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# Encryption[1] - Modern Cryptography and Mathematics By...

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Produced by the Further Mathematics Network, www.fmnetwork.org.uk and The University of Warwick, www2.warwick.ac.uk/fac/sci/maths with the support of Rolls-Royce plc, www.rolls-royce.com What is Cryptography? According to the Oxford English Dictionary cryptography is, "A secret manner of writing ... intelligible only to those possessing the key; also anything written in this way. Generally, the art of writing or solving ciphers." A secret code used in cryptography is called a cipher, the process of using a cipher to turn a plain document into a secret text is called encryption, and the reverse process is called decryption. Cryptography is an ancient subject that has changed a lot throughout the years. To quote Wikipedia: “In modern times, cryptography is considered to be a branch of both mathematics and computer science.” At one time the subject was mainly a linguistic one, the key concern being the ability to recognise words and make words unrecognisable with a simple cipher. Today, thanks to computers, the subject is very mathematical with the ciphers involved drawing from computer science and number theory. Problems with communication There are several issues that can arise when communicating over vast distances. The methods of modern encryption aim to solve two of them: Confidentiality: Will any information sent only be read by it's intended recipient? The world, both past and present, is full of confidential information, from bank account details to military strategies. There is always the risk that such information could fall into the wrong hands. Confidentiality can be achieved without cryptography, by using a reliable courier for example, but the modern internet is anything but secure with any information sent on it usually being routed through various computers around the world before reaching its destination. Authentication: Is any information received from the person it claims to be from? A naval captain receiving an order to scuttle his ship might wonder if the order came from his enemy. A bank confronted with a cheque might wonder who it was written by. In the context of cheques and paper documents and in the context of modern cryptographic techniques the authentication is usually called a “signature” or sometimes a “digital signature”. With a modern desire to communicate using the internet, authentication becomes a major issue. History: Simple Substitution Simple substitution, as the name implies, involves substituting some letters for others, as in this table: Substitute every letter in the top row with one in the bottom: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Q A Z W S X E D C R F V T G B Y H N U J M I K O L P “this text is going to be encrypted” becomes “jdcu jsoj cu ebcge jb as sgznlyjsw” Historically, once both parties have agreed upon a substitution, this method offered a reasonable degree of confidentiality. To anyone intercepting the message it would appear to be nonsensical. It also offers a degree of authentication since (hopefully!) only the two parties who wish to
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