数学代写|密码学作业代写Cryptography代考|Basic Information Theory

Doug I. Jones

Doug I. Jones

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如果你也在 怎样代写密码学Cryptography这个学科遇到相关的难题,请随时右上角联系我们的24/7代写客服。

密码学创造了具有隐藏意义的信息;密码分析是破解这些加密信息以恢复其意义的科学。许多人用密码学一词来代替密码学;然而,重要的是要记住,密码学包括了密码学和密码分析。

couryes-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography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代写方面经验极为丰富,各种代写密码学Cryptography相关的作业也就用不着说。

我们提供的密码学Cryptography及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (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代考|The Information Age

It is often stated that we live in an information age. This would clearly make information theory pertinent not only to an understanding of cryptography but also to an understanding of modern society. First, we must be clear on what is meant by the phrase “information age.” To a great extent, the information age and the digital age go hand in hand. Some might argue the degree of overlap; however, it is definitely the case that without modern computers, the information age would be significantly stifled. While information theory began before the advent of modern digital computers, the two topics are still inextricably intertwined.

From one perspective the information age is marked by information itself becoming a primary commodity. Clearly, information has always been of value. But it was historically just a means to a more concrete end. For example, even pre-historic people needed information, such as where to locate elk or other games. However, that information was just peripheral to the tangible commodity of food. In our example, the food was the goal; that was the actual commodity. The information age is marked by information itself being widely considered a commodity.

If you reflect on this just briefly, I think you will concur that in modern times information itself is often viewed as a product. For example, you purchased this book you now hold in your hands. Certainly, the paper and ink used to make this book were not worth the price paid. It is the information encoded on the pages that you paid for. In fact, you may have an electronic copy and not actually have purchased any pages and ink at all. If you are reading this book as part of a class, then you paid tuition for the class. The commodity you purchased was the information transmitted to you by the professor or instructor (and of course augmented by the information in this book!) So clearly information as a commodity can exist separately from computer technology. The efficient and effective transmission and storage of information, however, require computer technology.

Yet another perspective on the information age is the proliferation of information. Just a few decades ago, news meant a daily paper, or perhaps a 30 -minute evening news broadcast. Now news is 24 hours a day on several cable channels and on various internet sites. In my own childhood, research meant going to the local library and consulting a limited number of books that were, hopefully, not more than 10 years out of date. Now, at the click of a mouse button, you have access to scholarly journals, research websites, almanacs, dictionaries, encyclopedias, and avalanche of information. Thus, one could view the information age as the age in which most people have ready access to a wide range of information.

Younger readers who have grown up with the internet, cell phones, and generally being immersed in a sea of instant information may not fully comprehend how much information has exploded. It is important to understand the explosion of information in order to fully appreciate the need for information theory. To provide you some perspective on just how much information is being transmitted and consumed in our modern civilization, consider the following facts. As early as 2003 , experts estimated that humanity had accumulated a little over 12 exabytes of data over the entire course of human history. Modern media such as magnetic storage, print, and film had produced 5 exabytes in just the first 2 years of the twenty-first century. In 2009 , researchers claimed that in a single year, Americans consumed over 3 zettabytes of information. As of 2019 the World Wide Web is said to have had 4.7 zettabytes, or 4700 exabytes of data. That is just the internet, not including offline storage, internal network servers, and similar data. If you were to try to put all that data on standard external drives, such as 4 terabyte external drives that are quite common as of this writing, it would take $109,253,230,592$ such drives.

数学代写|密码学作业代写Cryptography代考|Claude Shannon

It is impossible to seriously examine information theory without discussing Claude Shannon. Claude Shannon is often called the father of information theory (Gray 2011). He was a mathematician and engineer who lived from April 30, 1916 until February 24,2001 . He did a great deal of fundamental work on electrical applications of mathematics and work on cryptanalysis. His research interests included using Boolean algebra (we will discuss various algebras at length in Chap. 5) and binary math (which we will introduce you to later in this chapter) in conjunction with electrical relays. This use of electrical switches working with binary numbers and Boolean algebra is the basis of digital computers.

During World War II, Shannon worked for Bell Labs on defense applications. Part of his work involved cryptography and cryptanalysis. It should be no surprise that his most famous work, information theory, has been applied to modern developments in cryptography. It should be noted that in 1943, Shannon became acquainted with Alan Turing, whom we discussed in Chap. 2. Turing was in the United States to work with the US Navy’s cryptanalysis efforts, sharing with the United States some of the methods that the British had developed.

Information theory was introduced by Claude Shannon in 1948 with the publication of his article A Mathematical Theory of Communication (Guizzo 2003). Shannon was interested in information, specifically in relation to signal processing operations. Information theory now encompasses the entire field of quantifying, storing, transmitting, and securing information. Shannon’s landmark paper was eventually expanded into a book. The book was entitled The Mathematical Theory of Communication and was co-authored with Warren Weaver and published in 1963.
In his original paper, Shannon laid out some basic concepts that might seem very elementary today, particularly for those readers with an engineering or mathematics background. At the time, however, no one had ever attempted to quantify information nor the process of communicating information. The relevant concepts he outlined are given below with a brief explanation of their significance to cryptography:

  • An information source that produces a message. This is perhaps the most elementary concept Shannon developed. There must be some source that produces a given message. In reference to cryptography, that source takes plain text and applies some cipher to create cipher text.
  • A transmitter that operates on the message to create a signal which can be sent through a channel. A great deal of Shannon’s work was about the transmitter and channel. These are essentially the mechanisms that send a message, in our case an encrypted message, to its destination.
  • A channel, which is the medium over which the signal, carrying the information that composes the message, is sent. Modern cryptographic communications often take place over the internet. However, encrypted radio and voice transmissions are often used. In Chap. 2 you were introduced to IFF (Identification Friend or Foe) systems.
  • A receiver, which transforms the signal back into the message intended for delivery. For our purposes the receiver will also decrypt the message, producing plain text from the cipher text that is received.
  • A destination, which can be a person or a machine, for whom or which the message is intended. This is relatively straightforward. As you might suspect, sometimes the receiver and destination are one and the same.

密码学代写

数学代写|密码学作业代写Cryptography代考|The Information Age

人们常说我们生活在信息时代。这显然会使信息论不仅与密码学的理解相关,而且与现代社会的理解相关。首先,我们必须弄清楚“信息时代”这个词的含义。在很大程度上,信息时代和数字时代齐头并进。有些人可能会争论重叠的程度;然而,如果没有现代计算机,信息时代肯定会受到严重阻碍。虽然信息论在现代数字计算机出现之前就开始了,但这两个主题仍然密不可分地交织在一起。

从一个角度来看,信息时代的标志是信息本身成为一种初级商品。显然,信息一直都是有价值的。但从历史上看,它只是达到更具体目的的一种手段。例如,即使是史前人类也需要信息,例如在哪里可以找到麋鹿或其他游戏。然而,这些信息只是食品这一有形商品的外围信息。在我们的示例中,食物是目标;那是实际的商品。信息时代的标志是信息本身被广泛认为是一种商品。

如果你只是简单地思考一下,我想你会同意在现代信息本身通常被视为一种产品。例如,您购买了现在手中拿着的这本书。当然,制作这本书所用的纸张和墨水不值这个价钱。它是在您付费的页面上编码的信息。事实上,您可能拥有电子版,实际上根本没有购买任何页面和墨水。如果您在上课时阅读本书,那么您已经支付了该课程的学费。您购买的商品是教授或讲师传递给您的信息(当然还有本书中的信息!)因此,作为商品的信息显然可以独立于计算机技术而存在。然而,高效和有效的信息传输和存储,

信息时代的另一个观点是信息的扩散。就在几十年前,新闻指的是日报,或者可能是 30 分钟的晚间新闻广播。现在新闻在几个有线频道和各种互联网站点上一天 24 小时播放。在我自己的童年,研究意味着去当地的图书馆并查阅数量有限的书籍,希望这些书籍不会超过 10 年。现在,只需单击鼠标按钮,您就可以访问学术期刊、研究网站、年历、词典、百科全书和海量信息。因此,人们可以将信息时代视为大多数人可以随时访问范围广泛的信息的时代。

伴随着互联网、手机长大,沉浸在即时信息海洋中的年轻读者可能无法完全理解信息量的爆炸式增长。为了充分理解信息论的必要性,理解信息爆炸是很重要的。为了让您了解在我们的现代文明中传输和消费了多少信息,请考虑以下事实。早在 2003 年,专家就估计人类在整个人类历史进程中积累了略高于 12 艾字节的数据。磁存储、印刷和电影等现代媒体仅在 21 世纪的头两年就产生了 5 艾字节。2009 年,研究人员声称,美国人在一年内消耗了超过 3 泽字节的信息。截至 2019 年,据说万维网拥有 4.7 泽字节,即 4700 艾字节的数据。那只是互联网,不包括离线存储、内部网络服务器和类似数据。如果您尝试将所有这些数据放在标准的外部驱动器上,例如在撰写本文时非常常见的 4 TB 外部驱动器,则需要109,253,230,592这样的驱动器。

数学代写|密码学作业代写Cryptography代考|Claude Shannon

不讨论克劳德·香农就不可能认真地研究信息论。克劳德·香农 (Claude Shannon) 通常被称为信息论之父 (Gray 2011)。他是一位数学家和工程师,生活于 1916 年 4 月 30 日至 2001 年 2 月 24 日。他在数学的电子应用和密码分析方面做了大量的基础工作。他的研究兴趣包括将布尔代数(我们将在第 5 章详细讨论各种代数)和二进制数学(我们将在本章后面介绍)与继电器结合使用。这种使用二进制数和布尔代数的电气开关是数字计算机的基础。

第二次世界大战期间,香农在贝尔实验室从事国防应用方面的工作。他的部分工作涉及密码学和密码分析。毫不奇怪,他最著名的著作信息论已应用于密码学的现代发展。应该指出的是,香农在 1943 年结识了我们在第 1 章中讨论过的艾伦图灵。2. 图灵在美国参与美国海军的密码分析工作,与美国分享英国人开发的一些方法。

信息论是克劳德·香农 (Claude Shannon) 于 1948 年发表的文章《通信的数学理论》(Guizzo 2003) 引入的。香农对信息很感兴趣,特别是与信号处理操作有关的信息。信息论现在涵盖了量化、存储、传输和保护信息的整个领域。香农具有里程碑意义的论文最终被扩展成一本书。该书名为《通信的数学理论》,与沃伦·韦弗 (Warren Weaver) 合着,于 1963 年出版。
在他的原始论文中,Shannon 列出了一些在今天看来可能非常初级的基本概念,特别是对于那些具有工程或数学背景的读者而言。然而,当时还没有人尝试过量化信息,也没有人尝试过量化信息交流的过程。下面给出了他概述的相关概念,并简要解释了它们对密码学的意义:

  • 产生消息的信息源。这也许是香农提出的最基本的概念。必须有一些来源产生给定的消息。关于密码学,该来源采用纯文本并应用一些密码来创建密文。
  • 对消息进行操作以创建可以通过通道发送的信号的发送器。香农的大量工作都是关于发射器和信道的。这些本质上是将消息(在我们的例子中是加密消息)发送到目的地的机制。
  • 信道,即承载构成消息的信息的信号通过其发送的媒介。现代密码通信通常通过互联网进行。但是,通常使用加密的无线电和语音传输。在第一章 2 向您介绍了 IFF(敌我识别)系统。
  • 接收器,它将信号转换回要传递的消息。出于我们的目的,接收方还将解密消息,从接收到的密文生成明文。
  • 目的地,可以是人或机器,消息是为谁或谁准备的。这是相对简单的。您可能会怀疑,有时接收者和目的地是同一个。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题,以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法,其中不假设数据来自于由少数参数决定的规定模型;这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型(GLM)归属统计学领域,是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。

有限元方法代写

有限元方法(FEM)是一种流行的方法,用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

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。

随机分析代写


随机微积分是数学的一个分支,对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。

回归分析代写

多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。

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。

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