Mathematical analysis
The Enigma transformation for each letter can be specified mathematically as a product of permutations. Assuming a three-rotor German Army/Air Force Enigma, let P denote the plugboard transformation, U denote that of the reflector ( U = U − 1 {\displaystyle U=U^{-1}} ), and L, M, R denote those of the left, middle and right rotors respectively. Then the encryption E can be expressed as
After each key press, the rotors turn, changing the transformation. For example, if the right-hand rotor R is rotated n positions, the transformation becomes
where ρ is the cyclic permutation mapping A to B, B to C, and so forth. Similarly, the middle and left-hand rotors can be represented as j and k rotations of M and L. The encryption transformation can then be described as
Combining three rotors from a set of five, each of the 3 rotor settings with 26 positions, and the plugboard with ten pairs of letters connected, the military Enigma has 158,962,555,217,826,360,000 different settings (nearly 159 quintillion or about 67 bits).[30]
A German Enigma operator would be given a plaintext message to encrypt. After setting up his machine, he would type the message on the Enigma keyboard. For each letter pressed, one lamp lit indicating a different letter according to a pseudo-random substitution determined by the electrical pathways inside the machine. The letter indicated by the lamp would be recorded, typically by a second operator, as the cyphertext letter. The action of pressing a key also moved one or more rotors so that the next key press used a different electrical pathway, and thus a different substitution would occur even if the same plaintext letter were entered again. For each key press there was rotation of at least the right hand rotor and less often the other two, resulting in a different substitution alphabet being used for every letter in the message. This process continued until the message was completed. The cyphertext recorded by the second operator would then be transmitted, usually by radio in Morse code, to an operator of another Enigma machine. This operator would type in the cyphertext and — as long as all the settings of the deciphering machine were identical to those of the enciphering machine — for every key press the reverse substitution would occur and the plaintext message would emerge.
In use, the Enigma required a list of daily key settings and auxiliary documents. In German military practice, communications were divided into separate networks, each using different settings. These communication nets were termed keys at Bletchley Park, and were assigned code names, such as Red, Chaffinch, and Shark. Each unit operating in a network was given the same settings list for its Enigma, valid for a period of time. The procedures for German Naval Enigma were more elaborate and more secure than those in other services and employed auxiliary codebooks. Navy codebooks were printed in red, water-soluble ink on pink paper so that they could easily be destroyed if they were endangered or if the vessel was sunk.
An Enigma machine's setting (its cryptographic key in modern terms; Schlüssel in German) specified each operator-adjustable aspect of the machine:
For a message to be correctly encrypted and decrypted, both sender and receiver had to configure their Enigma in the same way; rotor selection and order, ring positions, plugboard connections and starting rotor positions must be identical. Except for the starting positions, these settings were established beforehand, distributed in key lists and changed daily. For example, the settings for the 18th day of the month in the German Luftwaffe Enigma key list number 649 (see image) were as follows:
Enigma was designed to be secure even if the rotor wiring was known to an opponent, although in practice considerable effort protected the wiring configuration. If the wiring is secret, the total number of possible configurations has been calculated to be around 3×10114 (approximately 380 bits); with known wiring and other operational constraints, this is reduced to around 1023 (76 bits).[32] Because of the large number of possibilities, users of Enigma were confident of its security; it was not then feasible for an adversary to even begin to try a brute-force attack.
Most of the key was kept constant for a set time period, typically a day. A different initial rotor position was used for each message, a concept similar to an initialisation vector in modern cryptography. The reason is that encrypting many messages with identical or near-identical settings (termed in cryptanalysis as being in depth), would enable an attack using a statistical procedure such as Friedman's Index of coincidence.[33] The starting position for the rotors was transmitted just before the ciphertext, usually after having been enciphered. The exact method used was termed the indicator procedure. Design weakness and operator sloppiness in these indicator procedures were two of the main weaknesses that made cracking Enigma possible.
One of the earliest indicator procedures for the Enigma was cryptographically flawed and allowed Polish cryptanalysts to make the initial breaks into the plugboard Enigma. The procedure had the operator set his machine in accordance with the secret settings that all operators on the net shared. The settings included an initial position for the rotors (the Grundstellung), say, AOH. The operator turned his rotors until AOH was visible through the rotor windows. At that point, the operator chose his own arbitrary starting position for the message he would send. An operator might select EIN, and that became the message setting for that encryption session. The operator then typed EIN into the machine twice, this producing the encrypted indicator, for example XHTLOA. This was then transmitted, at which point the operator would turn the rotors to his message settings, EIN in this example, and then type the plaintext of the message.
At the receiving end, the operator set the machine to the initial settings (AOH) and typed in the first six letters of the message (XHTLOA). In this example, EINEIN emerged on the lamps, so the operator would learn the message setting that the sender used to encrypt this message. The receiving operator would set his rotors to EIN, type in the rest of the ciphertext, and get the deciphered message.
This indicator scheme had two weaknesses. First, the use of a global initial position (Grundstellung) meant all message keys used the same polyalphabetic substitution. In later indicator procedures, the operator selected his initial position for encrypting the indicator and sent that initial position in the clear. The second problem was the repetition of the indicator, which was a serious security flaw. The message setting was encoded twice, resulting in a relation between first and fourth, second and fifth, and third and sixth character. These security flaws enabled the Polish Cipher Bureau to break into the pre-war Enigma system as early as 1932. The early indicator procedure was subsequently described by German cryptanalysts as the "faulty indicator technique".
During World War II, codebooks were only used each day to set up the rotors, their ring settings and the plugboard. For each message, the operator selected a random start position, let's say WZA, and a random message key, perhaps SXT. He moved the rotors to the WZA start position and encoded the message key SXT. Assume the result was UHL. He then set up the message key, SXT, as the start position and encrypted the message. Next, he transmitted the start position, WZA, the encoded message key, UHL, and then the ciphertext. The receiver set up the start position according to the first trigram, WZA, and decoded the second trigram, UHL, to obtain the SXT message setting. Next, he used this SXT message setting as the start position to decrypt the message. This way, each ground setting was different and the new procedure avoided the security flaw of double encoded message settings.[35]
This procedure was used by Wehrmacht and Luftwaffe only. The Kriegsmarine procedures on sending messages with the Enigma were far more complex and elaborate. Prior to encryption the message was encoded using the Kurzsignalheft code book. The Kurzsignalheft contained tables to convert sentences into four-letter groups. A great many choices were included, for example, logistic matters such as refuelling and rendezvous with supply ships, positions and grid lists, harbour names, countries, weapons, weather conditions, enemy positions and ships, date and time tables. Another codebook contained the Kenngruppen and Spruchschlüssel: the key identification and message key.[36]
The Army Enigma machine used only the 26 alphabet characters. Punctuation was replaced with rare character combinations. A space was omitted or replaced with an X. The X was generally used as full-stop.
Some punctuation marks were different in other parts of the armed forces. The Wehrmacht replaced a comma with ZZ and the question mark with FRAGE or FRAQ.
The Kriegsmarine replaced the comma with Y and the question mark with UD. The combination CH, as in "Acht" (eight) or "Richtung" (direction), was replaced with Q (AQT, RIQTUNG). Two, three and four zeros were replaced with CENTA, MILLE and MYRIA.
The Wehrmacht and the Luftwaffe transmitted messages in groups of five characters and counted the letters.
The Kriegsmarine used four-character groups and counted those groups.
Frequently used names or words were varied as much as possible. Words like Minensuchboot (minesweeper) could be written as MINENSUCHBOOT, MINBOOT or MMMBOOT. To make cryptanalysis harder, messages were limited to 250 characters. Longer messages were divided into several parts, each using a different message key.[37][38]
Un-Supervised Learning
Jenis ini kebalikan dari supervised learning yaitu data yang diolah tidak memiliki label dan sistem tidak mengetahui output yang benar. Jenis ini memiliki dua tipe yaitu clustering dan dimensionality reduction yang biasa digunakan untuk data transaksional. Contoh machine learning jenis ini adalah identifikasi segmen konsumen, deteksi anomali, dan lain sebagainya.
General and cited references
Casino gambling machine
A slot machine, fruit machine (British English), poker machine or pokies (Australian English and New Zealand English) is a gambling machine that creates a game of chance for its customers.
A slot machine's standard layout features a screen displaying three or more reels that "spin" when the game is activated. Some modern slot machines still include a lever as a skeuomorphic design trait to trigger play. However, the mechanical operations of early machines have been superseded by random number generators, and most are now operated using buttons and touchscreens.
Slot machines include one or more currency detectors that validate the form of payment, whether coin, banknote, voucher, or token. The machine pays out according to the pattern of symbols displayed when the reels stop "spinning". Slot machines are the most popular gambling method in casinos and contribute about 70% of the average U.S. casino's income.[1]
Digital technology has resulted in variations in the original slot machine concept. As the player is essentially playing a video game, manufacturers can offer more interactive elements, such as advanced bonus rounds and more varied video graphics.
Belajar Workflow Machine Learning
Selanjutnya, kamu juga harus memahami proses atau workflow machine learning, yaitu:
Tipe Machine Learning Adalah:
Data yang diolah memiliki label. Jenis ini memiliki dua tipe yaitu klasifikasi dan regresi, jenis ini biasa digunakan pada aplikasi yang memprediksi kejadian di masa mendatang berdasarkan data historis.
Semi-Supervised Learning
Data yang diolah menggunakan data berlabel dan tidak berlabel. Biasanya digunakan dengan metode klasifikasi, regresi, dan prediksi. Contoh machine learning jenis ini adalah proses identifikasi wajah seseorang pada webcam atau kamera smartphone.
Machine learning adalah percabangan dari Artificial Intelligence atau AI yang fokus pada penggunaan data serta algoritma dalam meningkatkan keakuratan data. Wawasan yang dihasilkan melalui proses ini dapat mendorong pengambilan keputusan terhadap pembuatan aplikasi maupun kemajuan bisnis. Secara ideal, machine learning diperlukan dalam memengaruhi key growth metrics secara optimal. Terlebih lagi, teknologi ini sangat berperan dalam perkembangan dunia data.
Dengan pertumbuhan big data yang semakin pesat, tidak heran bila permintaan pasar dari profesi data terus meningkat. Di sinilah peran penting machine learning dalam memperhitungkan posisi big data perusahaan. Namun, meski vital dikuasai, survei dari Kaggle menunjukkan, masih sedikit tenaga profesional, khususnya Data Scientist, menguasai berbagai bidang dari machine learning, seperti supervised machine learning, unsupervised machine learning, computer vision, dan sebagainya.
Padahal, fungsi machine learning perlu diutamakan dalam dunia data. Sebagai salah satu skill yang relevan dan perlu dikuasai sebagai profesional data, baca lebih lanjut peran krusial machine learning bagi berbagai profesi yang ada. Jika kamu saat ini tertarik untuk berkarier di bidang machine learning, simak artikel ini sampai akhir untuk tahu info lengkap mengenai machine learning!
Bantu Pengambilan Keputusan
Algoritma machine learning bisa membantu perusahaan untuk membuat keputusan yang lebih baik berdasarkan data dan memberikan insight berdasarkan hasil analisis data.
Algoritma machine learning bisa digunakan untuk mempersonalisasi layanan dan produk untuk pelanggan, sehingga bisa meningkatkan kepuasan pelanggan.
Algoritma machine learning bisa digunakan di berbagai sektor atau industri bahkan bisa diterapkan di perusahaan skala kecil hingga besar.
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Standard SL-200 Automatic Slotting Machine:
An automatic slotting machine is a machine tool that is used to produce slots, or grooves, in a workpiece. It typically consists of a base, a table to hold the workpiece, and a slotting head that is mounted on a reciprocating ram. The slotting head contains a cutting tool, which is usually a rotary end mill, that is used to cut the slot into the workpiece. The machine is automatic because it is controlled by a computer numerical control (CNC) system, which allows the operator to input the desired dimensions and tolerances for the slot and to specify the cutting speed and feed rate. The CNC system also monitors the cutting process and makes adjustments as needed to ensure that the slot is produced to the required specifications.
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Tìm Người Yêu: Những Câu Chuyện Thành CôngTìm Người Yêu: Những Câu Chuyện Thành Công” là một chủ đề thú vị và đầy cảm hứng, đặc biệt trong bối cảnh hiện đại khi công nghệ và mạng xã hội ngày càng phát triển. Những câu chuyện thành công về hành trình tìm kiếm người yêu thường mang đến hy vọng và niềm tin cho những ai vẫn đang trên con đường tìm kiếm nửa kia của mình. Có người gặp được tình yêu đích thực qua một ứng dụng hẹn hò trực tuyến, người khác lại tìm thấy người bạn đời của mình trong một... Tìm Người Yêu: Những Câu Chuyện Thành CôngTìm Người Yêu: Những Câu Chuyện Thành Công” là một chủ đề thú vị và đầy cảm hứng, đặc biệt trong bối cảnh hiện đại khi công nghệ và mạng xã hội ngày càng phát triển. Những câu chuyện thành công về hành trình tìm kiếm người yêu thường mang đến hy vọng và niềm tin cho những ai vẫn đang trên con đường tìm kiếm nửa kia của mình. Có người gặp được tình yêu đích thực qua một ứng dụng hẹn hò trực tuyến, người khác lại tìm thấy người bạn đời của mình trong một buổi gặp gỡ bạn bè. Mỗi câu chuyện đều có những điểm chung là sự kiên nhẫn, niềm tin và lòng chân thành. Qua những câu chuyện này, chúng ta thấy rằng tình yêu không phân biệt tuổi tác, khoảng cách hay hoàn cảnh. Điều quan trọng là mỗi người đều có cơ hội tìm thấy tình yêu đích thực của mình, chỉ cần họ mở lòng và tin tưởng vào những điều tốt đẹp sẽ đến.Một trong những câu chuyện đáng nhớ là câu chuyện của Minh và Lan. Cả hai gặp nhau qua một ứng dụng hẹn hò trực tuyến, nơi họ bắt đầu bằng những cuộc trò chuyện đơn giản. Minh, một chàng trai trầm lắng và ít nói, đã dần dần mở lòng trước sự chân thành và ấm áp của Lan. Sau vài tháng trò chuyện, họ quyết định gặp nhau ngoài đời thực. Cuộc gặp gỡ đầu tiên tại một quán cà phê nhỏ đã trở thành điểm khởi đầu cho một mối quan hệ đẹp đẽ và lâu bền. Sự đồng điệu về sở thích và quan điểm sống đã giúp Minh và Lan xây dựng nên một tình yêu vững chắc, vượt qua mọi khó khăn và thử thách.Không chỉ có Minh và Lan, câu chuyện của Hùng và Mai cũng là một minh chứng cho việc tình yêu có thể đến từ những nơi bất ngờ nhất. Hùng và Mai gặp nhau trong một chuyến du lịch nhóm tổ chức bởi công ty. Ban đầu, họ chỉ xem nhau như những người bạn cùng đi du lịch, nhưng qua những hoạt động chung và những cuộc trò chuyện, họ dần nhận ra sự hòa hợp đặc biệt. Sau chuyến du lịch, Hùng quyết định tỏ tình với Mai và may mắn thay, cô cũng có tình cảm với anh. Họ đã cùng nhau vượt qua khoảng cách địa lý và xây dựng nên một mối tình bền chặt.Những câu chuyện này không chỉ là những minh chứng sống động cho sự tồn tại của tình yêu đích thực, mà còn mang lại niềm tin và hy vọng cho những ai vẫn đang tìm kiếm người bạn đời của mình. Dù là qua mạng xã hội, trong các chuyến du lịch hay trong những buổi gặp gỡ bạn bè, tình yêu có thể đến từ những nơi bất ngờ nhất và vào những thời điểm mà chúng ta không ngờ tới. Điều quan trọng là mỗi người cần mở lòng, kiên nhẫn và tin tưởng vào những điều tốt đẹp sẽ đến.Tình yêu không phân biệt tuổi tác, khoảng cách hay hoàn cảnh. Mỗi người đều có cơ hội tìm thấy tình yêu đích thực của mình, chỉ cần họ sẵn sàng mở lòng và tin tưởng vào hành trình tìm kiếm tình yêu của mình. Những câu chuyện thành công này là minh chứng rõ ràng nhất cho việc tình yêu đích thực vẫn tồn tại và luôn chờ đợi chúng ta tìm thấy. Xem thêm.
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German cipher machine
The Enigma machine is a cipher device developed and used in the early- to mid-20th century to protect commercial, diplomatic, and military communication. It was employed extensively by Nazi Germany during World War II, in all branches of the German military. The Enigma machine was considered so secure that it was used to encipher the most top-secret messages.[1]
The Enigma has an electromechanical rotor mechanism that scrambles the 26 letters of the alphabet. In typical use, one person enters text on the Enigma's keyboard and another person writes down which of the 26 lights above the keyboard illuminated at each key press. If plaintext is entered, the illuminated letters are the ciphertext. Entering ciphertext transforms it back into readable plaintext. The rotor mechanism changes the electrical connections between the keys and the lights with each keypress.
The security of the system depends on machine settings that were generally changed daily, based on secret key lists distributed in advance, and on other settings that were changed for each message. The receiving station would have to know and use the exact settings employed by the transmitting station to decrypt a message.
Although Nazi Germany introduced a series of improvements to the Enigma over the years that hampered decryption efforts, they did not prevent Poland from cracking the machine as early as December 1932 and reading messages prior to and into the war. Poland's sharing of their achievements enabled the Allies to exploit Enigma-enciphered messages as a major source of intelligence. Many commentators say the flow of Ultra communications intelligence from the decrypting of Enigma, Lorenz, and other ciphers shortened the war substantially and may even have altered its outcome.[3]
The Enigma machine was invented by German engineer Arthur Scherbius at the end of World War I.[4] The German firm Scherbius & Ritter, co-founded by Scherbius, patented ideas for a cipher machine in 1918 and began marketing the finished product under the brand name Enigma in 1923, initially targeted at commercial markets.[5] Early models were used commercially from the early 1920s, and adopted by military and government services of several countries, most notably Nazi Germany before and during World War II.[6]
Several Enigma models were produced,[7] but the German military models, having a plugboard, were the most complex. Japanese and Italian models were also in use.[8] With its adoption (in slightly modified form) by the German Navy in 1926 and the German Army and Air Force soon after, the name Enigma became widely known in military circles. Pre-war German military planning emphasized fast, mobile forces and tactics, later known as blitzkrieg, which depended on radio communication for command and coordination. Since adversaries would likely intercept radio signals, messages had to be protected with secure encipherment. Compact and easily portable, the Enigma machine filled that need.
Hans-Thilo Schmidt was a German who spied for the French, obtaining access to German cipher materials that included the daily keys used in September and October 1932. Those keys included the plugboard settings. The French passed the material to Poland. Around December 1932, Marian Rejewski, a Polish mathematician and cryptologist at the Polish Cipher Bureau, used the theory of permutations, and flaws in the German military-message encipherment procedures, to break message keys of the plugboard Enigma machine. Rejewski used the French supplied material and the message traffic that took place in September and October to solve for the unknown rotor wiring. Consequently, the Polish mathematicians were able to build their own Enigma machines, dubbed "Enigma doubles". Rejewski was aided by fellow mathematician-cryptologists Jerzy Różycki and Henryk Zygalski, both of whom had been recruited with Rejewski from Poznań University, which had been selected for its students' knowledge of the German language, since that area was held by Germany prior to World War I. The Polish Cipher Bureau developed techniques to defeat the plugboard and find all components of the daily key, which enabled the Cipher Bureau to read German Enigma messages starting from January 1933.[11]
Over time, the German cryptographic procedures improved, and the Cipher Bureau developed techniques and designed mechanical devices to continue reading Enigma traffic. As part of that effort, the Poles exploited quirks of the rotors, compiled catalogues, built a cyclometer (invented by Rejewski) to help make a catalogue with 100,000 entries, invented and produced Zygalski sheets, and built the electromechanical cryptologic bomba (invented by Rejewski) to search for rotor settings. In 1938 the Poles had six bomby (plural of bomba), but when that year the Germans added two more rotors, ten times as many bomby would have been needed to read the traffic.
On 26 and 27 July 1939, in Pyry, just south of Warsaw, the Poles initiated French and British military intelligence representatives into the Polish Enigma-decryption techniques and equipment, including Zygalski sheets and the cryptologic bomb, and promised each delegation a Polish-reconstructed Enigma (the devices were soon delivered).
In September 1939, British Military Mission 4, which included Colin Gubbins and Vera Atkins, went to Poland, intending to evacuate cipher-breakers Marian Rejewski, Jerzy Różycki, and Henryk Zygalski from the country. The cryptologists, however, had been evacuated by their own superiors into Romania, at the time a Polish-allied country. On the way, for security reasons, the Polish Cipher Bureau personnel had deliberately destroyed their records and equipment. From Romania they traveled on to France, where they resumed their cryptological work, collaborating by teletype with the British, who began work on decrypting German Enigma messages, using the Polish equipment and techniques.
Gordon Welchman, who became head of Hut 6 at Bletchley Park, wrote: "Hut 6 Ultra would never have got off the ground if we had not learned from the Poles, in the nick of time, the details both of the German military version of the commercial Enigma machine, and of the operating procedures that were in use." The Polish transfer of theory and technology at Pyry formed the crucial basis for the subsequent World War II British Enigma-decryption effort at Bletchley Park, where Welchman worked.
During the war, British cryptologists decrypted a vast number of messages enciphered on Enigma. The intelligence gleaned from this source, codenamed "Ultra" by the British, was a substantial aid to the Allied war effort.[a]
Though Enigma had some cryptographic weaknesses, in practice it was German procedural flaws, operator mistakes, failure to systematically introduce changes in encipherment procedures, and Allied capture of key tables and hardware that, during the war, enabled Allied cryptologists to succeed.
The Abwehr used different versions of Enigma machines. In November 1942, during Operation Torch, a machine was captured which had no plugboard and the three rotors had been changed to rotate 11, 15, and 19 times rather than once every 26 letters, plus a plate on the left acted as a fourth rotor.[19] From October 1944, the German Abwehr used the Schlüsselgerät 41.[20]
The Abwehr code had been broken on 8 December 1941 by Dilly Knox. Agents sent messages to the Abwehr in a simple code which was then sent on using an Enigma machine. The simple codes were broken and helped break the daily Enigma cipher. This breaking of the code enabled the Double-Cross System to operate.[19]
Like other rotor machines, the Enigma machine is a combination of mechanical and electrical subsystems. The mechanical subsystem consists of a keyboard; a set of rotating disks called rotors arranged adjacently along a spindle; one of various stepping components to turn at least one rotor with each key press, and a series of lamps, one for each letter. These design features are the reason that the Enigma machine was originally referred to as the rotor-based cipher machine during its intellectual inception in 1915.[21]
An electrical pathway is a route for current to travel. By manipulating this phenomenon the Enigma machine was able to scramble messages.[21] The mechanical parts act by forming a varying electrical circuit. When a key is pressed, one or more rotors rotate on the spindle. On the sides of the rotors are a series of electrical contacts that, after rotation, line up with contacts on the other rotors or fixed wiring on either end of the spindle. When the rotors are properly aligned, each key on the keyboard is connected to a unique electrical pathway through the series of contacts and internal wiring. Current, typically from a battery, flows through the pressed key, into the newly configured set of circuits and back out again, ultimately lighting one display lamp, which shows the output letter. For example, when encrypting a message starting ANX..., the operator would first press the A key, and the Z lamp might light, so Z would be the first letter of the ciphertext. The operator would next press N, and then X in the same fashion, and so on.
Current flows from the battery (1) through a depressed bi-directional keyboard switch (2) to the plugboard (3). Next, it passes through the (unused in this instance, so shown closed) plug "A" (3) via the entry wheel (4), through the wiring of the three (Wehrmacht Enigma) or four (Kriegsmarine M4 and Abwehr variants) installed rotors (5), and enters the reflector (6). The reflector returns the current, via an entirely different path, back through the rotors (5) and entry wheel (4), proceeding through plug "S" (7) connected with a cable (8) to plug "D", and another bi-directional switch (9) to light the appropriate lamp.[22]
The repeated changes of electrical path through an Enigma scrambler implement a polyalphabetic substitution cipher that provides Enigma's security. The diagram on the right shows how the electrical pathway changes with each key depression, which causes rotation of at least the right-hand rotor. Current passes into the set of rotors, into and back out of the reflector, and out through the rotors again. The greyed-out lines are other possible paths within each rotor; these are hard-wired from one side of each rotor to the other. The letter A encrypts differently with consecutive key presses, first to G, and then to C. This is because the right-hand rotor steps (rotates one position) on each key press, sending the signal on a completely different route. Eventually other rotors step with a key press.
The rotors (alternatively wheels or drums, Walzen in German) form the heart of an Enigma machine. Each rotor is a disc approximately 10 cm (3.9 in) in diameter made from Ebonite or Bakelite with 26 brass, spring-loaded, electrical contact pins arranged in a circle on one face, with the other face housing 26 corresponding electrical contacts in the form of circular plates. The pins and contacts represent the alphabet — typically the 26 letters A–Z, as will be assumed for the rest of this description. When the rotors are mounted side by side on the spindle, the pins of one rotor rest against the plate contacts of the neighbouring rotor, forming an electrical connection. Inside the body of the rotor, 26 wires connect each pin on one side to a contact on the other in a complex pattern. Most of the rotors are identified by Roman numerals, and each issued copy of rotor I, for instance, is wired identically to all others. The same is true for the special thin beta and gamma rotors used in the M4 naval variant.
By itself, a rotor performs only a very simple type of encryption, a simple substitution cipher. For example, the pin corresponding to the letter E might be wired to the contact for letter T on the opposite face, and so on. Enigma's security comes from using several rotors in series (usually three or four) and the regular stepping movement of the rotors, thus implementing a polyalphabetic substitution cipher.
Each rotor can be set to one of 26 starting positions when placed in an Enigma machine. After insertion, a rotor can be turned to the correct position by hand, using the grooved finger-wheel which protrudes from the internal Enigma cover when closed. In order for the operator to know the rotor's position, each has an alphabet tyre (or letter ring) attached to the outside of the rotor disc, with 26 characters (typically letters); one of these is visible through the window for that slot in the cover, thus indicating the rotational position of the rotor. In early models, the alphabet ring was fixed to the rotor disc. A later improvement was the ability to adjust the alphabet ring relative to the rotor disc. The position of the ring was known as the Ringstellung ("ring setting"), and that setting was a part of the initial setup needed prior to an operating session. In modern terms it was a part of the initialization vector.
Each rotor contains one or more notches that control rotor stepping. In the military variants, the notches are located on the alphabet ring.
The Army and Air Force Enigmas were used with several rotors, initially three. On 15 December 1938, this changed to five, from which three were chosen for a given session. Rotors were marked with Roman numerals to distinguish them: I, II, III, IV and V, all with single turnover notches located at different points on the alphabet ring. This variation was probably intended as a security measure, but ultimately allowed the Polish Clock Method and British Banburismus attacks.
The Naval version of the Wehrmacht Enigma had always been issued with more rotors than the other services: At first six, then seven, and finally eight. The additional rotors were marked VI, VII and VIII, all with different wiring, and had two notches, resulting in more frequent turnover. The four-rotor Naval Enigma (M4) machine accommodated an extra rotor in the same space as the three-rotor version. This was accomplished by replacing the original reflector with a thinner one and by adding a thin fourth rotor. That fourth rotor was one of two types, Beta or Gamma, and never stepped, but could be manually set to any of 26 positions. One of the 26 made the machine perform identically to the three-rotor machine.
To avoid merely implementing a simple (solvable) substitution cipher, every key press caused one or more rotors to step by one twenty-sixth of a full rotation, before the electrical connections were made. This changed the substitution alphabet used for encryption, ensuring that the cryptographic substitution was different at each new rotor position, producing a more formidable polyalphabetic substitution cipher. The stepping mechanism varied slightly from model to model. The right-hand rotor stepped once with each keystroke, and other rotors stepped less frequently.
The advancement of a rotor other than the left-hand one was called a turnover by the British. This was achieved by a ratchet and pawl mechanism. Each rotor had a ratchet with 26 teeth and every time a key was pressed, the set of spring-loaded pawls moved forward in unison, trying to engage with a ratchet. The alphabet ring of the rotor to the right normally prevented this. As this ring rotated with its rotor, a notch machined into it would eventually align itself with the pawl, allowing it to engage with the ratchet, and advance the rotor on its left. The right-hand pawl, having no rotor and ring to its right, stepped its rotor with every key depression.[23] For a single-notch rotor in the right-hand position, the middle rotor stepped once for every 26 steps of the right-hand rotor. Similarly for rotors two and three. For a two-notch rotor, the rotor to its left would turn over twice for each rotation.
The first five rotors to be introduced (I–V) contained one notch each, while the additional naval rotors VI, VII and VIII each had two notches. The position of the notch on each rotor was determined by the letter ring which could be adjusted in relation to the core containing the interconnections. The points on the rings at which they caused the next wheel to move were as follows.[24]
The design also included a feature known as double-stepping. This occurred when each pawl aligned with both the ratchet of its rotor and the rotating notched ring of the neighbouring rotor. If a pawl engaged with a ratchet through alignment with a notch, as it moved forward it pushed against both the ratchet and the notch, advancing both rotors. In a three-rotor machine, double-stepping affected rotor two only. If, in moving forward, the ratchet of rotor three was engaged, rotor two would move again on the subsequent keystroke, resulting in two consecutive steps. Rotor two also pushes rotor one forward after 26 steps, but since rotor one moves forward with every keystroke anyway, there is no double-stepping.[23] This double-stepping caused the rotors to deviate from odometer-style regular motion.
With three wheels and only single notches in the first and second wheels, the machine had a period of 26×25×26 = 16,900 (not 26×26×26, because of double-stepping).[23] Historically, messages were limited to a few hundred letters, and so there was no chance of repeating any combined rotor position during a single session, denying cryptanalysts valuable clues.
To make room for the Naval fourth rotors, the reflector was made much thinner. The fourth rotor fitted into the space made available. No other changes were made, which eased the changeover. Since there were only three pawls, the fourth rotor never stepped, but could be manually set into one of 26 possible positions.
A device that was designed, but not implemented before the war's end, was the Lückenfüllerwalze (gap-fill wheel) that implemented irregular stepping. It allowed field configuration of notches in all 26 positions. If the number of notches was a relative prime of 26 and the number of notches were different for each wheel, the stepping would be more unpredictable. Like the Umkehrwalze-D it also allowed the internal wiring to be reconfigured.[25]
The current entry wheel (Eintrittswalze in German), or entry stator, connects the plugboard to the rotor assembly. If the plugboard is not present, the entry wheel instead connects the keyboard and lampboard to the rotor assembly. While the exact wiring used is of comparatively little importance to security, it proved an obstacle to Rejewski's progress during his study of the rotor wirings. The commercial Enigma connects the keys in the order of their sequence on a QWERTZ keyboard: Q→A, W→B, E→C and so on. The military Enigma connects them in straight alphabetical order: A→A, B→B, C→C, and so on. It took inspired guesswork for Rejewski to penetrate the modification.
With the exception of models A and B, the last rotor came before a 'reflector' (German: Umkehrwalze, meaning 'reversal rotor'), a patented feature[26] unique to Enigma among the period's various rotor machines. The reflector connected outputs of the last rotor in pairs, redirecting current back through the rotors by a different route. The reflector ensured that Enigma would be self-reciprocal; thus, with two identically configured machines, a message could be encrypted on one and decrypted on the other, without the need for a bulky mechanism to switch between encryption and decryption modes. The reflector allowed a more compact design, but it also gave Enigma the property that no letter ever encrypted to itself. This was a severe cryptological flaw that was subsequently exploited by codebreakers.
In Model 'C', the reflector could be inserted in one of two different positions. In Model 'D', the reflector could be set in 26 possible positions, although it did not move during encryption. In the Abwehr Enigma, the reflector stepped during encryption in a manner similar to the other wheels.
In the German Army and Air Force Enigma, the reflector was fixed and did not rotate; there were four versions. The original version was marked 'A', and was replaced by Umkehrwalze B on 1 November 1937. A third version, Umkehrwalze C was used briefly in 1940, possibly by mistake, and was solved by Hut 6. The fourth version, first observed on 2 January 1944, had a rewireable reflector, called Umkehrwalze D, nick-named Uncle Dick by the British, allowing the Enigma operator to alter the connections as part of the key settings.
The plugboard (Steckerbrett in German) permitted variable wiring that could be reconfigured by the operator. It was introduced on German Army versions in 1928,[29] and was soon adopted by the Reichsmarine (German Navy). The plugboard contributed more cryptographic strength than an extra rotor, as it had 150 trillion possible settings (see below).[30] Enigma without a plugboard (known as unsteckered Enigma) could be solved relatively straightforwardly using hand methods; these techniques were generally defeated by the plugboard, driving Allied cryptanalysts to develop special machines to solve it.
A cable placed onto the plugboard connected letters in pairs; for example, E and Q might be a steckered pair. The effect was to swap those letters before and after the main rotor scrambling unit. For example, when an operator pressed E, the signal was diverted to Q before entering the rotors. Up to 13 steckered pairs might be used at one time, although only 10 were normally used.
Current flowed from the keyboard through the plugboard, and proceeded to the entry-rotor or Eintrittswalze. Each letter on the plugboard had two jacks. Inserting a plug disconnected the upper jack (from the keyboard) and the lower jack (to the entry-rotor) of that letter. The plug at the other end of the crosswired cable was inserted into another letter's jacks, thus switching the connections of the two letters.
Other features made various Enigma machines more secure or more convenient.[31]
Some M4 Enigmas used the Schreibmax, a small printer that could print the 26 letters on a narrow paper ribbon. This eliminated the need for a second operator to read the lamps and transcribe the letters. The Schreibmax was placed on top of the Enigma machine and was connected to the lamp panel. To install the printer, the lamp cover and light bulbs had to be removed. It improved both convenience and operational security; the printer could be installed remotely such that the signal officer operating the machine no longer had to see the decrypted plaintext.
Another accessory was the remote lamp panel Fernlesegerät. For machines equipped with the extra panel, the wooden case of the Enigma was wider and could store the extra panel. A lamp panel version could be connected afterwards, but that required, as with the Schreibmax, that the lamp panel and light bulbs be removed.[22] The remote panel made it possible for a person to read the decrypted plaintext without the operator seeing it.
In 1944, the Luftwaffe introduced a plugboard switch, called the Uhr (clock), a small box containing a switch with 40 positions. It replaced the standard plugs. After connecting the plugs, as determined in the daily key sheet, the operator turned the switch into one of the 40 positions, each producing a different combination of plug wiring. Most of these plug connections were, unlike the default plugs, not pair-wise.[22] In one switch position, the Uhr did not swap letters, but simply emulated the 13 stecker wires with plugs.
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