Enigma and Lorenz Machines Their Contribution to Computing

secret and Lorenz Machines Their comp mavennt part to ComputingThe purpose of this report is to understand the working of cryptography by studying the working of problem and Lorentz weapons which were utilise by Germans during legions personnel fight II. The report will in like manner discuss the effect of the invention of this forges on newfanglight-emitting diode day cryptography. coding has been hel ensnareg compassionate bes to transmit selective information in secured way but the popularity of cryptography was limited to certain individuals and it was non apply widely. During globe state of warfare II the demand of cryptography change magnitude which resulted in invention of Lorentz and mystery auto by Germans. The encrypted education was alpha to Britains to gain an edge everyplace the Germans war strategies, hence a look for center was constructed in Britains to decode the encoded development. The report discusses the working of Enigma and Lorentz guileless machine and the various methods adopt by Britains to decode the encoded tuition.The report will abstain by studying the effect of the creation of the encrypting and decrypting machines on the redbrick-day figuring.Cryptography play an fundamental role in humans daily fundamental interaction with technological devices, with the advent of computation devices and internet it has become extremely eventful to hide private in organiseation. We often wonder how we can transfer cash through internet or by using ATM cards. The mass medium in the flesh(predicate) discipline such(prenominal) as bank details be transferred securely through internet which is available to every(prenominal)one. This typography tracks the events which contributed to the development of new-fashioned day cryptography and discusses the development in the field of cryptanalysis.Cryptography is the wisdom of secretly transferring information from one point to another so that the information i s reliably transferred from one point to another, which is unintelligible to all receiver of information except the intended user. The aim of the cryptography is to prevent eavesdroppers from understanding the message. (A. Eskicioglu and L. Litwin, 2001)The human want of secrecy of information has resulted in the invention of cryptography. Ciphers were created to hide personal information. The acquire to securely transmit information has increase with the advent of modern communication. Confidential information such as Business plan, financial work which are send over internet needs to be transferred in a secured way. Since, internet is available to everyone it important to encrypt the information which is being transferred (Zwicke, 2003).The basic working of encoding can be divided into cardinal partsEncryptionCryptography works by modifies the original information (termed pellucid text in cryptography) which is in readable form to encrypted form (termed enroltext in cryptogr aphy) which is not soft interpreted by unauthorized person. The encryption emergence scrambles the plaintext by corporate trust it with a tell which is a hit-or-miss sequence of letters or numbers and let ons zero pointtext.TransmissionOnce the information is encrypted it is transferred to the intended user by various methods. For suit, it could be transferred by pen it on paper or can be send via abstruse modern wireless system.DecryptionAfter the information is received by the intended person the person tries to decode the information with a key. The key is unique and usually sole(prenominal) the receiver has the key to decode the information (An introduction to cryptography, n.d.).3.1 Stream cipherStream cipher is an encryption algorithmic rule which encrypts one bit of data in one cycle of its operation. The menses cipher uses infinite waterway of pseudorandom bits of key to encrypt the plaintext. The robustness of the well come forth cipher depends on the algorit hm which is apply to produce the key. Since, repetition in the key can cause the float cipher to be easily predicted and the encrypted text could be easily decrypted (Villanueva, 2015).The working of the stream cipher is explained downstairsAs discussed above encryption works by combining the plain text Xi with key Si to produce ciphertext Ci . The combining process uses modulo 2 operation which is the modulus among the bits of the plaintext and ciphertext. We can denote this numerally as Ci = Xi SiTo decrypt the message the identical key stream is utilise which was apply for encrypting the message.Mathematically this can be stated as Xi = Ci Si (C. Paar, J. Pelzl)The diagram down the stairs summarizes the entire processFigure 1 Encryption and decryption with stream cipher. Reprinted from Understanding cryptography, by C. Paar, J. Pelzl, (n.d.), Retrieved from http//bit.ly/2mEit9i Copy accountability by Springer-Verlag Berlin Heidelberg 2010Enigma machine eliminated the human effort of encryption by automating the process of encryption. The use of riddle machine during human beings War II was done to secretly transmit the categorize information to remote control military units.The enigma was electro-mechanical machine which encoded the character stream to cypher text. The simplest version of the enigma machine had one-third gos which are link with severally other. It also has a slog shape up which is a show panel to interconnect letters to improve the encryption of the enigma machine. A key display mount up was apply to input the characters to be encoded by the machine. A light board was utilize to display the encrypted letter of the plaintext character.Figure 2 Enigma How the machine worked. Reprinted from The withstander website, by Hern, Alex, (2014, Nov 14), Retrieved from https//www.theguardian.com/technology/2014/nov/14/how-did-enigma-machine-work-imitation-game Copyright Simon Singh.4.1WorkingThe working of enigma machine wa s simple. When the operator types the letter on keyboard electric call for is generated. The signal then passes through the plug board which substitutes the letter per the connection of the plug board. The signal then passes through the three rotors with internal equip. This is where the actual encryption takes places. As mentioned above each motor consists of 26 steps of rotary motion before make one complete cycle. The arrangement of the three motors was such that when the graduation motor completes a full rotation the second motor would move by one step. The alike(p) step is applicable for third motor.After passing through the connection of motors the signal is then reflected and once more(prenominal) passes thorough the plug board. After passing through the plug board the signal lights up the appropriate letter on the light board providing the encrypted letter of the plain text character.The Lorentz machine was developed by C. Lorentz in Berlin. In 1940s Germans saw the n eed to establish secured communication surrounded by German high command in Wnsdorf close to berlin and German army throughout Europe. With the invention of mechanical machine and electronic boards it became mathematical to build a machine equal of encrypting the message which was send to remote army. The Lorenz machine was used for sending tactical information (Smart, n.d.).Lorentz machine uses Lorentz cipher which was based on Baudot code. Lets discuss about the working of Baudot code.Baudot CodeIt used five bit of data to encode characters. Baudot code was a banal means of communication via teleprinter. Since five bits were insufficient to repre move all the characters on the keyboard. Hence the code was divided into two states called letter modifys and figures shifts. To toggle between the two states a control character was used, in that location were other characters which had limited functions such as space.To understand the working of Baudot code lets take an example o f encrypting the word Hello. The first step is to fill the Paper tape with holes and hold in the paper tape into telegraph to send the message. To punch holes in the paper tape the redact of the holes needs to be determined which was obtained from the Baudot code table. These holes were born-again to bits and then transferred by teleprinter.Figure 3 The Baudot printing telegraphy system. bet on Edition. Reprinted from Circuitousroot website, by Pendry, H, W. (1919) Retrieved from http//www.circuitousroot.com/artifice/telegraphy/tty/codes/5.1 Lorenz CipherThe Baudot code is taken as input by the Lorenz cipher. The Lorenz cipher consisted of 12 motors which are separated into 3 pairs. Each motor had different number of joints on it as shown in figure belowFigure 4 An Enigma machine rotor. Reprinted from sum magazine website, by Ellis Claire. (2005, Mar 1). Picture retrieved from https//plus.maths.org/content/exploring-enigma Copyright by Simon SinghEach pin could store either 0 or 1 based on the configuration of the machine. The configuration of the machine (setting the starting position of each motor) was performed by the operator of the machine and the same configuration of the machine was used at the receiving end to decrypt the message.The Lorentz machine was divided into three pairs of motors as shown belowFigure 5 The internal working of the Lorentz cipher machine. Reprinted from the Rochester institute website, by Payne, Japnce. (n.d.), Retrieved from https//people.rit.edu/japnce/payne/images/rotorsall.pngThe three pair of motors are termed as K, M, and S. The translation of each pair of motors is discussed belowK motors These consist of 5 motors with followers pin configuration K1=41, K2=31, K3=29, K4=26, K5=23. This set of motors shift by one pin for every character which was encoded.M motors These consist of 2 motors with following pin configuration M1=61, M2=37.This set of motors shift by one pin for every character which was encoded. Furth er the payoff of the M motors decided whether the S motors should be rotated by one pin or should remain unchanged.S motors These consist of 5 motors with following pin configuration S1=43, S2=47, S3=51, S4=53, S5=59. This set of motors shift by one pin based on the output of M motors.WorkingThe 5 bits of the characters are first X-OR with the 5 bits of K motor. The output is then again X-OR with the 5 bits of S motors to get the cypher text. At the receiving end since the Lorentz cipher is a symmetric cipher, the same configuration is used to set up the Lorentz machine at receiving end and the encrypted message is decrypted.The mathematical formula of the encryption and decryption process is as followsSuppose message = M, Cipher text = C, look = EM E = C (Encryption)C E = M (Decryption) (Smart, n.d.)Most of the technology that was in cosmos during ground War II was like that which was used in introduction War I. The telegraph, which was type-printed using a typewriter was w idely used commercially and by military personnel. In the late 1800s an Italian scientist, Guglielmo Marconi discovered the radio communication. However, it wasnt until the advance(prenominal) 1900s that this technology was adopted for military purposes. It was the year 1914 and most major military powers of the world has started relying extensively on this technology but there was a problem there were no security mechanisms in place for a wireless signal to hide the messages being transmitted. The U.S. soon used a more sophisticated version of this technology as soon as Frequency Modulation was invented in 1920.Figure 6 Soldier during field War II using telegraphic switchboardAnother important element of communication technology invented before and during the World War II was the RADAR technology. Developed by the U.S. navy for military use, these were signals sent in the microwave wave distance. It was an entirely new way of surveillance that enabled the allies to gossip in t otal darkness and muster up out about opposition ships in the distant sea or air. radio detection and ranging used small-short signals that were sent into a direction using an antenna. This would return the position and speed of an tendency which would serve as a critical early warning tool.Radar navigation implementation by the German bombers meant that the previous tactics of indiscriminate, area-based bombard was now replaced by more accurate precision targeting. Then there were the German fire control radars, Lichtenstein SN2 was mounted on top of airplanes and had an useful range of 2.5 miles.A methodology that had been in earthly concern for a rather a while but was found of immemorial use during the World War II was Cryptography. Cryptography emerged as the saving(a) grace to closure all questions about the immense need of secrecy. Cryptography had been in existence for over a thousand years but it wasnt until the early nineteenth century that mathematicians came to gether to build a machine that would be used for a very specific purpose send messages during times of war. During this period, Cypher machines were developed under extreme secrecy. These machines were of the mechanical and electromechanical kind. Out of the two, the after were developed by Germans into what they called the Enigma machineAllies and enemies developed and adopted the use of cryptographic communications of all straighten outs during this period. While Germans were focusing on techniques to build machines for encryption, the UK was busy trying to perform cryptanalysis on these machines. many machines came out of Germany that used cryptography in its own unique way. FISH, as the UKs Bletchley viridity codenamed them, were a series of German stream ciphers developed during the World War II era. The enigma in the early 1920s which was of the electro-mechanical sort that used a keyboard, rotors and a spindle to do the tricks. Another machine known as the Lorenz cipher w as simultaneously developed as a form was a rotor stream cipher and started its use in military since 1941 in a SZ form. The tunny cipher as it was called was used for wireless telegraphy which eventually and unfortunately for the Germans, quite soon led to the interception of its messages.Poland came up with its own cryptographic machine called Bomba, which meant cryptographic bomb in Polish. While there is less information available about why it was named so, Bomba was a glorified Enigma machine in more slipway than one. It was developed after the mathematician and its creator, Marian Rejewski studied by hesitateing aside an Enigma. Put simply, it was a multiple Enigma machine that used an galvanizing power aggregate of six Enigmas. Most countries like Poland, united States and the UK consecrate their time and resources in cryptanalysis of these machines.Bletchley Park in England was extremely implemental in bringing about a new era with the cryptanalysis or code breaking of messages that were being transmitted by the Germans during the World War II. The Lorenz machine was a stream cipher that encoded/streamed electrical pulses over a telephone line. The technique used was something we call XOR today which is an admission operation. A key property of XOR is that if one was to run the Ciphertext through the same key again, the original message could be found. The exploitation of this very purpose of the Lorenz cipher led to its success cryptanalysis.One day after a 4000-letter message was sent out to Vienna, the vector who encodes the message received a response from the receiver asking to resend the message since they had not received the message. The sender reset the Lorenz machine and started to abbreviate a few words to string the process quicker. At this time, Bletchley Park had two copies of the same message and the prime mistake was that both were sent using the same key. The folks at Bletchley park were not just great mathematicians, but the y also had an exceptional(a) sense of awareness. They proceeded to add the two messages together, essentially cancelling out the keys. They were now odd with two messages added together and then John Tiltman, an experience code breaker who not just able to figure out the message, but also figured out the key.John Tiltman gave this key to Bill Tutte, a infantile graduate from Cambridge who liked solving puzzles. He was able to out the length of the key by writing it down in rows with the aim to find out patterns. Bill Tutte found that the pattern of the wheel on the right had a period of 41. However, the pattern was not perfect and had an element of sec which suggested that a wheel on the left was used that moved only sometimes. This information was enough for other mathematicians to jump onboard and fully figure out the Lorenz machine.The Enigma on the other hand had multiple variations in the anatomical structure of the machine throughout its useful life to be cracked at one go. The earlier versions of the Enigma were using a 3-rotor structure which was used as the main subject by the Polish Cipher Bureau. Marian Rejewski who worked for the bureau made significant developments in breaking the Enigma, without having much rise to power to any of the official information about its inner workings.Rejewski developed a bomba machine in the process, this cryptanalysis machine was build using the observations Rejewski gathered that showed that the first three letters of a message were the same as the second three. Rejewskis method failed when in 1938 the Germans increased the rotors to include two excess ones. It was Alan Turing who developed a sophisticated Bombe that used statistics and the Bayes law for reason the probability to narrow down on the number of possibilities. The bombe machines were also quick updated to test the hypothesis.Figure 7 The British Bombe currently in display at the Bletchley ParkAlan Turings Bombe was composed of drums which tog ether simulated an enigma and each drum replicated the functioning of one rotor of the machine. The objective of the Turings bombe was to find out the key used by the Enigma, the starting position of the rotors and the steckers or plugs. The drums were knowing to move from a set starting position every time. The cause was designed with the help of statistics and the Bayes law, hence the key space was greatly reduced thereby reducing the run time.Alan Turing has been regarded as one of the biggest contributors to defeating the German navy by helping the Allied Forced during the World War II. It is believed that the British employed 200 Bombes during the Second World War and conjointly these Bombes decoded 4000 messages on any given day. The cryptanalysis of the Enigma is believed to have contributed to saving millions of lives and is identified as a prime reason why the war ended years before what it couldve lasted.Britains World War II codebreakers were centrally located at Bletch ley Park, a code-breaking center run by the United Kingdom Government Code and Cypher School (GCCS). They primarily center on deciphering German Enigma and Lorenz communications and producing ultra intelligence (Hinsley, 1996). radical was the designation for high level encrypted Axis-power intelligence the codebreakers intercepted and decrypted (Hinsley, 1993). Ultra-intelligence generated by decrypted Enigma and Lorenz signals is attribute with shortening the war, and without it the outcome of the war may have been different (Hinsley, 1996).The Enigma machine was the Germans primary encryption method during the war. Alan Turing, working at Bletchley Park in 1939, created the Bombe, which was an electromechanical machine used to decrypt Enigma ciphers (Smith, 2007). Gordon Welchman graceful the Bombe in 1940 with a diagonal board, increasing the Bombes efficiency (Budiansky, 2000). Welchmans diagonal board addressed the plug board vulnerability in the Enigma. The Bombe was based on the Bomba, a Polish machine designed to break Enigma ciphers, which was created by Marian Rejewski (Kozaczuk, 1984). The creation of the functional Bombes led to Allies deciphering of Enigma signals. set about in 1940, Germany started developing more advanced machines that used the Lorenz cipher. The first was called the SZ40 machine, which was codenamed tuna fish by the British codebreakers at Bletchley Park, and was followed by subsequent versions (SZ40A, SZ40B, and SZ42 (Copeland, 2006). These machines produced more heterogeneous ciphers than the Enigma, and were ultimately defeated by the 1+2 break in method created by Bill Tutte (Copeland, 2006).Multiple advanced decryption machines were designed to combat the Lorenz ciphers. First was the British Tunny Machine, which replicated the functions of the SZ40 machines. With the proper cam settings, it was able to produce clear text from cipher text that was input into it (Hinsley, 1993). Built on the Tunny machines, the Heath Robinson, or Robinsons, were created to automate the 1+2 break in (Copeland, 2006). They ran paper tapes to find the wheel settings of the Lorenz machine. Although they were functional, issues with keeping the paper tapes synchronised and slow processing speed limited their effectiveness (Copeland, 2006).Working on the Robinsons at Bletchley Park, Tommy Flowers was instrumental in the advancement of the hulk computer. demon was capable of faster processing than the Robinsons due to processing electronically. This also allowed for only one paper tape, which did not have to be synchronized with another and could be run at a faster speed, around 5,000 characters per second (Copeland, 2006).Although the giant computer was created first, the American ENIAC was often credited for being the first electronic digital computer ever made. This was caused by Colossus being shrouded in secrecy after World War II. The term computer before referred to a human operator who performed mathematic al computations. As the need for more demanding and complex computations increased, a push for electronic or digital computing began (Copeland, 2006).Computers like Colossus and ENIAC were called program-controlled computers, in which programs each computer was to process were not stored in the computers memory they had to be manually programmed. For Colossus and ENIAC, this involved modifying wiring by hand using plugs and switches. Modern computers utilize a stored-program concept, in which the programs a computer runs are stored in that computers memory (Copeland, 2006).The concept of the modern computer started with Alan Turing in 1936. He described a universal computing machine, containing limitless memory that stored both data and programs. A scanner would process the data based on the selected program. The use of any program with the data allowed the computer to process any calculation a human could, making it universal. Being universal allowed the computer to switch from on e task to another, as opposed to a completely different and unique machine needing to be created for each individual task (Copeland, 2006).Turings concept can be seen in modern computing today, where personal computers and mobile devices (smartphones, etcetera) store both data and programs, and can easily switch between different tasks based on the users needs. Programming to achieve a particular task is relatively simple in comparison installing a program in a modern computer is much less complex compared to rewiring something like the Colossus computer or creating a completely new machine entirely.As discussed, the Germans and Axis powers used Enigma and Lorenz ciphers heavily for their encrypted communications in World War II. The decryption of Enigma and Lorenz was key for the Allies and the development of Ultra intelligence, which likely shortened the war by years.In the end, the need for decrypting Enigma and Lorenz was the initial catalyst the eventually led to modern comput ing. Colossus, being the first electronic computer, spearheaded the push into the modern stored-program concept that computers and modern devices use today. Without this need for computing power, the world may well have progressed in a much different way.ReferencesBudiansky, S. (2000). Battle of Wits The Complete Story of Codebreaking in World War II. Free Press 1734.Cooper, S., Leeuwen, J. (2013). Alan Turing His Work and Impact. Saint Louis, U.S. Elsevier Science.Copeland, B., ed. (2006). Colossus The Secrets of Bletchley Parks Codebreaking Computers. Oxford Oxford University Press.Enigma Machine. (2006). In J. Merriman J. 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