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# 数学代写代考| Breaking the Enigma Codes 离散数学

## 数学代写| Breaking the Enigma Codes 代考

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## 离散数学代写

The Enigma codes were used by the Germans during the second world war for the secure transmission of naval messages to their submarines. These messages contained top-secret information on German submarine and naval activities in the Atlantic, and the threat that they posed to British and Allied shipping.

The codes allowed messages to be passed secretly using encryption, and this meant that any unauthorised inteception was meaningless to the Allies. The plaintext (i.e., the original message) was converted by the Enigma machine (Fig. 10.2) into the encrypted text, and these messages were then transmitted by the German military to their submarines in the Atlantic, or to their bases throughout Europe.

The Enigma machine was invented in 1918 and generated a polyalphabetic substitution cipher which the Germans believed to be unbreakable. A letter was typed in German into the machine, and electrical impulses through a series of rotating wheels and wires produced the encrypted letter which was lit up on a panel above the keyboard. The recipient typed the received message into his machine and the decrypted message was lit up letter by letter above the keyboard. The rotors and wires of the machine could be configured in many different ways, and during the war the cipher settings were changed at least once a day. The odds against anyone breaking the Enigma machine without knowing the setting were $150 \times 10^{18}$ to 1 .
The British code and cipher school was relocated from London to Bletchley Park (Fig. 10.3) at the start of the second world war. It was located is in the town of Bletchley near Milton Keynes (about fifty miles north west of London). It was commanded by Alistair Dennison and was known as Station X, and several thousands were working there during the second world war. The team at Bletchley Park Allied war effort.Polish cryptanalysts did important work in breaking the Enigma machine in the early $1930 \mathrm{~s}$, and they constructed a replica of the machine. They passed their knowledge on to the British and gave them the replica just prior to the German invasion of Poland. The team at Bletchley built upon the Polish work, and the team included Alan Turing $^{1}$ (Fig. 10.4) and other mathematicians.

The code-breaking teams worked in various huts in Bletchley park. Hut 6 focused on air force and army cyphers, and hut 8 focused on naval cyphers. The deciphered messages were then converted into intelligence reports, with air force and army intelligence reports produced by the team in hut 3 , and naval intelligence reports produced by the team in hut 4. The raw material (i.e., the encreted messages) to be deciphered came from wireless intercept stations dotted around Britain, messages, and sent them to Bletchley park to be deciphered and analysed.

Turing devised a machine to assist with breaking the codes (an idea that was originally proposed by the Polish cryptanalysts). This electromechanical machine was known as the bombe (Fig. 10.5), and its goal was to find the right settings of
${ }^{1}$ Turing made fundamental contributions to computing, including the theoretical Turing machine.
$10.2$ Breaking the Enigma Codes Fig. $10.5$ Replica of bombe
165
and the time required to determine the settings on the Enigma machime, and it and the time required to determine the settings on the Enigma machine, and it became the main tool for reading the Enigma traftic during the war. The bombe was tological device designed in 1938 by the Polish cryptologist, Marian Rejewski.
A standard Enigma machine employed a set of rotors, and each rotor could be in any of 26 positions. The bombe tried each possible rotor position and applied a test. The test eliminated almost all of the positions and left a smaller number of cases to be dealt with. The test required the cryptologist to have a suitable “crib”: i.e., a section of ciphertext for which he could guess the corresponding plaintext.

For each possible setting of the rotors, the bombe employed the crib to perform a chain of logical deductions. The bombe detected when a contradiction had occurred and it then ruled out that setting and moved onto the next. Most of the possible settings would lead to contradictions and could then be discarded. This would leave only a few settings to be investigated in detail.

The Government Communication Headquarters (GCHQ) was the successor of Bletchley Park, and it opened after the war. The site at Bletchley park was then used for training purposes.

The codebreakers who worked at Bletchley Park were required to remain silent about their achievements until the mid-1970s when the wartime information was declassified. ${ }^{2}$ The link between British Intelligence and Bletchley Park came to an end in the mid-1980s.

It was decided in the mid-1990s to restore Bletchley Park, and today it is run as a museum by the Bletchley Park Trust.

Enigma 机器是在 1918 年发明的，它产生了一种多字母替换密码，德国人认为这种密码是牢不可破的。在机器中输入一个德语字母，通过一系列旋转轮和电线的电脉冲产生加密的字母，该字母在键盘上方的面板上点亮。收件人将收到的消息输入他的机器，解密的消息在键盘上方一个字母一个字母地亮起。机器的转子和电线可以以多种不同的方式进行配置，在战争期间，密码设置至少每天更改一次。任何人在不知道设置的情况下破坏 Enigma 机器的几率是 $150 \times 10^{18}$ to 1 。

## 密码学代考

• Cryptosystem
• A system that describes how to encrypt or decrypt messages
• Plaintext
• Message in its original form
• Ciphertext
• Message in its encrypted form
• Cryptographer
• Invents encryption algorithms
• Cryptanalyst
• Breaks encryption algorithms or implementations

## 编码理论代写

1. 数据压缩（或信源编码
2. 前向错误更正（或信道编码
3. 加密编码
4. 线路码