described Diffie as “a brilliant, offbeat and unpredictable libertarian” and the paper whose results are detailed below as “the most famous paper in the history of cryptography.”6

Hellman’s home page” informs the reader that “he enjoys people, soaring, speed skating and hiking.” Following the links also reveals a passionate (and well-reasoned!) effort, sustained for over a quarter century by Hellman, against war and the threat of nuclear annihilation. He traced his interest in cryptography to three main sources, one of which was the appearance of David Kahn’s The Codebreakers. ${ }^8$ As this book was also an influence on Diffie (and many others!), its importance in the field is hard to overestimate. The scheme developed by Diffie and Hellman works as follows.

数学代写|密码学Cryptography Theory代考|A Revolutionary Cryptologist

$14 \quad 27 \quad 15 \quad 27$
$\begin{array}{lllllllllllllllllll}24 & 1 & 20 & 12 & 12 & 10 & 12 & 16 & 10 & 26 & 8 & 19 & 12 & 2 & 11 & 1 & 21 & 13 & 12 .\end{array}$
Lovell 向 John Adams 和 Ben Franklin 解释了这个系统，并试图用它与他们交流。他通过在密文前加上密钥 线索避免了必须提前就密钥达成一致，例如“你的字母表以查尔斯顿那个家庭名字的前 3 个字母开始，他的侄子 从这开始与你同行城市到波士顿。” 2 因此，对于 Lovell 使用此方穼发送的每条消息，如果没有提前商定密 钥，他必须考虑一些他和收件人共享的知识，这些知识可以在不允许拦截器的情况下被提示确定答案。这通常 可能比加密花费更长的时间! 此外，即使没有密钥恢复问题， Lovell 的密码对于 Adams 和 Franklin 来说似乎 过于复杂，因为他们都无法读取 Lovell 发送的消息。

数学代写|密码学Cryptography Theory代考|Diffie–Hellman Key Exchange

1976 年，Whitfield Diffie（图 14.1）和 Martin Hellman（图 14.2）在一篇题为“密码学新方向”的非常清晰的论文中提出了他们的解决方案。我们稍后将在本书中见到的尼尔·科布利茨 (Neal Koblitz) 将迪菲描述为“一位才华横溢、另类且不可预测的自由主义者”，其论文的结果详述如下，是“密码学史上最著名的论文”6。

Hellman 的主页”告诉读者“他喜欢人、翱翔、速滑和徒步旅行。” 访问这些链接还揭示了 Hellman 为反对战争和核毁灭威胁而持续了四分之一个世纪的热情（而且有充分理由！）的努力。他将自己对密码学的兴趣追溯到三个主要来源，其中之一是大卫·卡恩 (David Kahn) 的密码破译者 (The Codebreakers) 的出现。

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。