Number Theory and Cryptography

开始时间: 04/22/2022 持续时间: Unknown

所在平台: CourseraArchive

课程类别: 计算机科学

大学或机构: CourseraNew



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We all learn numbers from the childhood. Some of us like to count, others hate it, but any person uses numbers everyday to buy things, pay for services, estimated time and necessary resources. People have been wondering about numbers’ properties for thousands of years. And for thousands of years it was more or less just a game that was only interesting for pure mathematicians. Famous 20th century mathematician G.H. Hardy once said “The Theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics”. Just 30 years after his death, an algorithm for encryption of secret messages was developed using achievements of number theory. It was called RSA after the names of its authors, and its implementation is probably the most frequently used computer program in the word nowadays. Without it, nobody would be able to make secure payments over the internet, or even log in securely to e-mail and other personal services. In this short course, we will make the whole journey from the foundation to RSA in 4 weeks. By the end, you will be able to apply the basics of the number theory to encrypt and decrypt messages, and to break the code if one applies RSA carelessly. You will even pass a cryptographic quest! As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students. Do you have technical problems? Write to us:

数论和密码学:我们都从小开始学习数字。我们中有些人喜欢数数,其他人则讨厌它,但是任何人每天都使用数字来购买商品,支付服务,估计的时间和必要的资源。数千年来,人们一直在想知道数字的属性。几千年来,它或多或少只是一个纯粹的数学家才感兴趣的游戏。 20世纪著名数学家G.H.哈迪曾经说过:“数论一直被视为纯粹数学最无用的分支之一”。在他去世仅30年之后,利用数论成就开发了一种用于加密秘密消息的算法。它以其作者的名字命名为RSA,其实现可能是当今最常用的计算机程序。没有它,任何人都将无法通过Internet进行安全付款,甚至无法安全登录到电子邮件和其他个人服务。在这个简短的课程中,我们将在4周内完成从基金会到RSA的整个旅程。到最后,您将能够应用数字理论的基础来加密和解密消息,如果不小心应用RSA就会破坏代码。您甚至会通过加密任务! 作为前提条件,我们仅假设基本数学(例如,我们希望您知道什么是平方或如何添加分数),Python中的基本编程(函数,循环,递归),常识和好奇心。我们的目标受众是所有有志或计划在IT领域工作的人,从积极进取的高中生开始。 你有技术上的问题吗?写信给我们


In this week we will discuss integer numbers and standard operations on them: addition, subtraction, multiplication and division. The latter operation is the most interesting one and creates a complicated structure on integer numbers. We will discuss division with a remainder and introduce an arithmetic on the remainders. This mathematical set-up will allow us to created non-trivial computational and cryptographic constructions in further weeks.



We all learn numbers from the childhood. Some of us like to count, others hate it, but any person us


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