Branches of Mathematics

Pure mathematics

• Algebra
• Calculus
• Geometry
• Topology
• Trignometry
• Combinatorics
• Logic
• Number theory

Applied mathematics

• Dynamical systems and differential equations
• Mathematical physics
• Computing
• Information theory and signal processing
• Probability and statistics
• Game theory
• Operations research

Related Topics

• Electromagnetic Spectrum
• Linear Equations
• Applied Physics
• Nano Technology
• Engineering Sciences
• Mathematical Medicine
• Fluid dynamics
• Computational Mathematics
• Gamma Ray Optics
• Onfrared Optics
• Relative Velocity
• Iciam
• Intelligent Imaging Neuroscience
• Biomedical Engineering
• Neuroscience Research
• Quantum Cosmology
• Brain Research

• A5 2
• Abraham Sinkov
• Agnes Meyer Driscoll
• Al-Kindi
• Alan Turing
• Alastair Denniston
• Algorithm
• Alphabet
• Arab
• Arthur Scherbius
• Axis Powers
• Battle of Midway
• Betrayal
• Birthday attack
• Biuro Szyfrów
• Blaise de Vigenère
• Bletchley Park
• Block cipher
• Bomba (cryptography)
• Bombe
• Boomerang attack
• Bruce Schneier
• Brute force attack
• Brute-force search
• Bugging
• Charles Babbage
• Christopher Swenson
• Cipher
• Ciphertext
• Classical cipher
• CMEA (cipher)
• Code (cryptography)
• Codetext
• Coevolution
• Collision attack
• Colossus computer
• Colossus computers
• Cryptanalysis
• Cryptographic
• Cryptography
• Cryptologia
• Cryptosystem
• David Kahn (writer)
• Davies' attack
• DECT Standard Cipher
• DES
• Dilly Knox
• Discrete logarithm
• Don Coppersmith
• Dwight D. Eisenhower
• E
• EFF DES cracker
• Elizebeth Friedman
• English language
• Enigma machine
• Espionage
• Exclusive or
• F. W. Winterbotham
• F.W. Winterbotham
• FEAL
• Fialka
• Frank Rowlett
• Frequency analysis
• Friedrich Kasiski
• GCHQ
• Gilbert Vernam
• Giovanni Soro
• Greek language
• Grover's algorithm
• Harry Hinsley
• Herbert Yardley
• Ibrahim A. Al-Kadi
• Ibrahim Al-Kadi
• Index of coincidence
• Information entropy
• Information security
• Iran
• Italy
• Jack Copeland
• Japanese naval codes
• John Tiltman
• John Wallis
• Josef Pieprzyk
• Joseph Rochefort
• Kasiski examination
• Key (cryptography)
• Key size
• Lars Knudsen
• Lars R. Knudsen
• Linear cryptanalysis
• Linguistics
• Lorenz cipher
• Madryga
• Magic (cryptography)
• Marian Rejewski
• Mary, Queen of Scots
• Mathematical problem
• Mathematics
• MD5
• Meredith Gardner
• Military espionage
• Mobile phone
• Mod-n cryptanalysis
• Modular arithmetic
• Moore's law
• Nazi Germany
• NSA
• Orders of magnitude
• Permutation
• Peter Calvocoressi
• Plaintext
• Polymath
• Polynomial time
• Portal Cryptography
• Power analysis
• Public key
• Punched card
• Pure mathematics
• Purple code
• Quantum computer
• Quantum cryptography
• Rainbow table
• RC4
• Related-key attack
• Replay attack
• Reverse engineering
• Rotor cipher machine
• Sandwich attack
• Security engineering
• SHA-1
• Shannon
• Shor's Algorithm
• Side channel attack
• Side-channel attacks
• Simon Singh
• Slide attack
• Solomon Kullback
• Statistics
• Steganography
• Stream cipher
• The Codebreakers
• Thomas Phelippes
• Timing analysis
• Treason
• Ultra (cryptography)
• Vigenère cipher
• W. T. Tutte
• Wi-Fi
• William F. Friedman
• William Friedman
• Wireless network
• World War I
• World War II
• XSL attack
• Zendian Problem
• Zimmermann Telegram
• 
  

• 
  Bletchley Park
  Coordinates: 51°59′47″N 0°44′34″W / 51.99651°N 0.74276°W / 51.99651; -0.74276
  Bletchley Park is an estate located in the town of Bletchley, in Buckinghamshire, England, which currently houses the National Codes Centre and the National Museum of Computing. During the Second World War, Bletchley Park was the site of the United Kingdom's main decryption establishment, the Government Code and Cypher School (GC&CS), where ciphers and codes of several Axis countries were decrypted, most importantly the ciphers generated by the German Enigma and Lorenz machines. It also housed Station X, a secret radio intercept station. Although interception was soon moved to a location with better reception, the name persisted for the Bletchley Park wartime activities.
  The high-level intelligence produced at Bletchley Park, codenamed Ultra, provided crucial assistance to the Allied war effort. Sir Harry Hinsley, a Bletchley veteran and the official historian of British Intelligence during the Second World War, said that Ultra shortened the war by two to four years and that the outcome of the war would have been uncertain without it.
  
  wn.com/Bletchley_Park
• 
  Iran
  Coordinates: 32°N 53°E / 32°N 53°E / 32; 53
  Iran (ⁱ/ɪˈrɑːn/ or /aɪˈræn/;Persian: ایران‎ [ʔiˈɾɒn] ( listen)), officially the Islamic Republic of Iran (Persian: جمهوری اسلامی ایران‎ Jomhuri-ye Eslāmi-ye Irān), is a country in Southern and Western Asia. The name "Iran", which in Persian means "Land of the Aryans", has been in use natively since the Sassanian era. It came into use internationally in 1935, before which the country was known to the Western world as Persia ( /ˈpɜrʒə/ or /ˈpɜrʃə/). Both "Persia" and "Iran" are used interchangeably in cultural contexts; however, "Iran" is the name used officially in political contexts.
  The 18th-largest country in the world in terms of area at 1,648,195 km² (636,372 sq mi), Iran has a population of around 79 million. It is a country of particular geopolitical significance owing to its location in the Middle East and central Eurasia. Iran is bordered on the north by Armenia, Azerbaijan and Turkmenistan. As Iran is a littoral state of the Caspian Sea, which is an inland sea, Kazakhstan and Russia are also Iran's direct neighbors to the north. Iran is bordered on the east by Afghanistan and Pakistan, on the south by the Persian Gulf and the Gulf of Oman, on the west by Iraq and on the northwest by Turkey. Tehran is the capital, the country's largest city and the political, cultural, commercial and industrial center of the nation. Iran is a regional power, and holds an important position in international energy security and world economy as a result of its large reserves of petroleum and natural gas. Iran has the second largest proven natural gas reserves in the world and the fourth largest proven petroleum reserves.
  
  wn.com/Iran
• 
  Italy
  Italy ⁱ/ˈɪtəli/ (Italian: Italia [iˈtaːlja]), officially the Italian Republic or the Republic of Italy (Italian: Repubblica italiana), is a unitary parliamentary republic in south-central Europe. To the north, it borders France, Switzerland, Austria and Slovenia along the Alps. To the south, it consists of the entirety of the Italian Peninsula, Sicily, Sardinia–the two largest islands in the Mediterranean Sea–and many other smaller islands. The independent states of San Marino and the Vatican City are enclaves within Italy, while Campione d'Italia is an Italian exclave in Switzerland. The territory of Italy covers some 301,338 km² (116,347 sq mi) and is influenced by a temperate seasonal climate. With 60.6 million inhabitants, it is the fifth most populous country in Europe, and the 23rd most populous in the world.
  Rome, the capital of Italy, was for centuries a political and religious centre of Western civilisation as the capital of the Roman Empire and site of the Holy See. After the decline of the Roman Empire, Italy endured numerous invasions by foreign peoples, from Germanic tribes such as the Lombards and Ostrogoths, to the Byzantines and later, the Normans, among others. Centuries later, Italy became the birthplace of Maritime republics and the Renaissance, an immensely fruitful intellectual movement that would prove to be integral in shaping the subsequent course of European thought.
  
  wn.com/Italy
• 
  Nazi Germany
  The Third Reich, also Nazi Germany, is the common name for Germany when it was a totalitarian state ruled by Adolf Hitler and the National Socialist German Workers' Party (NSDAP). On 30 January 1933 Hitler became chancellor of Germany, quickly eliminating all opposition to rule as sole leader. The state idolized Hitler as its Führer ("leader"), centralizing all power in his hands. Historians have emphasized the hypnotic effect of his rhetoric on large audiences, and of his eyes in small groups. Kessel writes, "Overwhelmingly...Germans speak with mystification of Hitler's 'hypnotic' appeal..." Under the "leader principle", the Führer's word was above all other laws. Top officials reported to Hitler and followed his policies, but they had considerable autonomy. The government was not a coordinated, cooperating body, but rather a collection of factions struggling to amass power and curry favor with the Führer. In the midst of the Great Depression, the Nazi government restored prosperity and ended mass unemployment using heavy military spending and a mixed economy of free-market and central-planning practices. Extensive public works were undertaken, including the construction of the Autobahns. The return to prosperity gave the regime enormous popularity; the suppression of all opposition made Hitler's rule mostly unchallenged.
  
  wn.com/Nazi_Germany

• 
  Abraham Sinkov
  Dr. Abraham Sinkov (1907–1998) was a US cryptanalyst.
  Sinkov, the son of immigrants from Russia, was born in Philadelphia, but grew up in Brooklyn. After graduating from Boys High School—what today would be called a "magnet school" – he took his B.S. in mathematics from City College of New York. (By coincidence, one of his close friends at Boys High and CCNY was Solomon Kullback). Mr. Sinkov taught in New York City schools but was unhappy with the working conditions and anxious to use his mathematics knowledge in practical ways.
  The opportunity for a career change came in 1930. Sinkov and Kullback took the Civil Service examination and placed high. Both received mysterious letters from Washington asking about their knowledge of foreign languages. Sinkov knew French and Kullback, Spanish. This was acceptable to their prospective employer, and they were offered positions as junior cryptanalysts. Although neither was quite certain what a cryptanalyst did, they accepted.
  The small Signals Intelligence Service (SIS) organization (Sinkov and Kullback were the third and fourth employees there) had the primary mission of compiling codes and ciphers for use by the U.S. Army. Its secondary task was to attempt to solve selected foreign codes and ciphers—this was not necessarily done for intelligence purposes but to keep the cryptanalysts abreast of new developments in the field.
  
  wn.com/Abraham_Sinkov
• 
  Agnes Meyer Driscoll
  Agnes Meyer Driscoll (July 24, 1889 - September 16, 1971) was, known as Miss Aggie or Madame X, an American cryptanalyst during both World War I and World War II.
  Born in Illinois in 1889, Agnes May Meyer moved with her family to Westerville, Ohio in 1895 where her father, Gustav Meyer, had taken a job teaching music at Otterbein College. In 1909 he donated the family home to the Anti-Saloon League which recently moved its headquarters to Westerville.
  Meyer attended Otterbein College from 1907-1909. In 1911 she received an A.B. degree from Ohio State University, majoring in mathematics, physics, foreign languages, and music. From her earliest days as a college student, she pursued technical and scientific studies. After graduation, she moved to Amarillo, Texas, where she was director of music at a military academy, and, later, chair of the mathematics department at the local high school.
  On June 22, 1918, about one year after America entered World War I, Agnes Meyer enlisted in the United States Navy. She was recruited at the highest possible rank of chief yeoman and was assigned to the Code and Signal section of the Director of Naval Communications. Except for a two-year hiatus, when she worked for a private firm, she would remain a leading cryptanalyst for the U.S. Navy until 1949.
  
  wn.com/Agnes_Meyer_Driscoll
• 
  Alan Turing
  Alan Mathison Turing, OBE, FRS ( /ˈtjʊərɪŋ/ TEWR-ing; 23 June 1912 – 7 June 1954), was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a significant role in the creation of the modern computer. Turing is widely considered to be the father of computer science and artificial intelligence.
  During the Second World War, Turing worked for the Government Code and Cypher School (GCCS) at Bletchley Park, Britain's codebreaking centre. For a time he was head of Hut 8, the section responsible for German naval cryptanalysis. He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine that could find settings for the Enigma machine.
  After the war he worked at the National Physical Laboratory, where he created one of the first designs for a stored-program computer, the ACE. In 1948 Turing joined Max Newman's Computing Laboratory at Manchester University, where he assisted in the development of the Manchester computers and became interested in mathematical biology. He wrote a paper on the chemical basis of morphogenesis, and he predicted oscillating chemical reactions such as the Belousov–Zhabotinsky reaction, which were first observed in the 1960s.
  
  wn.com/Alan_Turing
• Alastair Denniston
  Commander Alexander Guthrie (Alastair) Denniston CMG CBE RNVR (1 December 1881, Greenock – 1 January 1961, Milford on Sea) was a British codebreaker in Room 40 and first head of the Government Code and Cypher School (GC&CS) and field hockey player. Denniston was appointed operational head of GC&CS in 1919 and remained so until February 1942.
  Denniston was born in Greenock, the son of a medical practitioner. He studied at the University of Bonn and the University of Paris. Denniston was a member of the Scottish Olympic Hockey team in 1908 and won a bronze medal.
  In 1914 he helped form Room 40 in the Admiralty, an organisation responsible for intercepting and decrypting enemy messages. In 1917 he married a fellow Room 40 worker, Dorothy Mary Gilliat.
  After World War I, Room 40 was merged with its counterpart in the Army, MI1b, to become the Government Code and Cypher School in 1919. Denniston was chosen to run the new organisation.
  On 26 July 1939, just five weeks before the outbreak of World War II, Denniston was one of three Britons (along with Dilly Knox and Humphrey Sandwith) who participated in the trilateral Polish-French-British conference held in the Kabaty Woods south of Warsaw, at which the Polish Cipher Bureau initiated the French and British into the decryption of German military Enigma ciphers.
  
  wn.com/Alastair_Denniston
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  Arthur Scherbius
  Arthur Scherbius (20 October 1878 – 13 May 1929) was a German electrical engineer who patented an invention for a mechanical cipher machine, later sold as the Enigma machine.
  Scherbius was born in Frankfurt am Main and his father was a small businessman. He studied electricity at the Technical College in Munich, and then went on to study at the Technical College in Hanover, finishing in March 1903. The next year, he completed a dissertation titled "Proposal for the Construction of an Indirect Water Turbine Governor", and was awarded a doctorate in engineering (Dr.-Ing.).
  Scherbius subsequently worked for a number of electrical firms in Germany and Switzerland. In 1918, he founded the firm of Scherbius & Ritter. He made a number of inventions, e.g. asynchronous motors, electric pillows and ceramic heating parts; his research contributions led to his name being associated with the Scherbius principle for asynchrous motors.
  Scherbius applied for a patent (filed 23 February 1918) for a cipher machine based on rotating wired wheels, what is now known as a rotor machine. Scherbius' company also purchased the rights to another patent for a rotor machine from Hugo Koch—patented in 1919. Business was slow enough that the firm was reorganized at least twice in the 1920s.
  
  wn.com/Arthur_Scherbius
• 
  Blaise de Vigenère
  Blaise de Vigenère (April 5, 1523–1596) was a French diplomat and cryptographer. The Vigenère cipher is so named due to the cipher being incorrectly attributed to him in the 19th century.
  Vigenère (French pronunciation: [viʒnɛːʁ]) was born in the village of Saint-Pourçain. At age 17 he entered the diplomatic service, and remained there for 30 years, retiring in 1570. Five years into his career he was sent to the Diet of Worms as a very junior secretary. At age 24, he entered the service of the Duke of Nevers. In 1549 he visited Rome on a two-year diplomatic mission, and again in 1566. On both trips, he came in contact both with books on cryptography and cryptologists themselves. When Vigenère retired aged 47, he donated his 1,000 livres a year income to the poor in Paris. He married a Marie Varé.
  In his retirement, he was author of over twenty books including,
  In Traicté des Chiffres he described an autokey cipher he had invented, it was the first cipher of this type after Bellaso not to be trivially breakable.
  
  wn.com/Blaise_de_Vigenère
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  Bruce Schneier
  Bruce Schneier ( /ˈʃnaɪər/; born January 15, 1963) is an American cryptographer, computer security specialist, and writer. He is the author of several books on general security topics, computer security and cryptography, and is the founder and chief technology officer of BT Managed Security Solutions, formerly Counterpane Internet Security, Inc.
  A son of Martin Schneier, a Brooklyn Supreme Court judge, Bruce grew up in Flatbush, attending P.S. 139 and Hunter High School. After receiving a physics bachelor's degree from the University of Rochester in 1984, he went to the American University in Washington, D.C. and got his master's degree in computer science in 1988. He was awarded an honorary Ph.D from the University of Westminster in London, England in November 2011. The award was made by the Department of Electronics and Computer Science in recognition of Schneier's 'hard work and contribution to industry and public life'.
  In 1994, Schneier published "Applied Cryptography", which details the design, use, and implementation of cryptographic algorithms. More recently he published "Cryptography Engineering", which is focused more on how to use cryptography in real systems and less on its internal design. He has also written books on security for a broader audience. In 2000, Schneier published Secrets and Lies: Digital Security in a Networked World. In 2003, Schneier published Beyond Fear: Thinking Sensibly About Security in an Uncertain World.
  
  wn.com/Bruce_Schneier
• 
  Charles Babbage
  Charles Babbage, FRS (26 December 1791 – 18 October 1871) was an English mathematician, philosopher, inventor and mechanical engineer who originated the concept of a programmable computer. Considered a "father of the computer", Babbage is credited with inventing the first mechanical computer that eventually led to more complex designs.
  Parts of his uncompleted mechanisms are on display in the London Science Museum. In 1991, a perfectly functioning difference engine was constructed from Babbage's original plans. Built to tolerances achievable in the 19th century, the success of the finished engine indicated that Babbage's machine would have worked. Nine years later, the Science Museum completed the printer Babbage had designed for the difference engine.
  Babbage's birthplace is disputed, but he was most likely born at 44 Crosby Row, Walworth Road, London, England. A blue plaque on the junction of Larcom Street and Walworth Road commemorates the event.
  His date of birth was given in his obituary in The Times as 26 December 1792. However after the obituary appeared, a nephew wrote to say that Charles Babbage was born one year earlier, in 1791. The parish register of St. Mary's Newington, London, shows that Babbage was baptised on 6 January 1792, supporting a birth year of 1791.
  
  wn.com/Charles_Babbage
• Dilly Knox
  Alfred Dillwyn 'Dilly' Knox CMG (23 July 1884 – 27 February 1943) was a classics scholar at King's College, Cambridge, and a British codebreaker. He was a member of the World War I Room 40 codebreaking unit, and later at Bletchley Park he worked on the cryptanalysis of Enigma ciphers until his death in 1943.
  Dillwyn Knox, the fourth of six children, was the son of Edmund Arbuthnott Knox and the brother of Ronald Knox, E. V. Knox, and Wilfred L. Knox. He was the father of Oliver Arbuthnot Knox.
  Dillwyn — known as "Dilly" — Knox was educated at Summer Fields School, Oxford, and then Eton College. While there he had an affair with John Maynard Keynes. He studied classics at King's College, Cambridge, and in 1909 was elected a fellow.
  During World War I, Knox was recruited to the Royal Navy's cryptological effort in Room 40 of the Admiralty Old Building, where among other tasks he was involved in breaking the Zimmermann Telegram which brought the USA into the war.
  In 1937 he cracked the code of the commercial Enigma machines used by Franco's Nationalists in the Spanish Civil War, but knowledge of this breakthrough was not passed on to the Republicans.
  
  wn.com/Dilly_Knox
• Don Coppersmith
  Don Coppersmith is a cryptographer and mathematician. He was involved in the design of the Data Encryption Standard block cipher at IBM, particularly the design of the S-boxes, strengthening them against differential cryptanalysis. He has also worked on algorithms for computing discrete logarithms, the cryptanalysis of RSA, methods for rapid matrix multiplication (see Coppersmith-Winograd algorithm) and IBM's MARS cipher. Don is also a co-designer of the SEAL and Scream ciphers.
  In 1972, Coppersmith obtained a Bachelor's degree in mathematics at the Massachusetts Institute of Technology, and a Masters and PhD in mathematics from Harvard University in 1975 and 1977 respectively. He was a Putnam Fellow each year from 1968–1971, becoming the first four-time Putnam Fellow in history. In 1998, he started Ponder This, an online monthly column on mathematical puzzles and problems. In October 2005, the column was taken over by James Shearer.
  In 2002, Coppersmith won the RSA Security Award for Mathematics.
  
  wn.com/Don_Coppersmith
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  Elizebeth Friedman
  Elizebeth Smith Friedman (August 26, 1892 – October 31, 1980) was a cryptanalyst and author, and a pioneer in U.S. cryptography. The special spelling of her name (more commonly spelled "Elizabeth") is attributed to her mother, who disliked the prospect of Elizebeth ever being called "Eliza." She has been dubbed "America's first female cryptanalyst".
  Although she is often referred to as the wife of William F. Friedman, a notable cryptographer credited with numerous contributions to cryptology, she enjoyed many successes in her own right, and it was Elizebeth who first introduced her husband to the field.
  Born in Huntington, Indiana to John M. Smith, a Quaker dairyman, banker, and politician, and Sopha Strock Smith, Mrs. Friedman was the youngest of nine children.
  After briefly attending The College of Wooster in Ohio, she graduated from Hillsdale College in Michigan with a major in English literature and was also a member of Pi Beta Phi. Having exhibited her interest in languages, she had also studied Latin, Greek, and German, and minored "in a great many other things." Only she and one other sibling were privileged to attend college.
  
  wn.com/Elizebeth_Friedman
• 
  Frank Rowlett
  Frank Byron Rowlett (May 2, 1908 - June 29, 1998) was an American cryptologist.
  Rowlett was born in Rose Hill, Lee County, Virginia and attended Emory & Henry College in Emory, Virginia. In 1929 he received a bachelor's degree in mathematics and chemistry. He was hired by William Friedman as a "junior cryptanalyst" for the Signals Intelligence Service (SIS) on April Fool’s Day, 1930; shortly after, he was followed into SIS by Abraham Sinkov and Solomon Kullback.
  During the 1930s, after a lengthy period of training, Rowlett and his colleagues compiled codes and ciphers for use by the U.S. Army and began solving a number of foreign, notably Japanese, systems. In the mid-1930s, they solved the first Japanese machine for encipherment of diplomatic communications, known to the Americans as RED. In 1939-40, Rowlett led the SIS effort that solved a more sophisticated Japanese diplomatic machine cipher, codenamed PURPLE by the U.S. Once, when asked what his greatest contribution to that effort had been, Rowlett said, "I was the one who believed it could be done."
  
  wn.com/Frank_Rowlett
• Friedrich Kasiski
  Major Friedrich Wilhelm Kasiski (29 November 1805 – 22 May 1881) was a German infantry officer, cryptographer and archeologist. Kasiski was born in Schlochau, Kingdom of Prussia (now Człuchów, Poland).
  Kasiski enlisted in East Prussia's 33rd Infantry Regiment on 20 March 1823 at the age of 17. In May 1824, he was promoted to the rank of Master Sergeant, and eight months later was commissioned as a Second Lieutenant in February 1825. It took fourteen years to earn his next promotion when, in May 1839, he advanced to the rank of First Lieutenant. His next advancement was quicker, promoted to Captain in November 1842. Kasiski finally retired from active service with the rank of Major on 17 February 1852.
  Between 1860 and 1868 he was the commander of a National Guard battalion.
  In 1863, Kasiski published a 95-page book on cryptography, Die Geheimschriften und die Dechiffrierkunst (German, "Secret writing and the Art of Deciphering"). This was the first published account of a procedure for attacking polyalphabetic substitution ciphers, especially the Vigenère cipher (although it is possible Charles Babbage was already aware of a similar method but had kept it secret). The method relied on the analysis of gaps between repeated fragments in the ciphertext; such analysis can give hints as to the length of the key used. This technique is known as Kasiski examination.
  
  wn.com/Friedrich_Kasiski
• Gilbert Vernam
  Gilbert Sandford Vernam (3 April 1890 – 7 February 1960) was an AT&T Bell Labs engineer who, in 1917, invented an additive polyalphabetic stream cipher and later co-invented an automated one-time pad cipher. Vernam proposed a teleprinter cipher in which a previously-prepared key, kept on paper tape, is combined character by character with the plaintext message to produce the ciphertext. To decipher the ciphertext, the same key would be again combined character by character, producing the plaintext. Vernam later worked for Postal Telegraph Co., and became an employee of Western Union when W.U. acquired Postal in 1943. His later work was largely with automatic switching systems for telegraph networks.
  The combining function Vernam specified in U.S. Patent 1,310,719, issued July 22, 1919, is the XOR operation, applied to the individual impulses or bits used to encode the characters in the Baudot code. Vernam did not use the term "XOR" in the patent, but he implemented that operation in relay logic. In the example Vernam gave, the plaintext is A, encoded as "++---" in Baudot, and the key character is B, encoded as "+--++". The resulting ciphertext will be "-+-++", which encodes a G. Combining the G with the key character B at the receiving end produces "++---", which is the original plaintext A. The NSA has called this patent "perhaps one of the most important in the history of cryptography.".
  
  wn.com/Gilbert_Vernam
• Giovanni Soro
  Giovanni Soro (died 1544) was a Venetian professional code-cracker. He was more than likely the Renaissance's first outstanding cryptanalyst and the Western world's first great cryptanalyst. Soro is known as the father of modern cryptography.
  Soro was employed in Venice in 1506 by the Council of Ten as cipher breaker-in-chief. They were the first secret service specializing in codebreaking. Soro ran the cryptanalysis operation in secret as the cipher secretary. Soro's tasks included deciphering secret messages captured from the messenger spies of Venice's rivals. At the time, Venice was plagued by espionage and subterfuge. The Council of Ten had its own ciphers changed often so as to impede competitors such as François Viète, a French mathematician (father of modern algebraic notation).
  Successful diplomacy depended on knowing the adjacent principalities' thoughts and ideas. Soro was able to decipher the ciphers of most other courts. By 1510, he had forced most of them to develop their ciphers to a much higher degree of sophistication. As a result, the Papal Curia hired him to break codes their own cipher analysts in Rome could not.Pope Clement VII often sent messages to Soro for cryptanalysis to test their impenetrability.
  
  wn.com/Giovanni_Soro
• Harry Hinsley
  Sir Francis Harry Hinsley OBE (26 November 1918 – 16 February 1998) was an English historian and cryptanalyst. He worked at Bletchley Park during the Second World War and wrote widely on the history of international relations and British Intelligence during the Second World War. He was known as Harry Hinsley.
  Hinsley was the son of a miner and was educated at Queen Mary's Grammar School, Walsall, and in 1937 won a scholarship to study history at St. John's College, Cambridge. In October 1939, while still studying at St. John's, he was summoned to an interview with Alastair Denniston, head of the Government Code and Cypher School (GC&CS), and was thereby recruited to Bletchley Park's naval section in Hut 4.
  At Bletchley Park, Hinsley studied the external characteristics of intercepted German messages, a process sometimes termed "traffic analysis": from call signs, frequencies, times of interception and so forth, he was able to deduce a great deal of information about the structure of the German Navy's communication networks, and even about the structure of the German Navy itself.
  
  wn.com/Harry_Hinsley
• 
  Herbert Yardley
  Herbert Osborne Yardley (April 13, 1889 – August 7, 1958) was an American cryptologist best known for his book The American Black Chamber (1931). The title of the book refers to the Cipher Bureau, the cryptographic organization of which Yardley was the founder and head. Under Yardley, the cryptanalysts of The American Black Chamber broke Japanese diplomatic codes and were able to furnish American negotiators with significant information during the Washington Naval Conference of 1921-1922. He later helped the Nationalists in China (1938–1940) to break Japanese codes. Following his work in China, Yardley worked briefly for the Canadian government, helping it set up a cryptological section (Examination Unit) of the National Research Council of Canada from June to December 1941. Yardley was let go due to pressure from Washington.^{[citation needed]}
  Yardley was born in 1889 in Worthington, Indiana. He learned to use the telegraph from his father, Robert Kirkbride Yardley, a station master and telegrapher for a railroad. His mother, Mary Emma Osborn Yardley, died when he was 13.
  
  wn.com/Herbert_Yardley
• Jack Copeland
  Brian Jack Copeland (born 1950) is Professor of Philosophy at the University of Canterbury, Christchurch, New Zealand and author of books on computing pioneer Alan Turing.
  His education includes a BPhil and a DPhil from the University of Oxford in philosophy, where he undertook research on modal and non-classical logic under the supervision of Dana Scott.
  Jack Copeland is the Director of the Turing Archive for the History of Computing, an extensive online archive on the computing pioneer Alan Turing. He has also written and edited books on Turing. He is one of the people responsible for identifying the concept of hypercomputation and machines more capable than Turing machines.
  Copeland has held visiting professorships at the University of Sydney, Australia (1997, 2002), the University of Aarhus, Denmark (1999), the University of Melbourne, Australia (2002, 2003), and the University of Portsmouth, United Kingdom (1997–2005). In 2000, he was a Senior Fellow in the Dibner Institute for the History of Science and Technology at the Massachusetts Institute of Technology, United States.
  
  wn.com/Jack_Copeland
• John Tiltman
  Brigadier John Hessell Tiltman MC (25 May 1894 – 10 August 1982) was a British Army officer who worked in intelligence, often at or with the Government Code and Cypher School (GC&CS) starting in the 1920s. His intelligence work was largely connected with cryptography, and he showed exceptional skill at cryptanalysis. His work in association with Bill Tutte on the cryptanalysis of the Lorenz cipher, the German teleprinter cipher, called "Tunny" at Bletchley Park, led to successful attack methods. It was to exploit those methods that Colossus, the first digital programmable electronic computer, was designed and built.
  Tiltman's parents were from Scotland, though he was born in London. He joined the British Army in 1914, and saw service at the front during World War I with the King's Own Scottish Borderers. He was wounded in France, and won the Military Cross for bravery. He was seconded to MI1 shortly before it merged with Room 40.
  From 1921–1929, he was a cryptanalyst with the Indian Army at Army Headquarters, Simla. They were reading Russian diplomatic cypher traffic from Moscow to Kabul, Afghanistan and Tashkent, Turkestan. In the small section of five or less he was involved in all aspects, directing interception and traffic analysis as well as working on cyphers; he said he was exceptionally lucky to have this experience in other branches of Signals Intelligence.
  
  wn.com/John_Tiltman
• 
  John Wallis
  John Wallis (23 November 1616 – 28 October 1703) was an English mathematician who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal court. He is also credited with introducing the symbol Failed to parse (Missing texvc executable; please see math/README to configure.): {\infty}
  John Brehaut Wallis was born in Ashford, Kent, the third of five children of Reverend John Wallis and Joanna Chapman. He was initially educated at a local Ashford school, but moved to James Movat's school in Tenterden in 1625 following an outbreak of plague. Wallis was first exposed to mathematics in 1631, at Martin Holbeach's school in Felsted; he enjoyed maths, but his study was erratic, since: "mathematics, at that time with us, were scarce looked on as academical studies, but rather mechanical" (Scriba 1970).
  As it was intended that he should be a doctor, he was sent in 1632 to Emmanuel College, Cambridge. While there, he kept an act on the doctrine of the circulation of the blood; that was said to have been the first occasion in Europe on which this theory was publicly maintained in a disputation. His interests, however, centred on mathematics. He received his Bachelor of Arts degree in 1637, and a Master's in 1640, afterwards entering the priesthood. From 1643–49, he served as a non-voting scribe at the Westminster Assembly. Wallis was elected to a fellowship at Queens' College, Cambridge in 1644, which he however had to resign following his marriage.
  
  wn.com/John_Wallis
• Josef Pieprzyk
  Josef Pieprzyk (born 1949) is a professor at Macquarie University in Sydney, Australia.
  He has worked on cryptography, in particular the XSL attack. He collaborated in the invention of the LOKI and LOKI97 block ciphers and the HAVAL cryptographic hash function.
  
  wn.com/Josef_Pieprzyk
• 
  Joseph Rochefort
  Joseph John Rochefort (May 12, 1900 in Dayton, Ohio - July 20, 1976 in Torrance, California ) was an American Naval officer and cryptanalyst. His contributions and those of his team were pivotal to victory in the Pacific War.
  Rochefort was a major figure in the United States Navy's cryptographic and intelligence operations from 1925 to 1946, particularly in the Battle of Midway.
  In 1917, Rochefort had joined the Navy while still in high school in Los Angeles. He enlisted in the Navy in 1918. He was commissioned as an ensign after graduation from the Stevens Institute of Technology, and in 1919 became engineering officer of the tanker USS Cuyama.
  A fellow officer observed that Rochefort had a penchant for solving crossword puzzles and adept skills at playing the advanced card game auction bridge and recommended him for a Navy cryptanalysis class in Washington, D.C.
  Rochefort's tours ashore included cryptanalytic training under Captain Laurance Safford as his assistant, and worked with the master codebreaker Agnes Meyer Driscoll in 1924.
  
  wn.com/Joseph_Rochefort
• Lars Knudsen
  Lars Ramkilde Knudsen (born 21 February 1962) is a Danish researcher in cryptography, particularly interested in the design and analysis of block ciphers, hash functions and message authentication codes (MACs).
  After some early work in banking, Knudsen enrolled at Aarhus University in 1984 studying mathematics and computer science, gaining an MSc in 1992 and a PhD in 1994. From 1997-2001, he worked at the University of Bergen, Norway. Currently, Knudsen is a professor in the Department of Mathematics at the Technical University of Denmark. His Erdős number is 3, via his work with noted cryptographers Don Coppersmith and Ivan Damgård. Ivan was Lars' teacher and mentor during his studies at Aarhus University, and according to Lars was a deciding factor in his choice to study differential cryptanalysis. His Ph.D. was refereed by Bart Preneel.
  Knudsen has published analyses of a wide variety of cryptographic designs, including the R-MAC scheme, the SHA-1 and MD2 hash functions, and at least a dozen block ciphers: DES, DFC, IDEA, ICE, LOKI, MISTY, RC2, RC5, RC6, SC2000, Skipjack, Square and SAFER—it has been hinted that the "SK" in the "SAFER-SK" variant means Stop Knudsen after he had found weaknesses in a previous version.
  
  wn.com/Lars_Knudsen
• 
  Marian Rejewski
  Marian Adam Rejewski [ˈmarjan reˈjefski] ( listen) (16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist who in 1932 solved the plugboard-equipped Enigma machine, the main cipher device used by Germany. The success of Rejewski and his colleagues Jerzy Różycki and Henryk Zygalski jump-started British reading of Enigma in World War II; the intelligence so gained, code-named "Ultra", contributed, perhaps decisively, to the defeat of Nazi Germany.^{(Note 1)}
  While studying mathematics at Poznań University, Rejewski had attended a secret cryptology course conducted by the Polish General Staff's Biuro Szyfrów (Cipher Bureau), which he joined full-time in 1932. The Bureau had achieved little success reading Enigma and in late 1932 set Rejewski to work on the problem. After only a few weeks, he deduced the secret internal wiring of the Enigma. Rejewski and his two mathematician colleagues then developed an assortment of techniques for the regular decryption of Enigma messages. Rejewski's contributions included devising the cryptologic "card catalog," derived using his "cyclometer," and the "cryptologic bomb."
  
  wn.com/Marian_Rejewski
• 
  Meredith Gardner
  Meredith Knox Gardner (October 12 (or 20), 1912–August 9, 2002) was an American linguist and codebreaker. Gardner worked in counter-intelligence, decoding Soviet intelligence traffic regarding espionage in the United States, in what came to be known as the Venona project.
  Gardner was born in Okolona, Mississippi and grew up in Austin, Texas. After graduating from the University of Texas at Austin, he earned a master's degree in German from University of Wisconsin–Madison, where he was a teaching assistant from 1938 to 1940. He was a linguist and professor of German at the University of Akron when the United States Army's Signals Intelligence Service recruited him to work on breaking German codes. Soon after, he started working on the Japanese codes instead, mastering the Japanese language in only a few months.
  In 1946, Gardner began work on a highly-secret project (later codenamed VENONA) to break the Soviet cryptosystems. The Soviet encryption system involved the use of one-time pads, and thus was thought to be unbreakable. However, the Soviets made the mistake of reusing certain pages of their pads.
  
  wn.com/Meredith_Gardner
• Peter Calvocoressi
  Peter John Ambrose Calvocoressi (17 November 1912 – 5 February 2010) was a British political author, historian and a former intelligence officer at Bletchley Park during World War II.
  Calvocoressi was born in Karachi, now in Pakistan, to a family of Greek origins from the island Chios. His mother, Irene née Ralli, was descended from one of the founders of Ralli Brothers, who were prominent Greek families of Chios who came to London at the time of the Greek Diaspora. When he was three months old, the family moved to Liverpool, England. Calvocoressi's father Pandia had spent the first seven years of his life in Manchester and the next ten at San Stefano (on the outskirts of Istanbul). He attended the Sorbonne from the age of 17 for three years and then joined the family firm in New York. Pandia Calvocoressi and Irene Ralli married in London in 1910. Shortly afterwards Pandia was posted to India where Calvocoressi was born. His mother and maternal grandmother were both born in India but spent most of their lives in England.
  
  wn.com/Peter_Calvocoressi
• 
  Simon Singh
  Simon Lehna Singh, MBE (born 1 January 1964) is a British author who has specialised in writing about mathematical and scientific topics in an accessible manner. His written works include Fermat's Last Theorem (in the United States titled Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem), The Code Book (about cryptography and its history), Big Bang (about the Big Bang theory and the origins of the universe) and Trick or Treatment? Alternative Medicine on Trial (about complementary and alternative medicine).
  He has also produced documentaries and works for television to accompany his books, is a trustee of NESTA, the National Museum of Science and Industry and co-founded the Undergraduate Ambassadors Scheme.
  In 2008, Singh was unsuccessfully sued for libel by the British Chiropractic Association for criticising their activities in a column in The Guardian. A "furious backlash" to the lawsuit resulted in the filing of formal complaints of false advertising against more than 500 individual chiropractors within one 24 hour period, with one national chiropractic organisation ordering its members to take down their websites, and Nature Medicine noting that the case had gathered wide support for Singh, as well as prompting calls for the reform of English libel laws. On 1 April 2010, Simon Singh won his court appeal for the right to rely on the defence of fair comment. On 15 April 2010, the BCA officially withdrew its lawsuit, ending the case.
  
  wn.com/Simon_Singh
• 
  Solomon Kullback
  Solomon Kullback (1907 – 1994) was an American cryptanalyst and mathematician, who was one of the first three employees hired by William F. Friedman at the US Army's Signal Intelligence Service (SIS) in the 1930s, along with Frank Rowlett and Abraham Sinkov. He went on to a long and distinguished career at SIS and its eventual successor, the National Security Agency (NSA). Kullback was the Chief Scientist at the NSA until his retirement in 1962, whereupon he took a position at the George Washington University.
  The Kullback-Leibler divergence is named after Kullback and Richard Leibler.
  Kullback was born in Brooklyn, New York and attended Boy's High School there. He then went to City College of New York, graduating with a BA in 1927 and an MA in math in 1929. He completed a doctorate in math from George Washington University in 1934. His intention had been to teach, and he returned to Boy's High School to do so, but found it not to his taste; he discovered his real interest was using mathematics, not teaching it.^{[citation needed]}
  
  wn.com/Solomon_Kullback
• 
  Thomas Phelippes
  Thomas Phelippes (1556–1625) was a forger and intelligence gatherer. He served mainly under Sir Francis Walsingham, in the time of Elizabeth I, deciphering the codes of those plotting against her. He is most remembered for his adding of a postscript to the "bloody letter" sent by Mary, Queen of Scots, to Anthony Babington regarding the Babington plot. This scene is recreated in the 2006 TV miniseries The Virgin Queen, starring Anne-Marie Duff as Elizabeth I, and Vincent Franklin as Phelippes. According to historian Neville Williams, the notes were smuggled to Mary via empty barrels from a brewer in Burton upon Trent who supplied her house at Chartley Manor. Phelippes was kept busy with a backlog of correspondence requested by Her Majesty whose letters contained day to day matters as well as those of a more sensitive type. Walshingham had to wait a whole seven months before he got what he wanted. This postscript asked Babington for the names of the plotters involved in the planned assassination of Queen Elizabeth I, and hence Francis Walsingham was able to prove Mary's direct involvement in the plot, and have her executed.
  
  wn.com/Thomas_Phelippes
• 
  World War I
  World War I (WWI), which was predominantly called the World War or the Great War from its occurrence until 1939 (World War II), and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918. It involved all the world's great powers, which were assembled in two opposing alliances: the Allies (based on the Triple Entente of the United Kingdom, France and Russia) and the Central Powers (originally centred around the Triple Alliance of Germany, Austria-Hungary and Italy; but, as Austria–Hungary had taken the offensive against the agreement, Italy did not enter into the war). These alliances both reorganised (Italy fought for the Allies), and expanded as more nations entered the war. Ultimately more than 70 million military personnel, including 60 million Europeans, were mobilised in one of the largest wars in history. More than 9 million combatants were killed, largely because of enormous increases in lethality of weapons, thanks to new technology, without corresponding improvements in protection or mobility. It was the sixth-deadliest conflict in world history, subsequently paving the way for various political changes such as revolutions in the nations involved.
  
  wn.com/World_War_I

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